An overview of the dynamic load algorithm is shown inFigure 5-1. The input data follow two major paths: the DAREA method versus the LSEQ method. The details of the data inputs are given in the appendices and in the NX Nastran Basic Dynamic Analysis User’s Guide.
Advanced Dynamic Analysis User’s Guide 5-3
Figure 5-1. Input Data Relationships for Dynamic Loads
• The LSEQ Bulk Data act much like a set of Case Control commands to generate static loads and assign them to a specific static load vector. These vectors are assembled, reduced, and combined for all superelements. A different load vector may be required for each unique function of time or frequency.
• The DAREA, DPHASE, and DELAY Bulk Data provide a direct method of distributing the dynamic loads over the grid points. The DAREA factors correspond to a specific load factor for a specific degree-of-freedom, much like an area under a pressure load. The DPHASE and DELAY data are used when the same load versus time function is applied to different points at different times. An example of a DPHASE application is the frequency response of an automobile traveling over a highway with a sinusoidal undulation. As the speed increases the input frequency changes, but the phase difference between the axles is constant.
The TLOADi Bulk Data inputs each define a function of time with coefficients or TABLEDi references. The RLOADi Bulk Data inputs each define a function of load versus frequency with complex TABLEDi inputs. The DLOAD entry is used to combine the different load functions, either time or frequency dependent. These functions may be associated with LSEQ-type vectors or DAREA coefficients, or both.
Recommendations
The following guidelines should be observed when applying dynamic loads.
TABLEDi
1. Remember that the tables are extrapolated at each end from the first or last two points. If the load actually goes to zero, add two points with values of y = 0.
2. Linear interpolation is used between tabular points. This may lead to accumulated roundoff and drift errors over a long-period transient analysis. Fix this problem by adding a correcting load function to the same points on subsequent runs.
3. If a jump occurs (two points with equal values of X), the value of Y at the jump is the average of the two points.
Static Preloads
1. An initial linear static preload that is released suddenly for a transient analysis may be performed in two stages in one run. In stage 1, apply the static loads and use large time steps to suppress the higher frequency motions. In stage 2, remove the loads and use small time steps to capture the dynamic action. Alternatively, a nonlinear analysis may be restarted from a nonlinear static analysis, making the process nearly automatic.
2. Simple static loads may be included through the dynamic load methods. Define a TLOAD2 or an RLOADi with a constant function and add it via the DLOAD Bulk Data input.
3. Thermal loads may be applied via the LSEQ method, but note that the dynamic stress recovery method will not account for the additional strain or stress.
Matching Initial Conditions
1. In linear transient analysis, the load at time, t = 0.0 is always ignored. If the load is actually a preload, the initial conditions (TIC data) should correspond to this condition. Otherwise, if the load is being suddenly applied, the loading functions will start at t = Δt.
Advanced Dynamic Analysis User’s Guide 5-5
2. If a free body is being accelerated by an applied load, the calculated response will also be delayed by a fraction of a time step.
Setup for Random Analysis
An NX Nastran random analysis requires a preliminary frequency response analysis to generate the proper transfer functions that define the output/input ratios. The squared magnitudes of the results are then multiplied by the spectral density functions of the actual loads. Normally, the inputs are unit loads (e.g., one g constant magnitude base excitation or a unit pressure on a surface).
Fluids and Acoustic Loads
Normally, fluid and acoustic elements are not loaded directly, but are excited by the connected structures. However, loads on these special grid points may be used to represent sources of fluid motion such as a small loudspeaker. The actual units of these loads are the second derivative of volume flow with respect to time. See“Axisymmetric Fluids in Tanks”for details.
5.3 Complex Eigenvalue Analysis
Complex eigenvalue analysis is necessary when the equation of motion for a mechanical system contains any of the following:
• A damping matrix (to account for viscous damping).
• A complex stiffness matrix (to account for structural damping).
• An unsymmetrical mass or stiffness matrix.
• A mass matrix that is not positive semidefinite.
Complex eigenvalue analysis is required in the analysis of aeroelastic flutter, acoustics, and rotating bodies, among others. The results of a complex eigenvalue analysis are typically used to examine the effect of damping or determine the stability of a system when the system contains sources of energy like rotating components.
You can use either of two solution sequences to perform complex eigenvalue analysis:
• SOL 107 Direct Complex Eigenvalue Analysis
• SOL 110 Modal Complex Eigenvalue Analysis
When you use either solution sequence, you must specify the complex eigenvalue method. NX Nastran uses this method to calculate the eigenvalues and eigenvectors.
Although both solution sequences have the same applicability, modal complex analysis allows you to reduce the size of the complex eigenvalue problem. The corresponding computational efficiency is advantageous when the model is very large. However, reducing the size of the complex eigenvalue problem can lead to the loss of accuracy in the results.