S6-1NAS105, Section 6, May 2005 SECTION 6 DYNAMIC ANALYSIS

S6-2NAS105, Section 6, May 2005

S6-3NAS105, Section 6, May 2005 TABLE OF CONTENTS SectionPage RECOMMENDATIONS FOR DYNAMIC SOLUTIONS……………………………………….6-5 POSSIBLE USES FOR GUYAN REDUCTION (ASET, OMIT)………………………………6-6 MODIFYING DYNAMIC BEHAVIOR……………………………………………………………6-7 APPROXIMATING FREQUENCIES USING STATIC ANALYSIS………………………… SIMULATE STATICS IN MODAL SOLUTIONS……………………………………………….6-11 SELECTING TRANSIENT PARAMETERS…………………………………………………….6-12 USING RESIDUAL VECTOR TO IMPROVE ACCURACY IN MODAL SOLUTIONS…………………………………………………………………………….6-13 SAMPLE 7-STATIC RESIDUAL VECTORS FOR A FLAT PLATE………………………….6-18

S6-4NAS105, Section 6, May 2005

S6-5NAS105, Section 6, May 2005 RECOMMENDATIONS FOR DYANMIC SOLUTIONS n For Modal Analysis u Lanczos method is recommended. u Determine the correct frequency range in advance l Hopefully someone else will set it l Based on the frequency content of the applied loading l Wild Guess?????? n For Response Calculations u Use direct solution for small problems and/or when many modes lie in the frequency range. u Use modal method for most problems for efficiency. u Use a combination (superelements direct with mode synthesis upstream) when detailed results are needed at few selected points. n Dont forget damping !!!!!!!!!!!!!!!!!!!!!

S6-6NAS105, Section 6, May 2005 POSSIBLE USES FOR GUYAN REDUCTION (ASET, OMIT) n Remove local dynamic effects. Example: Remove panel modes n Evaluate dynamic test setups. Example: ASET=Accelerometer and excitation degrees of freedom n Isolate numerical problems. Examples: 1. Stiff joints and couplers in a truss 2. Normal rotations in a shallow shell

S6-7NAS105, Section 6, May 2005 MODIFYING DYNAMIC BEHAVIOR n Understanding the loading u In transient, create a shock spectrum on the input to determine frequency content (see the MSC.NASTRAN Advanced Dynamics Users Guide). u In modal solutions, determine modes are being excited by applied loads. l use alters to print out PHDH = modal forces Let x = { mode shapes modal coordinates Premultiply by F = modal forces = PHDH Compile SEMTRAN alter call.*gma.*phdh Matprn phdh//$

S6-8NAS105, Section 6, May 2005 MODIFYING DYNAMIC BEHAVIOR (Cont.) n Determine which modes are contributing to the response u Frequency Response – l Use modconta.v2004 to determine modal contributions at selected DOF l Use mfreqea.v2004 to determine modal contributions to the total solution u Transient – use mtranea.v2004 to determine modal contributions to the total solution u Either solution – request SDISP in the Case Control – this provides the solution in modal coordinates n Modify modes with high response by shifting frequencies away from Input load peaks. u Print ESE for modes of interest. l Look at this output for modes with high response. l Change element properties in areas with high ESE in those modes. Note: Lowering the frequency might also reduce the response. Look at the spectrum (frequency content) for the applied load.

S6-9NAS105, Section 6, May 2005 MODIFYING DYNAMIC BEHAVIOR (Cont.) Shock Spectrum of Applied Loading If peak response occurs in a mode at 3 Hz, raising the frequency (up to 5 Hz) increases the response; but lowering the frequency reduces the response of that mode.

S6-10NAS105, Section 6, May 2005 APPROXIMATING FREQUENCIES USING STATIC ANALYSIS In statics, solve For normal modes, solve Perform the following steps to approximate the primary frequencies of a model: Perform static analysis with a. Three separate loadings (1-g; x,y,z) b. Param, Grdpnt to locate the center of gravity Obtain the displacement at the ( for each load Calculate approximate frequencies using the following substitutions: for an equivalent SDOF oscillator This provides an estimate of the primary frequencies of the model. Note: Since 1-g checkout runs are recommended, this is a no-cost estimate.

S6-11NAS105, Section 6, May 2005 SIMULATE STATICS IN MODAL SOLUTION n Use modevala.v2004 to determine how well the modes can represent the static solution or: n In frequency response analysis run with F = 0.0 u Use RLOAD=F (static load). u Watch out for G damping. u Do not try this on a free-free structure n In transient analysis run with big delta-time u Use TLOAD=F (static load). u Use PARAM, RESVEC, YES if modal transient (SOL 112) u High frequencies are suppressed. u Only two steps are necessary. u Does not work (without damping) with NOLINi data.

S6-12NAS105, Section 6, May 2005 SELECTING TRANSIENT PARAMETERS n Time step: Use at least 12 steps/period for Important modes n Add damping: No such thing as an undamped system! (add structural damping by using parameters G and W3, and/or GE on MATi, and W4; viscous damping by CDAMPi, CVISC, CBUSH, CBUSH1D, TABDMP1)

S6-13NAS105, Section 6, May 2005 USING RESIDUAL VECTORS TO IMPROVE ACCURACY IN MODAL SOLUTIONS n Whenever a modal approach is used, an approximation is made that the modes are capable of representing the complete dynamic solution to the applied loadings. n This assumption may be dangerous - if the modes are not capable of representing the dynamic response, incorrect answers will result with no warning. n There is no method to verify that sufficient modes have been obtained. The following approaches are commonly used to try to account for this: u Compare to a direct solution (expensive). u Solve again with more modes of appropriate kind and compare. If there is a change, repeat the process until the results do not change (expensive). u Use Mode-Acceleration data recovery to attempt to correct for the high- frequency truncation (may be expensive and is not available for superelements). u Append static residual vectors (RESVEC) to the modes and solve.

S6-14NAS105, Section 6, May 2005 USING RESIDUAL VECTORS TO IMPROVE ACCURACY IN MODAL SOLUTIONS (Cont.) n The idea of residual vectors is that any residuals of the static solutions which the modes cannot represent are appended onto the modes as pseudo-modes and orthogonalized to the modes n These static solution are generated by the program based on any loadings defined using the LOADSET- LSEQ approach and any DOF defined in the U6 set (a separate unit load applied to each of these DOFs). n The resulting set of modal coordinates is capable of exactly representing the static solution to the applied loading and therefore is much more likely to provide correct answers in the modal solution.

S6-15NAS105, Section 6, May 2005 USING RESIDUAL VECTORS TO IMPROVE ACCURACY IN MODAL SOLUTIONS (Cont.) User Interface n Bulk Data PARAM, RESVEC, YES (default = NO) = this parameter enables residual vectors = MANDATORY if you want residual vectors.

S6-16NAS105, Section 6, May 2005 USING RESIDUAL VECTORS TO IMPROVE ACCURACY IN MODAL SOLUTIONS (Cont.) Output Standard output for the solution plus the following: After the eigenvalue (before augmentation by the residual vector) summary table, the program prints a second eigenvalue summary table that includes one or more additional mode (normally high-frequency).

S6-17NAS105, Section 6, May 2005 USING RESIDUAL VECTORS TO IMPROVE ACCURACY IN MODAL SOLUTIONS (Cont.) Limitations This approach does not work on structures with singular matrices. If the singularity occurs in the residual structure, then a SUPORT entry may be used in a manner similar to inertia relief when calculating the residual vectors. This approach does not support automatic restart. (If a loading change is made, the new vectors are not found unless the superelement eigenvalue solution is reprocessed for another reason). You can manually force the re-calculation of residual vectors by doing the following: It is recommended to include modal damping for the high-frequency modes that represent the static residuals. If none is present, high-frequency oscillation about the correct answer may occur. param, serst, manual set 999 = ….. $ superelements to re-process residual vectors for selg = 999 selr = 999 semr = 999

S6-18NAS105, Section 6, May 2005 SAMPLE 7 - STATIC RESIDUAL VECTORS FOR A FLAT PLATE n The problem is a flat rectangular cantilevered plate with a load applied at the center of the free end n The applied loading can be described by the x, y, and z components: u F x = 100. F y = 100 F z = 1. u The x and y components of the loading are in-plane, while the z- component is out-of-plane n The load is a ½ sine pulse at 10hz.

S6-19NAS105, Section 6, May 2005 SAMPLE 7 – STATIC RESIDUAL VECTORS FOR A FLAT PLATE (Cont.)

S6-20NAS105, Section 6, May 2005 SAMPLE 7 – STATIC RESIDUAL VECTORS FOR A FLAT PLATE (Cont.) n First step – see if modes can represent the static solution SOL, 101 include 'pchdispa.v2004' CEND TITLE = sample7a - static solution of plate with point loads SUBTITLE=Static Case Control SPC = 1 DISP(PLOT)=ALL SUBCASE 1 LOAD = 1 SUBCASE 2 LOAD = 2 SUBCASE 3 LOAD = 3 SUBCASE 4 LOAD = 4 BEGIN BULK include 'plate.dat' PARAM POST 0 PARAM AUTOSPC YES FORCE, 1, 105, 0, 1., 100., 100., 1. FORCE, 2, 105, 0, 1., 100.,, 0. FORCE, 3, 105, 0, 1.,, 100., 0. FORCE, 4, 105, 0, 1.,,, 1. ENDDATA Input for static run (sample7a.dat)

S6-21NAS105, Section 6, May 2005 SAMPLE 7 – STATIC RESIDUAL VECTORS FOR A FLAT PLATE (Cont.) n See if modes can represent the static solution to the applied loading n Input for modeval run (sssalter – modevala.vxx) (file: sample7b.dat) SOL, 103 include 'modevala.v2004' CEND TITLE = sample7b - Evaluate ability to represent static solution ECHO = SORT DISP(PLOT)=ALL SUBCASE 1 SPC = 1 METHOD = 1 BEGIN BULK include 'sample7a.pch' include 'plate.dat' PARAM AUTOSPC YES PARAM, EVAL, -2 $ See modevalr.rdm in sssalter dir EIGRL, 1, -1.,, 20 ENDDATA

S6-22NAS105, Section 6, May 2005 OUTPUT FROM MODEVAL RUN – SAMPLE 7B SAMPLE7B - EVALUATE ABILITY TO REPRESENT STATIC SOLUTION R E A L E I G E N V A L U E S MODE EXTRACT EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+04 SAMPLE7B - EVALUATE ABILITY TO REPRESENT STATIC SOLUTION R E A L E I G E N V A L U E S MODE EXTRACT EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+04

S6-23NAS105, Section 6, May 2005 SAMPLE 7 – STATIC RESIDUAL VECTORS FOR A FLAT PLATE (Cont.) ^^^ ^^^ RESULTS FOR LOADING NUMBER 1 ^^^ ^^^ STRAIN ENERGY FRACTIONS FOR EACH MODE ^^^ MODE NO 1 = E-01 ^^^ MODE NO 2 = E-22 ^^^ MODE NO 3 = E-02 ^^^ MODE NO 4 = E-26 ^^^ MODE NO 5 = E-03 ^^^ MODE NO 6 = E-25 ^^^ MODE NO 7 = E-03 ^^^ MODE NO 8 = E-04 ^^^ MODE NO 9 = E-26 ^^^ MODE NO 10 = E-04 ^^^ MODE NO 11 = E-04 ^^^ MODE NO 12 = E-04 ^^^ MODE NO 13 = E-25 ^^^ MODE NO 14 = E-04 ^^^ MODE NO 15 = E-06 ^^^ MODE NO 16 = E-29 ^^^ MODE NO 17 = E-22 ^^^ MODE NO 18 = E-04 ^^^ MODE NO 19 = E-22 ^^^ MODE NO 20 = E-05 ^^^ ^^^ TOTAL STRAIN ENERGY IN INPUT VECTOR = E+00 ^^^ TOTAL STRAIN ENERGY REPRESENTED BY MODES = E+00 ^^^ ^^^ TOTAL FRACTION FOR ALL MODES = E-01

S6-24NAS105, Section 6, May 2005 OUTPUT FROM MODEVAL RUN – SAMPLE 7B (Cont.) ^^^ ^^^ RESULTS FOR LOADING NUMBER 2 ^^^ ^^^ STRAIN ENERGY FRACTIONS FOR EACH MODE ^^^ MODE NO 1 = E-40 ^^^ MODE NO 2 = E-39 ^^^ MODE NO 3 = E-41 ^^^ MODE NO 4 = E-37 ^^^ MODE NO 5 = E-38 ^^^ MODE NO 6 = E-41 ^^^ MODE NO 7 = E-42 ^^^ MODE NO 8 = E-40 ^^^ MODE NO 9 = E-40 ^^^ MODE NO 10 = E-39 ^^^ MODE NO 11 = E-37 ^^^ MODE NO 12 = E-40 ^^^ MODE NO 13 = E-33 ^^^ MODE NO 14 = E-30 ^^^ MODE NO 15 = E-32 ^^^ MODE NO 16 = E-29 ^^^ MODE NO 17 = E-25 ^^^ MODE NO 18 = E-23 ^^^ MODE NO 19 = E-24 ^^^ MODE NO 20 = E-22 ^^^ ^^^ TOTAL STRAIN ENERGY IN INPUT VECTOR = E-03 ^^^ TOTAL STRAIN ENERGY REPRESENTED BY MODES = E-24 ^^^ ^^^ TOTAL FRACTION FOR ALL MODES = E-22

S6-25NAS105, Section 6, May 2005 OUTPUT FROM MODEVAL RUN – SAMPLE 7B (Cont.) ^^^ ^^^ RESULTS FOR LOADING NUMBER 3 ^^^ ^^^ STRAIN ENERGY FRACTIONS FOR EACH MODE ^^^ MODE NO 1 = E-38 ^^^ MODE NO 2 = E-37 ^^^ MODE NO 3 = E-36 ^^^ MODE NO 4 = E-36 ^^^ MODE NO 5 = E-36 ^^^ MODE NO 6 = E-39 ^^^ MODE NO 7 = E-37 ^^^ MODE NO 8 = E-35 ^^^ MODE NO 9 = E-34 ^^^ MODE NO 10 = E-34 ^^^ MODE NO 11 = E-32 ^^^ MODE NO 12 = E-33 ^^^ MODE NO 13 = E-30 ^^^ MODE NO 14 = E-26 ^^^ MODE NO 15 = E-28 ^^^ MODE NO 16 = E-24 ^^^ MODE NO 17 = E-21 ^^^ MODE NO 18 = E-20 ^^^ MODE NO 19 = E-21 ^^^ MODE NO 20 = E-18 ^^^ ^^^ TOTAL STRAIN ENERGY IN INPUT VECTOR = E-01 ^^^ TOTAL STRAIN ENERGY REPRESENTED BY MODES = E-19 ^^^ ^^^ TOTAL FRACTION FOR ALL MODES = E-18

S6-26NAS105, Section 6, May 2005 OUTPUT FROM MODEVAL RUN – SAMPLE 7B (Cont.) ^^^ RESULTS FOR LOADING NUMBER 4 ^^^ ^^^ STRAIN ENERGY FRACTIONS FOR EACH MODE ^^^ MODE NO 1 = E-01 ^^^ MODE NO 2 = E-22 ^^^ MODE NO 3 = E-02 ^^^ MODE NO 4 = E-26 ^^^ MODE NO 5 = E-03 ^^^ MODE NO 6 = E-25 ^^^ MODE NO 7 = E-03 ^^^ MODE NO 8 = E-04 ^^^ MODE NO 9 = E-26 ^^^ MODE NO 10 = E-04 ^^^ MODE NO 11 = E-04 ^^^ MODE NO 12 = E-04 ^^^ MODE NO 13 = E-25 ^^^ MODE NO 14 = E-04 ^^^ MODE NO 15 = E-06 ^^^ MODE NO 16 = E-25 ^^^ MODE NO 17 = E-23 ^^^ MODE NO 18 = E-04 ^^^ MODE NO 19 = E-23 ^^^ MODE NO 20 = E-05 ^^^ ^^^ TOTAL STRAIN ENERGY IN INPUT VECTOR = E+00 ^^^ TOTAL STRAIN ENERGY REPRESENTED BY MODES = E+00 ^^^ ^^^ TOTAL FRACTION FOR ALL MODES = E-01

S6-27NAS105, Section 6, May 2005 SAMPLE 7 – STATIC RESIDUAL VECTORS FOR A FLAT PLATE (Cont.) n As you can see from the previous output, the modes can represent better than 99% of the solution in the z-direction, but less than 1% of the solution in the x- or y-direction. The modes are capable of representing 93% of the static solution to the total applied loading. This indicates that an answer found using these modes may be incorrect for any x- or y-direction response. n Input file (sample7c.dat) for modal transient without residual vectors SOL, 112 CEND TITLE =sample7c -Modal Transient with NO RESVEC DISP(PLOT)=ALL SUBCASE 1 SPC = 1 METHOD = 1 DLOAD = 20 SDAMP = 30 TSTEP = 40 LOADSET = 50 BEGIN BULK include 'plate.dat' PARAM POST 0 PARAM AUTOSPC YES $Define Half Sine Wave TLOAD2, 20, 100,,,0., 0.05, 10., 90. $Use LSEQ, to convert static load to dynamic LSEQ, 50, 100, 1 TABDMP1, 30, CRIT,.1, 0.01, 200., 0.01, ENDT TSTEP,40, 400, 0.001, 2 EIGRL, 1, -1.,, 20 FORCE, 1, 105, 0, 1., 100., 100., 1. FORCE, 2, 105, 0, 1., 100.,, 0. FORCE, 3, 105, 0, 1.,, 100., 0. FORCE, 4, 105, 0, 1.,,, 1. ENDDATA

S6-28NAS105, Section 6, May 2005 SAMPLE 7 – STATIC RESIDUAL VECTORS FOR A FLAT PLATE (Cont.) Results of Modal Transient Analysis with 20 modes (NO RESVEC)

S6-29NAS105, Section 6, May 2005 SAMPLE 7 – STATIC RESIDUAL VECTORS FOR A FLAT PLATE (Cont.) Input file (sample7d.dat) to include static residual vectors SOL, 112 CEND TITLE = sample7d -Modal Transient with RESVEC ECHO = SORT DISP(PLOT)=ALL SUBCASE 1 SPC = 1 METHOD = 1 DLOAD = 20 SDAMP = 30 TSTEP = 40 LOADSET = 50 BEGIN BULK include 'plate.dat' PARAM POST 0 PARAM AUTOSPC YES PARAM RESVEC YES $Define Half Sine Wave TLOAD2, 20, 100,,,0., 0.05, 10., 90. $Use LSEQ, to convert static load to dynamic LSEQ, 50, 95, 2 LSEQ, 50, 96, 3 LSEQ, 50, 97, 4 LSEQ, 50, 100, 1 TABDMP1, 30, CRIT,.1, 0.01, 200., 0.01, ENDT TSTEP,40, 400, 0.001, 2 EIGRL, 1, -1.,, 20 FORCE, 1, 105, 0, 1., 100., 100., 1. FORCE, 2, 105, 0, 1., 100.,, 0. FORCE, 3, 105, 0, 1.,, 100., 0. FORCE, 4, 105, 0, 1.,,, 1. ENDDATA

S6-30NAS105, Section 6, May 2005 SAMPLE 7 – STATIC RESIDUAL VECTORS FOR A FLAT PLATE (Cont.) n In this case, the static deformed shape due to the dynamic loading is appended into the modes as pseudo-modes. n In the output on the following pages you will see: u The original eigenvalue summary table. u A final eigenvalue summary table including 1 new eigenvector which represents the static residual vector.

S6-31NAS105, Section 6, May 2005 OUTPUT FROM RUN WITH RESIDUAL VECTOR (BEFORE AUGMENTATION OF RESIDUAL VECTORS) MODE EXTRACT EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+04

S6-32NAS105, Section 6, May 2005 OUTPUT FROM RESIDUAL VECTOR DMAP ALTER (Cont.) (AFTER AUGMENTATION OF RESIDUAL VECTORS) MODE EXTRACT EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+05

S6-33NAS105, Section 6, May 2005 SAMPLE 7 – STATIC RESIDUAL VECTORS FOR A FLAT PLATE (Cont.) Results with 20 modes plus residual vector

S6-34NAS105, Section 6, May 2005 SAMPLE 7 – STATIC RESIDUAL VECTORS FOR A FLAT PLATE (Cont.) Results of Direct Transient Analysis

S6-35NAS105, Section 6, May 2005 SAMPLE 7 – STATIC RESIDUAL VECTORS FOR A FLAT PLATE (Cont.) Comparison of Methods: sample7c (No RESVEC), sample7d (RESVEC), and Sampl7e ( Direct Transient)

S6-36NAS105, Section 6, May 2005