Case Control Commands
90- TRIM 1 0.0 4.0075 URDD4 0.0 AILE 1.0 ENDDATA
TOTAL COUNT= 91
Listing 6-9. Sorted Bulk Data Entries for Jet Transport Wing in Roll
EXAMPLE HA144B: BAH JET TRANSPORT WING DYNAMIC ANALYSIS PAGE 15 ANTISYMMETRIC, 58 BOXES, DOUBLET-LATTICE AERO
AILERON ROLL, STATIC AERO SOLUTION
O U T P U T F R O M G R I D P O I N T W E I G H T G E N E R A T O R REFERENCE POINT = 11
M O
* 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 * * 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 * * 0.000000E+00 0.000000E+00 4.191900E+04 5.128960E+06 -1.642074E+05 0.000000E+00 * * 0.000000E+00 0.000000E+00 5.128960E+06 1.350243E+09 -2.381847E+07 0.000000E+00 * * 0.000000E+00 0.000000E+00 -1.642074E+05 -2.381847E+07 4.458796E+09 0.000000E+00 * * 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 *
S
* 1.000000E+00 0.000000E+00 0.000000E+00 * * 0.000000E+00 1.000000E+00 0.000000E+00 * * 0.000000E+00 0.000000E+00 1.000000E+00 * DIRECTION
MASS AXIS SYSTEM (S) MASS X-C.G. Y-C.G. Z-C.G. X 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 Y 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 Z 4.191900E+04 3.917256E+00 1.223541E+02 0.000000E+00
I(S)
* 7.226942E+08 3.727022E+06 0.000000E+00 * * 3.727022E+06 4.458153E+09 0.000000E+00 * * 0.000000E+00 0.000000E+00 0.000000E+00 *
I(Q)
* 4.458157E+09 *
* 7.226906E+08 *
* 0.000000E+00 *
Q
* 9.977400E-04 9.999995E-01 0.000000E+00 * * -9.999995E-01 9.977400E-04 0.000000E+00 * * 0.000000E+00 0.000000E+00 1.000000E+00 * N O N - D I M E N S I O N A L S T A B I L I T Y A N D C O N T R O L
D E R I V A T I V E C O E F F I C I E N T S
MACH = 0.0000E+00 Q = 4.0075E+00 TRANSFORMATION FROM BASIC TO REFERENCE COORDINATES:
{ X } [ -1.0000 0.0000 0.0000 ] { X } { 0.0000E+00 } { Y } = [ 0.0000 1.0000 0.0000 ] { Y } + { 0.0000E+00 } { Z }REF [ 0.0000 0.0000 -1.0000 ] { Z }BAS { 0.0000E+00 }
TRIM VARIABLE COEFFICIENT RIGID ELASTIC
UNSPLINED SPLINED RESTRAINED UNRESTRAINED INTERCEPT CX 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CY 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CZ 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CMX 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CMY 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CMZ 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 ROLL CX 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CY 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CZ 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CMX -4.414531E-01 -4.414531E-01 -5.189431E-01 -5.059597E-01 CMY 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CMZ 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 URDD4 CX 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CY 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CZ 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CMX 0.000000E+00 0.000000E+00 -1.064108E-01 0.000000E+00 CMY 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CMZ 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 AILE CX 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CY 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CZ 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CMX 1.448708E-01 1.448708E-01 1.054927E-01 1.028534E-01 CMY 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CMZ 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
INTERMEDIATE MATRIX ... HP COLUMN 1 3.054546E-01 COLUMN 2 2.098385E+00 COLUMN 3 -7.304801E-02 A E R O S T A T I C D A T A R E C O V E R Y O U T P U T T A B L E AEROELASTIC TRIM VARIABLES
TRIM VARIABLE VALUE OF UX ROLL 2.032838E-01 URDD4 0.000000E+00 AILE 1.000000E+00
A E R O S T A T I C D A T A R E C O V E R Y O U T P U T T A B L E MACH = 0.000000E+00 Q = 4.007500E+00
AERODYNAMIC FORCES AERODYNAMIC AERODYNAMIC PRES. AERODYNAMIC
GRID LABEL COEFFICIENTS PRESSURES EXTERNAL ID LABEL NORMAL FORCES(T3) MOMENTS(R2) 1 LS -1.354849E-01 -5.429556E-01 1001 LS -1.071998E+03 -1.175848E+04
2 LS -4.765255E-02 -1.909676E-01 1002 LS -3.770417E+02 -4.135676E+03 3 LS -2.612218E-02 -1.046846E-01 1003 LS -2.066867E+02 -2.267095E+03 4 LS -1.495107E-02 -5.991640E-02 1004 LS -1.182974E+02 -1.297575E+03 5 LS -7.376158E-03 -2.955995E-02 1005 LS -5.836243E+01 -6.401630E+02 6 LS -3.648801E-01 -1.462257E+00 1006 LS -3.619086E+03 -3.732182E+04 7 LS -1.464361E-01 -5.868426E-01 1007 LS -1.452435E+03 -1.497824E+04 8 LS -8.362006E-02 -3.351074E-01 1008 LS -8.293911E+02 -8.553097E+03 9 LS -4.900119E-02 -1.963723E-01 1009 LS -4.860213E+02 -5.012094E+03 10 LS -2.503084E-02 -1.003111E-01 1010 LS -2.482700E+02 -2.560284E+03 11 LS -6.398618E-01 -2.564246E+00 1011 LS -5.884946E+03 -5.627479E+04 12 LS -2.556842E-01 -1.024655E+00 1012 LS -2.351582E+03 -2.248700E+04 13 LS -1.459844E-01 -5.850326E-01 1013 LS -1.342650E+03 -1.283910E+04 14 LS -8.575688E-02 -3.436707E-01 1014 LS -7.887239E+02 -7.542170E+03 15 LS -4.417319E-02 -1.770241E-01 1015 LS -4.062703E+02 -3.884959E+03 16 LS -9.208332E-01 -3.690239E+00 1016 LS -7.804856E+03 -6.878029E+04 17 LS -3.609245E-01 -1.446405E+00 1017 LS -3.059147E+03 -2.695873E+04 18 LS -2.014354E-01 -8.072526E-01 1018 LS -1.707340E+03 -1.504593E+04 19 LS -1.155547E-01 -4.630855E-01 1019 LS -9.794256E+02 -8.631187E+03 20 LS -5.842042E-02 -2.341198E-01 1020 LS -4.951635E+02 -4.363628E+03 21 LS -1.163823E+00 -4.664021E+00 1021 LS -8.304871E+03 -6.721755E+04 22 LS -4.398006E-01 -1.762501E+00 1022 LS -3.138353E+03 -2.540105E+04 23 LS -2.303485E-01 -9.231217E-01 1023 LS -1.643734E+03 -1.330397E+04 24 LS -1.207852E-01 -4.840466E-01 1024 LS -8.619053E+02 -6.976046E+03 25 LS -5.559115E-02 -2.227816E-01 1025 LS -3.966904E+02 -3.210713E+03 26 LS -1.347419E+00 -5.399781E+00 1026 LS -8.032175E+03 -5.973930E+04 27 LS -4.651038E-01 -1.863904E+00 1027 LS -2.772556E+03 -2.062088E+04 28 LS -1.955689E-01 -7.837424E-01 1028 LS -1.165817E+03 -8.670762E+03 29 LS -5.785358E-02 -2.318482E-01 1029 LS -3.448742E+02 -2.565002E+03 30 LS -1.905612E-03 -7.636740E-03 1030 LS -1.135965E+01 -8.448740E+01 31 LS -1.437025E+00 -5.758880E+00 1031 LS -6.334769E+03 -4.355154E+04 32 LS -4.041525E-01 -1.619641E+00 1032 LS -1.781605E+03 -1.224854E+04 33 LS -2.264492E-02 -9.074951E-02 1033 LS -9.982446E+01 -6.862932E+02 34 LS 2.357795E-01 9.448866E-01 1034 LS 1.039375E+03 7.145705E+03 35 LS 2.615480E-01 1.048154E+00 1035 LS 1.152969E+03 7.926661E+03 36 LS -1.530291E+00 -6.132641E+00 2001 LS -5.864338E+03 -3.504858E+04 37 LS -3.360160E-01 -1.346584E+00 2002 LS -1.287671E+03 -7.695847E+03 38 LS 2.695004E-01 1.080023E+00 2003 LS 1.377029E+03 1.097320E+04 39 LS 1.497109E+00 5.999664E+00 2004 LS 3.824786E+03 1.523938E+04 40 LS 3.661325E+00 1.467276E+01 2005 LS 9.353885E+03 3.726939E+04 41 LS 1.145043E+00 4.588762E+00 2006 LS 2.925336E+03 1.165563E+04 42 LS -1.569205E+00 -6.288589E+00 2007 LS -5.541820E+03 -3.052331E+04 43 LS -2.701145E-01 -1.082484E+00 2008 LS -9.539389E+02 -5.254117E+03 44 LS 4.182711E-01 1.676221E+00 2009 LS 1.969560E+03 1.446396E+04 45 LS 1.815431E+00 7.275338E+00 2010 LS 4.274261E+03 1.569455E+04 46 LS 4.017232E+00 1.609906E+01 2011 LS 9.458201E+03 3.472934E+04 47 LS 1.380969E+00 5.534232E+00 2012 LS 3.251362E+03 1.193859E+04 48 LS -1.562750E+00 -6.262719E+00 2013 LS -4.686912E+03 -2.370004E+04 49 LS -2.563097E-01 -1.027161E+00 2014 LS -7.687097E+02 -3.887089E+03 50 LS 3.775468E-01 1.513019E+00 2015 LS 1.509757E+03 1.017906E+04 51 LS 1.684529E+00 6.750751E+00 2016 LS 3.368097E+03 1.135417E+04 52 LS 3.921867E+00 1.571688E+01 2017 LS 7.841497E+03 2.643442E+04 53 LS 1.306940E+00 5.237563E+00 2018 LS 2.613135E+03 8.809122E+03 54 LS -1.122619E+00 -4.498896E+00 3001 LS -1.188721E+03 -6.040188E+03 55 LS -1.255417E-01 -5.031084E-01 3002 LS -1.329338E+02 -6.754702E+02 56 LS 2.223080E-01 8.908994E-01 3003 LS 2.353979E+02 1.196116E+03 57 LS 6.150346E-01 2.464751E+00 3004 LS 6.512489E+02 3.309158E+03 58 LS 8.130676E-01 3.258368E+00 3005 LS 8.609423E+02 4.374663E+03 *** LABEL NOTATIONS: LS = LIFTING SURFACE, ZIB = Z INTERFERENCE BODY ELEMENT,
ZSB = Z SLENDER BODY ELEMENT, YIB = Y INTERFERENCE BODY ELEMENT, YSB = Y SLENDER BODY ELEMENT.
D I S P L A C E M E N T V E C T O R
POINT ID. TYPE T1 T2 T3 R1 R2 R3
7 G 0.0 0.0 -5.400196E+00 0.0 0.0 0.0 8 G 0.0 0.0 -1.110230E+01 0.0 0.0 0.0 9 G 0.0 0.0 -1.101022E+01 0.0 0.0 0.0 10 G 0.0 0.0 -1.777396E+01 0.0 0.0 0.0 11 G 0.0 0.0 0.0 0.0 0.0 0.0 12 G 0.0 0.0 -1.563730E+01 0.0 -5.064504E-02 0.0
6.4
A 15-Degree Sweptback Wing in a Wind Tunnel (Example
HA144C)
A simple flat-plate wing with 15 deg of sweepback is shown inFigure 6-4. This wing has been tested in a wind tunnel for flutter at subsonic and supersonic speeds, and the results have been reported by Tuovila and McCarty (1955). A number of models of the same shape, but of different materials, were tested. The models were made of 0.041 in thick sheet metal with their leading and trailing edges beveled 0.25 in to form a symmetric hexagonal airfoil shape. The 15 deg swept model had a constant chord of 2.07055 in. and a semispan of 5.52510 in. (and an effective span with wall reflection of 11.0502 in). The low-speed models were made of aluminum, and the high-speed models were made of magnesium. The subsonic flutter test was run at Mach number
m = 0.45. In the present example, the aluminum model is treated as if it were tested for its static
aeroelastic characteristics in the wind tunnel at m = 0.45.
Figure 6-4. A 15-Degree Sweptback Wing Model
The method of solution for the restrained wind tunnel model employs the “large mass” method discussed in Enforced Motion in the NX Nastran Basic Dynamic Analysis User’s Guide for enforced motion. A large support mass is assumed (chosen approximately six orders of magnitude larger than the system mass) which in turn is reacted by an equally large force so there is a very small consequent acceleration of the system. A gravity force is included to account for the weight of the system.
The present example represents the plate model appropriately by plate elements. The basic structural model consists of GRID and CQUAD4 entries. The plate wing is divided into seven strips of equal width and four chordwise elements separated along the one-eighth, one-half, and seven-eighths chord lines; its idealization into 28 structural plate elements is shown in Figure (a). The leading- and trailing-edge CQUAD4 elements taper in thickness to zero at the edges on their corresponding CQUAD4 entries, whereas the interior elements have the constant thickness of 0.041 in. as given on the PSHELL entry. The MAT1 entry lists the moduli E = 10.3 × 106and G = 3.9 × 106, and the weight density of r = 0.100 lb/in3for aluminum. Three grid
points are constrained to simulate a perfectly clamped root chord. However, the root leading and trailing edge grid points are assumed to be free because a clamp would not restrain the beveled edges. GRIDs 9 and 25 (at the one-eighth and seven-eighths chord points at the root) are connected to GRID 17 by rigid bars (RBAR 101 and RBAR 102), and GRID 17 is constrained in all degrees of freedom except the support (SUPORT) degrees of freedom, vertical translation (T3), and pitch (R2). GRIDs 1 through 8, 10 through 16, 18 through 24, and 26 through 40 are constrained against in-plane rotation (R3) because the CQUAD4 element has no in-plane rotational stiffness. ASET1 entries are included to reduce the size of the problem by restricting the degrees of freedom to the normal deflections of the wing (the GRID T3 degrees of freedom), which are the only deflections required to determine the aerodynamic loads. This plate model is used in several subsequent examples. The Bulk Data entries are contained in the separate input file PLATE_STRUCT. DAT that is presented inListing 6-11.
The density on the MAT1 entry and PARAM,COUPMASS,1 result in the generation of the coupled (note that a coupled mass matrix is not a consistent mass matrix) mass matrix of the plate, while the GRAV entry introduces the weight of the model into the problem. Although the weight of a wind tunnel model is usually small, it is not negligible and is just as easily included. The large mass is placed at the support point GRID 17 and is chosen arbitrarily as 105 on a
CONM2 entry with its pitching moment of inertia also chosen arbitrarily as 105lb-in2. These
are converted to mass units by the parameter WTMASS. The additional PARAM,AUNITS is included to permit accelerations to be specified in units of Gs both in the input (on the TRIM entry) and in the output (the values of the UX for accelerations in the Aerostatic Data Recovery Output Table). The reacting force of 105is also placed at GRID 17 on the FORCE entry. The
LOAD entry combines the gravity load with the reacting force. (Note that the load and the force are in opposite directions.)
Figure 6-5. A 15-Degree Sweptback Wing Model