Aeroelasticity

Aeroelasticity

13 January 2016

LECTURE L02. 2D AEROELASTICITY

1- Explain the physical concept of divergence (with your own words)

Physical phenomena in which, for a specific conditions, the elastic restoring forces acting on the wing are lower than the aerodynamic forces, producing a high increase of the twist angle and a high increase in lift that can yield to the wing break.

Divergence occurs when a lifting surface deflects under aerodynamic load so as to increase the applied load, or move the load so that the twisting effect on the structure is increased. The increased load deflects the structure further, which eventually bring the structure to the divergence point.

2- 2D airfoil divergence. (Equations. From the equilibrium equation

of a 2D airfoil forces deduce the expression for q

div

)

Terms that factorize θ to the left, others to the right. || There is a mathematical expression for the equilibrium, showing the twist angle in which the elastic restoring forces equal the steady aerodynamic forces. The dynamic pressure that makes denominator in twist angle eq. equal to 0 is qdiv. Then:

𝜃 =

𝑞/𝑞

𝑑𝑖𝑣

1 − 𝑞/𝑞

_𝑑𝑖𝑣

(𝛼

0

+

𝑐𝐶

_𝑀𝐴𝐶

3- Is the divergence speed dependent on the mass?

Since the mass is independent of θ in the equilibrium equation, the denominator will

be independent of the mass so Qdiv will be independent on the mass. From this

statement can be deduced that the effect of mass modifies the elastic twist behavior

but not Qdiv. It can be appreciated in equations of next question.

4- From the equilibrium equation of a 2D airfoil forces, deduce the

expression for q

div

when Nz ≠ 0.

Same equations as in question 2 but adding NzmgXcg.

5- Compressibility effects on divergence dynamic pressure. Introduce

the concepts of “unmatched” solution and “matched” solution.

Unmatched solution does not take into account the standard ISA. For a constant divergence dynamic pressure, the relation with ρ·V2 _{is constant. In order to add the compressibility}

effects, a correction factor qdiv=qidv|inc·√1 − 𝑀2 is introduced. Unmatched solution is

obtained and can be plotted into a Mach & TAS vs Altitude plot (Page 27) in which it can be appreciated that for higher Mach, higher is the difference between the incompressible and compressible Qdiv.

For the case of the matched solution, the standard ISA is introduced as the altitude affects the value of the density as well as the value of speed of sound.

So once obtained the Mach for different altitudes, a divergence envelope can be obtained for the Matched Solution (to plot in the Mach & TAS vs Altitude plot). This divergence envelope should be at least a 15% outside of the aircraft flight envelope (1.15·VD/MD).

6- 2D Quasi-steady aerodynamics (heave/pitch). Why is it not

suitable for aeroelasticity?

Having an airfoil undergoing a general motion in heave and pitch and assuming:

In this simplified approach, the changes in the wake due to the airfoil motion are not accounted, hence, 2D quasi-steady aerodynamics is not suitable for aeroelasticity.

7- Unsteady aerodynamics. Response to a sudden change of angle of

attack. Description of Wagner function. Physical insight.

In a 2D quasi-steady aerodynamic model if it is subjected to an instantaneous change in angle of attack of α= α/2 the lift would increase instantaneously by 50%, but this does not

occur in practice. L = Lsteady·Φ (τ) where Φ (τ) is the Wagner’s function.

Unsteady lift changes instantaneously by a 25% increase and then increases asymptotically towards the final steady value. This asymptotic behavior occurs due to the change of the vortex strength, releasing the starting vortex rearwards.

By definition, Wagner’s function is used to model how the lift acting at the quarter chord on the airfoil builds up following the step change of incidence.

8- Unsteady aerodynamics. Description of Küssner function.

In a 2D quasi-steady aerodynamic model if suddenly encounters a sharp-edged gust of velocity wg its lift would increase instantaneously due to the increase in angle of attack, but

this does not occur in practice. L = Lsteady·Φ (τ) where Ψ(τ) is the Küssner’s function which describes how the aerodynamic forces build up upon entering a step gust (lift increases proportionally as the gust enters to the airfoil without sudden increase of lift).

9- Why Wagner and Küssner functions are different between?

(Especially for small distance of travelled semi-chords). Elaborate

qualitatively the answer.

Wagner’s function represents the build of lift due to sudden increase of AoA. The entire airfoil exhibits immediately the increase of AoA. The vortex released from the TE is responsible that a τ=0 the increase of lift is only 0.5 and subsequently, for large travelled semi-chords, the increase of lift tends asymptotically to 1.0 once the released vortex is far downstream.

Figure 1: Wagner’s function (Left) & Küssner’s function (Right) lift increase.

Küssner’s function represent the build of lift due to airfoil penetration in a step gust. The airfoil is entering the gust progressively. Just after τ=0 only a very small portion of the airfoil is inside the gust, therefore, there is no significant increase of lift yet. This is why the Küssner function value starts at 0.0. When the entire airfoil is inside the step gust, the Küssner function value is 0.55 (A similar value 0.55 is obtained with the Wagner function with 2 semi-chords travelled (2·c/2).)

10- Unsteady aerodynamics. Description of Theodorsen function.

Theodorsen’s function is used to model the changes in amplitude and phase of the sinusoidal unsteady aerodynamic forces relative to quasi-steady forces for different reduced frequencies. It behaves as the Fourier transform of Wagner’s function.

The amplitude and phase of Theodorsen’s function shows that for an oscillating airfoil at different reduced frequencies (k=ωc/V) the amplitude decreases and tends to 0.5 while the phase lag increases up to a value around k=0.3 and then reduces again.

11- Unsteady aerodynamics. Description of Sears function.

In a 2D quasi-steady aerodynamic model if a sinusoidal gust field having a vertical velocity as a function of time is encountered, the lift would increase instantaneously due to the increase of AoA, but this does not occur in practice. L = Lsteady· ϕ (τ) where ϕ (τ) is the Sears’ function which is defined as a (approx.) combination of Theodorsen and Bessel functions.

Amplitude and phase of Sears’ function shows that frequency decreases to 0 a k increases and the phase lag increases only for very low k and then reduces significantly. THEODORSEN’S AND SEARS’S ARE VERY SIMILAR FUNCTIONS FOR SMALL k.

12- Definition (and physical concept) of reduced frequency k

Reduced frequency is interpreted as the relationship between the time for a particle to fly over the airfoil and the time that the particle oscillates in the airfoil.

The lines of k are straight lines in the frequency-speed diagram. Amplitude attenuation and phase lag are functions of k.

LECTURE L03. 2D AND 3D STATIC AEROELASTICITY

1.

Evolution of first control surface normal mode (frequency and

mode shape) with control-chain stiffness

2.

Explain the physical concept of Control Reversal (with your own

words)

Briefly, control reversal is an effect happening in aircraft that makes controls to reverse, such that for the pilot to carry out a maneuver, it has to order the aircraft to do the opposite maneuver, since the controls are “reversed”.

Physically, when dynamic pressure increases, control surface effectiveness falls up to the point in which 0 effectiveness is reached, that is, the point at which control reversal occurs and lift vanishes (the flexibility considering lift, 𝐿𝑓𝑙𝑒𝑥 ).

As wing has greater flexibility than ailerons, rudder and elevator, reversal will occur firstly in these surfaces, and particularly in ailerons, the surface with lowest reversal speed, and consequently the limiting element.

3.

2D control effectiveness equations

4.

Deduce the expression for the twist induced by an aileron

deflection in a 2D airfoil with torsion stiffness

EQUATIONS OF SLIDE 13 & 14

5.

Deduce the expression for the flexible lift due to an aileron

deflection in a 2D airfoil with torsion stiffness

EQUATIONS OF SLIDE 13 & 14

6.

Deduce the expression for the reversal dynamic pressure

EQUATIONS OF SLIDES 13 TO 19

7.

In which conditions L

flex

/L

rigid

is reduced linearly with dynamic

pressure?

Since;

Then for R<1  Lf>Lrig (rare case). Only obtained with forward sweep For R>1  Lf<Lrig (normal case). Only obtained with straight or aft sweep. When R>>1 the expression becomes:

This condition follows for the case of aft swept wings, with a relatively large

swept angle.

The condition of R=1 is extremely unlikely.

8.

Why q

reversal

is not dependent on e?

Control surface reversal happens because there are two effect that compensate each other. On the one hand, the increase of lift due to control surface deflection (that is proportional to e) and on the other hand the decrease of lift produced by negative twist (that is also proportional to e). When equaling these effects, e is eliminated from the equations.

Recalling the qdiv expression,

Equating both it yields that:

As expected, it is not dependent on e.

9.

3D wing divergence using the slender straight wing approach

EQUATIONS SLIDES 28 TO 36

10.

Qualitative description of the effect of wing sweep angle on

wing divergence speed

Note that for swept angle positive is for swept back and negative for swept forward.

As the swept angle is increased, divergence dynamic pressure increases and since dynamic pressure is proportional to V, it can be concluded that for swept forward wing velocities have to be much lower than for swept back wings.

11.

Describe coupling between bending and torsion in a swept

back wing

It is clear from figure below that for a swept back, wing bending results in a positive bending (counterclockwise), which in turn produces a negative twisting in the wing (see red arrow in rightmost image) that increases the negative twist (see orange arrow).

Therefore, swept back produces a bending moment that increases the negative twisting of the airfoil (pitch down)

12.

Effect of wing sweep on the evolution of the frequency of

the wing bending mode with flight speed

It is fairly obvious from picture above that for a wing with no sweep, the frequency of the bending mode is independent of the speed. On the other hand, swept-back wings increase their their natural frequency with velocity, while swept-forward wings behave in the other way round.

LECTURE 04. THE STRUCTURAL MODEL AND THE

NORMAL MODES

1. Describe the building of the structural model (for aeroelastics).

A FEM model is created by using elements related with geometry (coordinate system, grid points), elements (rods, bars, beams, CQUAD4, shells…), properties and material

characteristics, CONM2 for lumped masses, RBE3 to connect masses or apply forces, in order to represent the stiffness properties of the structure and the load path of the structure that predicts accurately the displacements at the tip of the lifting surfaces (for aeroelasticians) but many stress engineers are more concerned about the displacements at the root so this may have consequences.

The best model is a balanced model in complexity and fidelity to physics in which answer the key questions. Any FE model suitable for aeroelastic analyses should be able to represent adequately the normal modes up to 50Hz.

2. The stiffness model (and way of validation).

Stiffness model is created to represent the stiffness of the aircraft. Stiffness model is validated through static tests performed in the aircraft.

3. Properties of the stiffness matrix [K]

Stiffness matrix is real (all components do not contain imaginary numbers), symmetric with respect to the diagonal and positive definite (all eigenvalues are non-negative). The stiffness matrix is used with the mass matrix to get the natural frequencies of the system (one for each DoF) with an eigenvalue problem.

4. Describe the “natural mesh” approach for FE modeling of structures.

It is the most suitable mesh for structural dynamics and aeroelasticity. Finer meshes are undesirable because of its cost. It creates a mesh in which their elements are clearly defined by the components of the aircraft. As an example: For the wings, in the skin there is only 1 element between ribs and stringers, in the spars only 1 element between ribs and upper & lower skin; for the fuselage skin, there is 1 element between frames and stringers…

5. Which are the structural details important for aeroelastics?

The aeroelasticians would have a model that accurately predicts the displacements at the tip of the lifting surfaces (surface with more aeroelastic behavior). Need of especial attention to the details (leading edges, pylons, control surface fittings, fairings…). For example, in the

control surface fittings, the aeroelasticians need out-of-plane bending of these fittings to avoid spurious control surface lateral modes while stress engineers work with in-plane only.

6. The building of the mass model (lumped masses; types of aircraft

masses; etc.)

Masses are treated in a matrix form with the same characteristics of the stiffness matrix but this is not suitable for a complete aircraft, then lumped masses are used. Lumped masses represents strips/slices of the aircraft splitting structure fixed part from movable part. Once the aircraft is modelled as lumped masses, it can give mass data like total mass, center of gravity, moments of inertia and reference grid point. In MSC NASTRAN, designed with CONM2.

The aircraft mass is split in:

Each lumped mass should be distributed to several adjacent “hard points”, this require a specific FEM element: RBE3 in NASTRAN.

The RBE3 allows connecting masses to the structure without adding undesirable extra stiffness. The RBE3 allocates the mass to structural “hard points”.

7. Conceptual difference between consistent and lumped mass approach

Consistent masses are treated in a matrix form with the same characteristics of the stiffness matrix. This is very accurate for a single beam but it is not suitable for a complete aircraft. Instead of using these for an aircraft, it is used the lumped masses which represent

8. What has to be considered with payload masses (how should be

connected to the structure, considerations)

Payload masses have to be considered as lumped masses. A generalized grid in the center of the fuselage is connected with RBE3 to the structural grids in the lower part of the fuselage representing the seat, passengers and cargo. Payload is typically less relevant for stability (flutter) problems but it is very important in response (dynamic loads) problems.

9. What has to be considered with fuel masses

Within fuel masses, the fueling sequence and the cold and hot temperature must be considered.

10. How are the lumped masses connected to the structure? (Use as an

example the NASTRAN element RBE3)

RBE3 allows connecting masses to the structure without adding undesirable extra stiffness. It connects a reference point with the mass allocated to it with the rest of the structure

considered as ‘hard’ points through many legs.

11. Properties of the mass matrix [M]

It is real, symmetric, positive definite and “banded”.

12. The mass model is obtained using densities in the FE model?

(YES/NO)

No, the FEM does not represent the volume of the structure, so there is no possibility to obtain the mass distribution by multiplying by the densities.

13. Why the dynamic model in the g-set has to be reduced?

CPU of Normal modes computation may be affordable for a few runs, but it may be problematic for thousands of runs. The CPU cost of running thousands of aeroelastic and dynamic load cases using complete aircraft FE models is not manageable even with today computers. Therefore, dynamic model in the G-set has to be reduced.

Dynamic FE models size continues growing with time thanks to the improvement of the computers that follow the Moore’s law: Microprocessors double in power every 2 years.

14.

Dynamic model reduction: the Guyan theory.

The idea is to make a partitioning of the dynamic equation between A-set and O-set. All grid points with mass or applied forces (note that points with mass may be interpreted as points where inertia forces will be applied) and some more needed will constitute the Analysis set = A-set. Most of the grid points with no applied forces: Omitted set: O-set.

15. Explain qualitatively the super-element technique

The super-element technique assembles together all the reductions of the aircraft components to get a complete aircraft dynamic model. Super-element technique is an

efficient/simple/versatile method for dynamic models set-up.

16. Equation to be solved to obtain the structure normal modes

17. Explain a given mode shape plot

Here, one has to study a mode shape plot by taking into account that: red color and green color accounts for opposite directions. Blue lines accounts for static lines that do not move. Blue lines are a key point when analyzing the mode shape plot

This is the first symmetric wing bending mode. The wing tips are bending symmetrically.

Outer engines have a pitching motion due to the bending of the wing. Maximum displacement seems to be in the Z direction for the wing tips.

This is the first anti-symmetrical wing bending mode,

Maximum displacement seems to be in the Z direction for the wing tips in an anti-symmetrical mode.

HTP have anti-symmetrical bending as well as the wing.

This is the anti-symmetric O/B engine pitch mode.

There is anti-symmetric bending in the wings and also in the HTP.

The HTP as well is yawing.

Outer engines have a pitch motion due to the bending of the wings.

Maximum displacement seems to be in the X direction due to the HTP

anti-symmetrical yaw.

18. The order of magnitude of aircraft normal mode frequencies

They vary from 7.0 Hz for fighters to 0.7 Hz for very large airliners (effect of mass larger than the stiffness) for the 1st Symmetric Wing Bending Frequency and from N/A for fighters to 4.2 Hz for very large airliners for the 1st Symmetric HTP Bending Frequency.

19. A dynamic model consisting in a clamped beam with 8 grid points

has 3 lumped masses. What is the expected number of modes of

these models?

8 grids have 6 degrees of freedom each, so 48 modes are possible. Since there are only 3 lumped masses, there are only 3x6 modes. 18 MODES.

20. Mathematical properties of normal mode shapes (eigenvectors) [ɸ]

There are eigenvectors as many natural frequencies are. They are orthogonal with respect to the mass and stiffness matrix.

The wing have a torsional moment and also some bending at the tip. The wing as well has a yawing moment. The HTP has anti-symmetrical bending moment as well as a small yawing moment.

The fuselage is having anti-symmetrical torsion.

It can be said that we are dealing with a chordwise torsional antisymmetric mode.

This is the first anti-symmetrical wing bending mode,

Maximum displacement seems to be in the Z direction for the wing tips in an anti-symmetrical mode.

HTP have anti-symmetrical bending as well as the wing.

LECTURE 05.GROUND VIBRATION TEST (GVT) &

EXPERIMENTAL MODAL ANALYSIS (EMA). DYNAMIC

MODEL VALIDATION

1. Dynamic model validation flowchart

2. The Ground Vibration Test (GVT). Definition and objectives.

Aspects to consider (specimen, bc, excitation, response

measurements, scaffolding…).

The GVT is a non-destructive structural test performed on-ground on a complete aircraft “ready for flight” with the aim to obtain experimentally the normal modes of the aircraft. During the GVT the aircraft is dynamically excited in a controlled way in one or more points and the response of the aircraft is measured. Its objectives are devoted to the

experimental modal analysis (EMA) of the aircraft in frequency range where potentially dynamic amplifications or destructive aeroelastic instabilities can take place. The results obtained are natural frequencies, modal shapes, damping and masses. These results are used to update the dynamic FEM.

In order to perform a GVT, some aspects must be considered:

o Specimen and configurations: Aircraft in “ready for flight” condition must be tested in different configurations. (i.e. OEW, flaps extended, feed tanks filled) o BC: Free-free conditions through the use of bungees (preferred option), pneumatic

platforms (add some uncertainty to damping), deflated tires (not recommended for new designs) or jacks (bad results because not represent free-free condition). o Scaffolding: To access the aircraft for installation or instrumentation and place

structural exciters (need of stiffer scaffoldings to minimize perturbation from platform resonances).

o Controlled excitation: Structure has to be excited through Operation Modal Analysis, using control surfaces (FVT), by hand, instrumented impact hammer, shakers or hydraulic exciters. Applied energy must be in all axes, high enough to avoid noise threshold and low enough to avoid damaging the structure.

o Transducers (Accelerometers and cabling): Accelerometers must be adequate in terms of frequency range and sensitivity (location known from FEM). Cables are deployed through structure to connect accelerometers. Special attention to minimize added weight and allow load without restraints in the structural displacement under load. Wiring is time consuming (need of verification in connections and alignments) [FOR A400M 690 ACCELEROMETERS USED] o Data acquisition and test performance: Check 5 critical points:

o Rigid Body motion and mode shapes. (Largest RBM frequency should be 3 times lower than first flexible mode)

o Correct accelerometers identification and orientation using RBM o Verification od excitations level and direct FRFs

o Coherence verification (verify measured output due to excitation input and not from other source)

o Reciprocity (Maxwell reciprocity principle: if excite 1 and obtain response in 2, then if excite 2, obtain response in 1)

3. Provide to the student a 3D plot of an aircraft and ~2-300

accelerometers available. Ask him to define a suitable

accelerometers distribution for a GVT

Depending on what it is asked, accelerometers have to be located. (I.e. in a wing usually put accelerometers each 2-3 ribs and in the TE and LE)

4. Digital Signal Processing (DSP). Define sampling and design the

suitable sampling for a given problem. Typical problems in DSP

(aliasing, leakage, signal noise…) and how to solve them. (Long

Answer)

It deciphers the accelerometers signals to obtain the frequency contents though the Fourier transformation. DSP considerations:

o Aliasing: Is a numerical problem in DSP that arises when there is a high frequency content in the signal but the signal is sampled at low sampling ratio. The high frequency signal sampled at too low sampling ratio appears as a fake low frequency mode. Need of use of anti-aliasing filters.

o

Leakage: Dynamic Flight Test DFT takes a cyclic extension of data through rectangular windows. In order to not to lose information, use Hanning Windows which decreases side-lobes and widens main lobe.

o

Signal Noise: To avoid this, split data span into overlapping segments, apply window to each segment, apply DFT to each windowed segment and make and average of the DFT modules. (30-50 averages with 50-75% overlap)

5. Why may you need an anti-aliasing filter?

An anti-aliasing filter is a low pass filter that eliminates high frequencies in the signal and prevents the appearance of aliasing. A suitable anti-aliasing filter is usually 60%-80% of Nyquist frequency.

6. Why may you need to window the signal?

Because DFT assumes a cyclic extension of the data, so a specific repetitive data can be obtained for simplicity.

7. The Experimental Modal Analysis (EMA)

Structure characteristics: time invariant, observable, linear and obeys the Maxwell reciprocity theory.

Test in GVT can be performed through two methods:

o Phase Separation Method: many modes are excited simultaneously. o Phase Resonance Method or modal tuning: modes excited one by one.

The Phase Separation Method (PSM) excite randomly many modes, hence, the result that are going to be obtained are not precise (are correct but not exact) because exciting various modes at the same time it can be obtained one exact mode but the other ones are not exact. It will measure the FRF and then using Modal Parameter Estimator the Experimental Modal Model will be obtained.

The Phase Resonance Method (PRM) excite each mode one by one, hence, the result that is going to be obtained is exact.

One classical excitation of the GVT or FVT is a frequency sweep from very low frequencies to large frequencies with a constant spectrum. The Frequency Response Function FRF is the ratio H (w) = X (w)/Y (w). The Dynamic Amplification Factor is obtained once known the value of H (w) normalized to 1.0 at w0 D = |H (w)|.

The critical damping is the damping needed to change from an oscillating solution to a non-oscillating solution.

1-dof Experimental Modal Analysis using FRF’s or Dynamic Amplification Factor is a problem of curve fitting: Determine Omega_n and damping factor that better match the test result using:

8. Why may it be necessary to update the dynamic FE model?

Because it is important to match the structural and mass model results with respect to the GVT results. If this is achieved, the Dynamic Model is validated. If not, the structural model has to be updated until the results match.

9. How to compare experimental and theoretical normal modes.

Modal Assurance Criterion (MAC).

The MAC is defined as a scalar constant relating the degree of consistency between one modal vector and another reference modal vector as follows:

Through a frequency comparison in which GVT modes and FEM modes are plotted. If a 45 degrees slope is obtained, both modes are considered good matching.

10. Techniques to update dynamic FE models to match GVT results.

There are basically 4 techniques:

o [Kaa] matrix update: by changing terms or introducing a global factor on the stiffness matrix

o Adding absent components in FE models: in order to include the effect of these components considered important in the analysis

o Optimization techniques: NASTRAN SOL 200: it computes the sensitivities of the frequency of all modes with respect to the FEM variables.

o Delta stick Approach: Missing stiffness due to the assumptions (i.e. minimum thickness instead of chemical milling is assumed in the FEM). Thus, extra stiffness is included but not the mass.

11. Highlight the pros and cons of the different techniques to update

dynamic FE models to match GVT results.

The preferred approach for a dynamic FEM updating to match GVT is the “delta-stick approach”. But there are other techniques to update the FE models to match GVT.

o [Kaa] matrix update: Improve the dynamic FEM model but changing terms do not have a physical interpretation and only applicable to tested configurations

o Adding absent components in FE models: Relevant components are included in the analysis.

o Optimization techniques: NASTRAN SOL 200: Identifies and select

variables that are relevant for the analysis but the resulting dynamic FEM has different properties than the check stress model used for static test (diverge from check stress model). May lead to problems with

Airworthiness Authorities.

o Delta stick Approach: It keeps the original check stress model and add missing stiffness to the mode as a backbone of check stress model. The stick models runs along the elastic axis of wing, HTP, VTP and fuselage. Conservative assumptions embodied in the check stress model make the model slightly less stiff than reality (that’s why Delta stick is the preferred). This way allows keeping the check stress model as it is while the delta stick adds or remove the stiffness in the components that need to be updated.

LECTURE 06. 3D UNSTEADY AERODYNAMICS.

DLM

1. Conceptual introduction to Finite Element Method in 2D steady aerodynamics, (using 1 element, using 2 elements, using 3

elements)

2. Conceptual description of the Doublet Lattice Method

Vortex Lattice Method (VLM) takes into account only the wing, but in unsteady aerodynamics, the wake needs also to be modeled.

Departing from the unsteady potential equation:

And deriving w.r.t t and x, the two equations obtained are combined yielding:

This is the equation of the pressure potential which solution, that satisfies all constraints, is the pressure doublet. It can be solved with some integrals and algebra,

In the pressure potential, the doublets are the equivalent to velocity potential vortices. If the VLM is extended to account for oscillatory motion by adding a line of incremental oscillatory doublets of constant strength to the bound vortex along the c/4 of each box, the DLM is obtained.

DLM scope is: Linear Aerodynamic Potential Theory, Subsonic, and Harmonic Variation of w (t).

3D cases should be solved by using FEM technique (with “strong” assumptions like: linearity, small motions, harmonic motion, neglect viscosity and thickness

effects, subsonic, etc…)

DLM is modelled using flat thin panels subdivided in trapezoidal boxes.

Singularities are located in the c/4 line with collocation points at 3c/4 of each box. The steady part is solved using the VLM where singularities are horseshoe vortices. The unsteady part is solved by using the DLM where singularities are pressure doublets.

3. Provide to the student with a 3D view of an aircraft wing an

ask him to design a DLM wing model.

Additional recommendations:

- Spanwise divisions must be maintained along the different panels located at the same plane.

- Chordwise divisions should be maintained along the span - Surface intersection must be coincident with panel divisions

- Locate more aerodynamic boxes where higher pressure gradients are expected: wing tips, leading edges…

- Use a regular distribution of aerodynamic boxes, take advantage of the

symmetry of the A/C and use different aerodynamic panels for control surfaces.

4. Provide to the student with a 3D view of an aircraft wing and an HTP an ask him to design a DLM model of wing and HTP

5. Given a set of normal modes frequencies of interest (and a value of c and V) ask for definition of 10 reduced frequencies suitable for the analyses using those modes.

With known c, V and f, reduced frequency range can be calculated with:

6. How to build a good DLM model (mesh size, spanwise and chordwise divisions, etc.)

- Mess size as a balance between CPU cost and the highest normal mode that has to be represented because higher normal modes use to have more nodal lines both spanwise and chordwise that requires an increased number of boxes - Spanwise divisions must be maintained along the different panels located at the

same plane.

- Chordwise divisions should be maintained along the span - Surface intersection must be coincident with panel divisions

- Locate more aerodynamic boxes where higher pressure gradients are expected: wing tips, leading edges…

- Use a regular distribution of aerodynamic boxes, take advantage of the

symmetry of the A/C and use different aerodynamic panels for control surfaces.

7. Aero-structure coupling: description of the splining matrix [G] and its properties. Conditions needed to determine [G] matrix

components.

In all professional FEM solvers with aeroelastic capabilities, any number of structural and aerodynamic models may exist and may be connected to each other in such a way that the aerodynamic forces can be mapped to the structural model and the structural deformation can be mapped to the aerodynamic model to allow aeroelastic forces to be computed. Aeroelastic coupling bring these two models together using splining concepts that define the Spline Methods (Displacement, Force or General). Splines provide interpolation capability that couples the disjoint structural and aerodynamic models for two purposes:

o Force Interpolator to compute a structurally equivalent force distribution on the structure given a force distribution on the aerodynamic mess.

o Displacement interpolator to compute a set of aerodynamic displacements given a set of structural displacements.

Here G is the spline matrix, that relates the forces and displacements between structure and aerodynamic models and allows the force and displacement interpolations.

This matrix G is computed internally by the FEM solver using several assumption/constraints:

o Structural displacements are assumed to be part of an infinite thin plate o Force transformation must be computed such that the resultant

structural load are statically equivalent to the aerodynamic loads

o Similar condition must be satisfied for moments

9. DLM model checking (4 steps)

- Check geometry: Check correct modeling of the FEM and that a correct meshing has been performed.

- Check interpolated displacements: Check same normal mode shape plotted in structural (displacements) and aerodynamic (displacements) grids.

- Check steady pressures distribution: Check quality of the unitary cases pressures, unitary angle of attack and unitary control surface rotation.

- Check steady aerodynamic derivatives: Quality of main aerodynamic derivatives comparing Aerodynamic Data Base with Double Lattice Method Results and verify evolution with Mach is as expected, etc.

10. Describe a process to update DLM model to match CFD or test data

- The DLM model of the wing is divided in Spanwise strips. The total

aerodynamic lift and total aerodynamic moment of each strip is obtained by both, the DLM method and the CFD or test and compared between them - In the process to update DLM model, each box of the DLM model strip will

have a pondering factor a.

- An optimization loop is performed to obtain the set of pondering factors ai such

that the DLM strip lift and moment match ADB strip data. The additional optimization constraint is to select the pondering factors as close to 1.0 possible.

LECTURE L07. THE FLUTTER EQUATION AND ITS

SOLUTION

1- Derive the flutter equation from the Lagrange equations and present

the k-method to solve it.

Equations of slides 7 to 18.

2- Describe what a V-g plot is and how to interpret it.

For each reduced frequency (k) the complex eigenvalue-eigenvector problem is solved. Once the problem is solved the frequency is obtained from the real part of the eigenvalue and the damping from the imaginary part. The process is repeated for all the reduced frequencies k. By plotting the root loci of all the eigenvalues in the f-V and g-V, it is possible to track the evolution of the frequency and damping of the normal modes with the flight speed.

This way of representing the evolution of the frequency and damping of the normal modes is called the V-g plot. When the curve of damping crosses from the stable region to the unstable region, the crossing speed is the flutter speed VF (and the corresponding frequency is the flutter

frequency).

In a V-g plot, a negative damping obtained from the eigenvalue means that the system is STABLE (because negative damping should be added to a damped motion to obtain a harmonic solution). On the other hand, positive damping means that the system is UNSTABLE.

When damping curve crosses the g=0 line, this is the flutter speed and when it crosses the g=0.03 is an indication on how severe is the flutter mechanism (from Abrupt V<10KEAS to Mild V>200KEAS.)

When the curve never crosses the g=0.03 line, flutter can be categorized as benign. In addition if the curve never goes beyond 0.01 it could be categorized as a “hump mode”.

3- Meaning of damping sign in the flutter equation solution.

In the STABLE region, any perturbation that moves the system away from its equilibrium condition produces a subsequent damped motion but this motion is not harmonic, it converges after a while. Negative damping should be added to the damped motion to obtain a harmonic motion (and then fulfill the assumptions used to derive the flutter equation and the DLM unsteady aerodynamics).

In a V-g plot, a negative damping obtained from the eigenvalue means that the system is STABLE (because negative damping should be added to a damped motion to obtain a harmonic solution).

In the UNSTABLE region, any perturbation that moves the system away from its equilibrium condition produces a subsequent divergent motion, but this divergent motion is not harmonic.

Positive damping should be added to the divergent motion to obtain an harmonic motion.

In a V-g plot, a positive damping obtained from the eigenvalue, means that the system is UNSTABLE (because positive damping should be added to a divergent motion to obtain a harmonic solution)

5- Why the engines are located forward from wing elastic axes in the

current airliners design?

In order to shift forward the Xcg the engines are located forward from wing elastic axes. Shifting forward the Xcg any up-bending motion will cause a nose down movement, thus stabilizing the motion from the aeroelastic standpoint.

6- Why are the external stores located forward from wing elastic axes

in current fighters design?

In order to shift forward the Xcg the external stores are located as forward as possible in military airplanes. Shifting forward the Xcg any up-bending motion will cause a nose down movement, thus stabilizing the motion from the aeroelastic standpoint.

7- Why a control surface should be mass balanced?

In an aircraft with manual controls, a control surface rotation mode is a mechanism at almost zero frequency. The frequency of this mode increases with flight speed. On the other hand the

lifting surface bending mode frequency has a smooth evolution with flight speed. Therefore, there is a range of velocities in which there is a coalescence of frequencies between the control surface rotation mode and the lifting surface bending mode.

If the control surface is not mass balanced, the control surface center of gravity lies well behind the hinge line. An up movement of the lifting surface will generate a positive rotation on the control surface due to inertia coupling by the rear c.g. position. This will create a curvature in the airfoil that will create additional positive lift that in turn will tend to increase the movement. Similarly, a down movement of the lifting surface will generate a negative rotation of the control surface. This creates a curvature in the airfoil that will generate negative lift again tending to increase the movement. This is an unstable behavior: flutter.

In the plot showing the damping evolution with flight speed, the mode corresponding to the control surface will be always well damped but the mode corresponding to the lifting surface will exhibit flutter in the same velocity range of frequency coalescence.

The stability situation of the system can be reserved by mass balancing the control surface. If weight is added ahead of the hinge line, the coupling between control surface and bending will be progressively removed. If the control surface c.g. lies ahead of the hinge line, the physical behavior of the control surface following a movement of the lifting surface will be exactly the opposite as the one described above, and therefore, the effect of the resulting airfoil induced curvature will always have a stabilizing effect.

8- Flutter unmatched points vs. flutter matched points

Up to the end of the XX century, the flutter analyses were “unmatched”, meaning that the Mach number selected, the altitude and the obtained flutter speed were not a single point of the standard atmosphere. Therefore, unmatched flutter boundaries were calculated to estimate conservative flutter margins.

In the 90’s, the increase of the computer power allowed to perform matched flutter analyses meaning that the analyses are made at constant Mach number. The flutter solver includes another internal loop: V-g plot computed in KEAS. For each value of KEAS and at that Mach number, there is an altitude that matches the ISA conditions. The loop is continued speed after speed until the maximum speed (KEAS) of interest is reached.

Elaborated plots of flutter boundaries versus flight envelope for each mass configuration are obtained from the successive V-g plots calculated for each Mach number. From them the flutter mechanisms are identified and classified: Symmetric or Antisymmetric, Flutter speed and flutter frequency, Whether they are inside, close to or outside the flight envelope, whether they are mild, moderate, severe, abrupt… & Level of reliability of the mechanism.

One way to assess the reliability is by the isolation of the mechanism. In the aeroelasticians jargon, isolation of flutter mechanism means determine the minimum number of normal modes that reproduces the instability.

10-

Explain what are the aeroelastic stability margins required by

civil airworthiness regulations in the paragraph 25.629

11-

Flutter is a stability problem: Does it depend on the initial

conditions?

Like all the stability problems, flutter does not depend of the initial conditions.

12-

Given an aircraft with well-known wing flutter results… If a

new under-wing heavy pod is installed in the wing… Are the original

wing flutter analysis still valid or have they to be re-computed for

the new system wing-pod?

If the position of the center of mass is changed with this new system, flutter analysis have to be redo. (Remind that just an additional paint layer can change the CG position).

LECTURE L08. FLUTTER SPEED SENSITIVITIES.

MASSBALANCE. FCS.

1- Explain reasons why flutter sensitivities are needed.

This part of the analysis start when the “nominal” analysis have been already performed and the basic flutter mechanisms of the aircraft have been identified. Each flutter mechanism will have a critical set of specific mass config. and Mach number that produces the lowest flutter speed from the entire range. For each flutter mechanism, the flutter sensitivities have two missions:

- Find solutions. Explore in the design envelope what has to be changed to remove the flutter instability: mass balance; c.g. position; structural reinforcement; aerodynamic changes…

- Cover any possible uncertainty in:  Structural modeling

 Mass modeling

 Unsteady aerodynamics modeling

2- Control surface aerodynamic hinge moment flutter sensitivity.

The control surface aerodynamic hinge moment has a top relevance in aeroelasticity:

- The frequency of the control surface rotation mode increases with flight speed (V) - The rate of change of the frequency with V depends on the CHδ

- The larger the CHδ the fastest the increase of frequency with V

- Therefore the velocity of the potential couplings with another mode (i.e. a bending mode) change with CHδ

The flutter analysis sensitivity is to repeat the flutter analysis by varying the pressure correction factor in the control surface:

- A typical range of variation is between [0.1 - 2.0] where 1.0 corresponds to the pure DLM results.

- This wide variation allows to the aeroelasticians to have a good insight on all - This sensitivity is performed to all flutter mechanisms and all control surfaces (x3)

3- In an aircraft with manual controls, why control surfaces must be

mass balanced?

In an aircraft with manual controls, a control surface rotation mode is a mechanism at almost zero frequency. The frequency of this mode increases with flight speed. On the other hand the lifting surface bending mode frequency has a smooth evolution with flight speed.

Therefore, there is a range of velocities in which there is a coalescence of frequencies between the control surface rotation mode and the lifting surface bending mode.

If the control surface is not mass balanced, the control surface center of gravity lies well behind the hinge line. An up movement of the lifting surface will generate a positive rotation on the control surface due to inertia coupling by the rear c.g. position. This will create a curvature in the airfoil that will create additional positive lift that in turn will tend to increase the movement. Similarly, a down movement of the lifting surface will generate a negative rotation of the control surface. This creates a curvature in the airfoil that will generate negative lift again tending to increase the movement. This is an unstable behavior: flutter.

In the plot showing the damping evolution with flight speed, the mode corresponding to the control surface will be always well damped but the mode corresponding to the lifting surface will exhibit flutter in the same velocity range of frequency coalescence.

The stability situation of the system can be reserved by mass balancing the control surface. If weight is added ahead of the hinge line, the coupling between control surface and bending will be progressively removed. If the control surface c.g. lies ahead of the hinge line, the physical behavior of the control surface following a movement of the lifting surface will be exactly the opposite as the one described above, and therefore, the effect of the resulting airfoil induced curvature will always have a stabilizing effect.

4- Why an unauthorized repaint of a control surface must be

prohibited?

Because a new paint layer will put the control surface out of massbalance tolerances. It is forbidden in the Aircraft Maintenance Manual to repaint a control surface without removing previous painting before.

5- Describe a procedure to fine tuning of massbalance during control

surface final assembly.

Mount the control surface fully equipped at the hinge position.

Measure the force, F (N), at a known position, F is considered positive (+) downwards, meaning that the center of gravity of the control surface is behind the hinge line according to the flight direction. F is considered negative (-) upwards, meaning that the center of gravity of the control surface is in front of the hinge line according to the flight direction.

Install or remove the necessary amount of balance weight at the specified location to meet the balance requirements. Table defining quantities of mass balance will be provided for each control surface in terms of the measured force F.

Obtain the new value of F by repeating steps 1) and 2). If this force is not within the specified limits, corresponding to the balance requirements, the amount of balance weight must be corrected until the final force lies inside the required tolerances.

6- Comment on the amount of mass required for massbalancing. Is it a

significant percentage of the control surface total weight?

The amount of mass required for massbalancing must be sufficiently large to avoid positive damping (meaning unstable system) for a specific range of velocities.

7- Control surface actuator stiffness flutter sensitivity.

In order to solve the probability of failure of actuators, put two actuators to avoid failure.

8- External stores flutter sensitivity.

The addition of heavy under wing masses modifies the wing normal modes and requires to perform a complete set of new flutter analyses. Under wing heavy masses include:

- Engines

- Air-to-air Refuelling pods - External Fuel tanks - External stores, etc…

The following sensitivities have to be performed:

- Mass characteristics of the engine, pods or external store - Stiffness characteristics of the pylon

- Local stiffness of the attachments

- In case of external stores, all subsequent release sequences including failure

cases and antisymmetric configurations.

9- What of the following design changes need to be flutter

substantiated?

1. Add winglets at the wing tip (YES/NO)

2. Open the rear door (YES/NO)

3. Deflect the ailerons (YES/NO)

4. Etc

For the first case, YES. Winglets will modify all aspect related with flutter analysis: winglet mass affects wing modes, winglet aerodynamics modify wing aerodynamic and stiffness is affected due to the addition of reinforcements.

For the second case, YES. As the structure pass from a closed section to an open section, modifying the rear fuselage stiffness and therefore a significant drop in frequency of rear fuselage anti-symmetric torsion modes. Here, the anti-symmetric tail flutter mechanisms are significantly affected by this drop of stiffness.

For the third case, NO. As ailerons are already mounted in the wing it will not affect the mass aspect.

For the rest of cases, every aircraft feature that may have an effect on the normal modes should be substantiated from the flutter standpoint.

10-

What is the control surface fitting failure usually most critical

for flutter?

The failure cases are modelled in the FEM model by removing the corresponding elements, one by one. The most critical fitting failure in a control surface use to be the one located most outboard.

In this case of a VTP, the Hinge 8.

11-

What is the delamination zone in a control surface usually most

critical for flutter?

In current composite control surfaces, the effect of composite delamination should be assessed from the flutter standpoint.

The control surface area most critical use to be the area located immediately outboard of the actuators.

As the delaminated area increases, the flutter mechanism tends to become severe. This information is used to define the maximum allowable delamination inside the Aircraft Maintenance Manual.

12-

Describe the analysis needed to cover water ingress in a

sandwich structure of a control surface from flutter standpoint.

Water that remains in the honeycomb cells during aircraft operation and moves Xcg rearwards, what is a potential threat of aeroelastic couplings.

Water ingress in control surfaces is modelled in two ways: either distributed (yellow dots) or concentrated in the trailing edge (red whichever is worst. A typical value accepted by Airworthiness Authorities is 1 kg/m concentrated in the trailing edge. The elaborated plot of (flutter speed) vs (kg/m) in the trailing edge, shows no problem for 1.0 kg/m, a flutter mechanism starts around 1.4 kg/m and it becomes severe (i.e. crosses also g=0.03 line) around 1.7-1.8 kg/m.

13-

Definition of aeroservoelasticity and physical description of an

example of longitudinal FCS (symmetric) potentially unstable

coupling.

Aeroservoelasticity is the study of the interaction of all elements relevant for aeroelasticity plus Flight Control System laws. (Requested in Airworthiness Regulations).

The solution options are limited to filtering the gyro output signal or moving the gyro to a different location. The gyro can be relocated from the forward position to the anti-node which eliminates the vibration [Notch filter to eliminate all the undesired responses but adds a delay]

14-

Example of lateral FCS (antisymmetric) potentially unstable

coupling

LECTURE L09. FLIGHT FLUTTER TEST (FVT).

AEROELASTIC MODEL VALIDATION.

1- Define Flight Vibration Test

Flight Flutter Test is aimed to:

- Determine experimentally the evolution of normal modes frequency and damping with flight speed.

- Ensure that the aircraft is free from flutter in all its envelope up to Vd/Md, - Validate the aeroelastic model

In order to avoid confusion with the Fast Fourier Transform (FFT) acronym, the acronym for Flight Flutter Test is FVT.

It is explicitly required by the administrator in CS25.629. The test has to be performed when a change in the structure is applied, although the change include an improvement in the flutter behavior. When the change is insignificant such as including an antenna there is no need to do the test.

2- Describe the objectives of the FVT.

The objectives of the Flight Flutter Test are:

- Determine experimentally the evolution of frequency and damping of the aircraft normal modes with flight speed

- Ensure that all modes are properly damped and that there is not rapid decrease of damping of any mode inside the aircraft flight envelope. (Clear the flight envelope from the flutter standpoint).

- Contribute to validate the aeroelastic model.

3- In what situations is the FVT required by the Airworthiness

Regulations in CS25.629?

It is always mandatory for new type designs and for all design modifications unless the effect is insignificant (even if the change include an improvement of the flutter behavior).

4- Describe the FVT by explaining the different components of this test

The test has to be planned years in advance.

Specimen: It is the first prototype of an aircraft configured in the most critical configuration from the flutter standpoint.

Controlled excitation: There are several ways to excite the aircraft like natural turbulence, bonkers (but they change the aerodynamics of the wing), external aerodynamic vanes (located at the wing tip): Oscillatory vanes & Aerodynamic vanes with slotted Trailing Edge and the control surfaces of the aircraft. From this last one, in aircraft with manual controls, stick raps are used (pilot hit the stick with a hammer and it is excited); in aircraft with actuators and FCS, pulses and sine sweeps are used. When the aircraft can fly at stabilized conditions, it is better to use sweep and pulse. In flight points that can only be achieved by diving, only pulses can be performed when aircraft crosses exactly the flight point conditions. At Vd/Md the aircraft may be excited only with natural turbulence.

Transducers: Accelerometers, normally located at wing and tail tips, engines and rear and forward fuselage.

Data acquisition: The same considerations as for GVT.

- Sampling. Should be large enough to capture all phenomena. The typical value are on the range of 128-512 samples per second. Nyquist frequency is half of the sampling frequency.

- Aliasing: Prevent it using a low-pass filter.

- Leakage: Avoid by windowing the signal (Hanning windows)

- Noise: To avoid this, split data span into overlapping segments, apply window to each segment, apply DFT to each windowed segment and make and average of the DFT modules. (30-50 averages with 50-75% overlap).

Real Time Analysis: FVT are analyzed at the same time as it is being performed. Aircraft data and voice is received in the telemetry room of the flight test center so decisions can be made at real time.

5- Means of exciting the aircraft in a FVT

- Natural turbulence (controlled excitation) - Bonkers (pyrotechnic devices)

- External aerodynamic vanes (located at wing tip): o Oscillatory vanes

o Aerodynamic vanes with slotted Trailing Edge - The same control surfaces of the aircraft

o In aircraft with manual controls,  Stick raps

o In aircraft with actuators and FCS,  Pulses

The preferred option is logically the use of the same control surfaces of the aircraft: in this way, the configuration of the aircraft being tested in FVT is identical to the series aircraft.

- In the flight points that the aircraft can fly at stabilized conditions; both, sweep and pulses are performed

- In the flight points that can only be achieved by diving, only pulses can be performed when the aircraft crosses exactly the flight point conditions

- For the final point at Vd/Md the aircraft is excited only with natural turbulence

6- Explain the similitude and the differences between GVT and FVT

7- Describe how are the excitations in a FVT depending on the flight

envelope point that is going to be tested.

The preferred option is logically the use of the same control surfaces of the aircraft: in this way, the configuration of the aircraft being tested in FVT is identical to the series aircraft.

- In the flight points that the aircraft can fly at stabilized conditions; both, sweep and pulses are performed

- In the flight points that can only be achieved by diving, only pulses can be performed when the aircraft crosses exactly the flight point conditions

8- Present the aeroelastic model validation flowchart.

9- Explain briefly the contents of each of the boxes of the aeroelastic

model validation flowchart

On one hand, the integrated aeroelastic model is obtained from the unsteady aerodynamic and dynamic models. With the model, both theoretical normal eigenvalues and numeric response to excitation are achieved.

On the other hand, with the FVT and the excitation of the aircraft by a pulse or a sweep, experimental modal and signal analysis can be performed giving the experimental normal eigenvalues and the aircraft response.

Experimental and theoretical results are compared and if the match is good, the integrated aeroelastic model is validated, otherwise, dynamic flight loads model has to be updates, thus, new integrated aeroelastic model is obtained.

LECTURE L10. THE CONCEPT OF LOADS. MS.

TRANSIENT RESPONSE.

1- Which are the structural sizing cases in a modern aircraft?

Symmetric bending of the fuselage  During dynamic landing Wing  During pull-up maneuver (Load factor of the aircraft) Wing up bending of the aircraft  During vertical gusts Wing down bending of the aircraft  During taxi loads

HTP area  Taking off on a hot day with CG forward (extreme case) VTP dimensioning  Lateral gusts.

2- Define loads

Aircraft structural loads or actions are forces, deformations or accelerations applied to the structure or its components.

- Loads causes stresses, deformations and displacements in structures. Assessment of their effects is carried out by the methods of structural analysis

- Excess load or overloading may cause structural failure, and hence such possibility should be either considered in the design or strictly controlled

Loads are consequences of the aircraft operations (loads due to taxi, take-off, etc.…)

3- List several forms of loads classification

Depending on the type of structural analysis they are aimed for, the loads can be classified as: - Checkstress loads (limit loads and ultimate loads) for exceptional operation

- Fatigue loads for normal operation

Depending on the aircraft operation phase in which they can be met, the loads can be classified as:

- Flight Loads

- Ground Loads

Depending on whether they are steady or variable, the loads can be classified as: - Static Loads

4- What the airworthiness regulations (CS25.301) say about loads?

- Strength requirements are specified in terms of limit loads (the maximum loads expected in service) and ultimate loads (limit loads multiplied by safety factor). Unless otherwise provided, prescribed loads are limit loads

- Unless otherwise provided the specified air, ground and water loads must be placed in equilibrium with inertia forces, considering each item of mass in the airplane. These loads must be distributed to conservatively approximate or closely represent actual conditions. Methods used to determine load intensities and distribution must be validated by flight load measurement unless the methods used for determining those loading conditions are shown to be reliable

- If deflections under load would significantly change the distribution of external or internal loads, this redistribution must be taken into account.

5- Why static loads are different from dynamic loads?

The difference is mainly due to the inertia forces. Example: exciting a clamped beam with a transient input force at the free end. In case of an applied static load at the beam

tip, inertia forces do not play any role in static deformation nor in the distribution of internal forces (shear, bending). On the other hand, when the applied load is a transient excitation, depending on the frequency and shape of the dynamic excitation, inertia forces may be determinant in the subsequent response of the dynamic system completely changing the internal loads distribution.

If the frequency of the excitation is close to the first beam bending mode, the response will be close to this first bending mode. The evolution of shear force along the beam will always be positive (line in the static case) but larger than the static case because of the dynamic amplification.

On the other hand, if the frequency of the excitation is close to the second bending mode, the response will be in the second bending mode, very different from a static solution. The evolution of shear force along the beam may even change of sign (not intuitive if compared with a static solution).

6- Use a clamped beam example to illustrate difference between static

and dynamic loads

7- Dynamic loads process flowchart

Final Conceptual flowchart:

9- What is a 2d envelope

2D envelopes are the combination of the Bending Moment (Mx) vs time and Torsion Moment (My) vs time plots in a single plot. The combination of both graphs forms a 2dimensional envelope.

10-

The concept of nodal loads

Nodal loads are those nodes that has a point/nodal load. In order to select which nodes have loads, a criteria is followed: Max/Min criteria (looking at moment vs time plot and finding max and min) & 2D envelopes criteria (selecting the critical points/corners of the 2D envelope).

LECTURE L11. GROUND DYNAMIC LOADS

1- Define dynamic landing and why this scenario is relevant in

aeroelasticity and structural dynamics

During landing, the vertical velocity or sinking speed of an airplane is quickly reduced to zero when the wheels strike the ground. This process is accomplished by a transfer of kinetic energy of the sinking airplane to internal energy in the shock absorption system where it is dissipated. The vertical velocity of the airplane is brought to zero within a fraction of a second, and hence the forces applied to the structure through shock strut change from zero to a maximum, also in a fraction of a second. This rapid change in velocity, or equally rapid application of force, excites the lower vibration modes of the structure. Therefore the structural dynamics characteristics of the structure should be taken into account.

The relevant aircraft components affected by dynamic landing are: - The landing gear itself

- The entire fuselage (symmetric bending and shear force)

- The wing down bending

- The engine vertical force and vertical acceleration Dynamic landing loads are used for:

- Design and Checkstress of the structure  Certify the aircraft - Fatigue analysis  Define inspections intervals

- Analysis of operational firm or hard landings  Define maintenance operations.

2- Define taxi and why this scenario is relevant in aeroelasticity and

structural dynamics

Taxiing is the entire phase of straight line motion on the ground prior to final take off and following landing. (Braking and turning are considered separate phases). Paved runways have some degree of roughness that may excite the normal modes of the structure when taxiing. Depending on the taxis speed, a tuning between the roughness excitation and the normal modes of the aircraft may cause significant response amplification and dynamic loads on the structure.

The relevant aircraft components affected by taxi loads are: - The landing gear itself (strokes)

- The nose fuselage (vertical force)

The phenomenon is exacerbated in military aircraft that must operate in unpaved runways. Taxi loads are used for:

- Design and Checkstress of the structure  Certify the aircraft - Fatigue analysis  Define inspections interval

- Operation on unpaved surfaces  Defines maintenance operations. Define number of allowable runs in soft soil, etc. …

3- Specific civil requirements in CS25 for dynamic landing.

Complement with examples of more exigent military requirements

For military tactical aircraft Vz = 12 ft/s while for On-board carrier aircraft Vz = 18ft/s.

4- Specific civil requirements in CS25 for taxi loads. Complement with

examples of more exigent military requirements