S12-1 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation SECTION 12 RESIDUAL VECTOR METHOD

S12-2 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation

S12-3 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation RESIDUAL VECTOR METHOD n For many problems the solutions involve only the lower normal modes, not those above a threshold value of frequency. n The modes above the threshold only respond statically. n For these cases, only a relatively small subset of the set of all normal modes need to be computed. The normal modes above the threshold do not need to be computed. n The specification of the subset of normal modes is termed modal truncation.

S12-4 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation n Transform from modal to physical coordinates. n Partition the equation for {u(t)} into the kept (k) and truncated (t) modes. where the number of modes of [ k ] may be much less than the number of modes of [ ] (the total number of modes). n Static response of the truncated modes. RESIDUAL VECTOR METHOD (Cont.)

S12-5 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation Assume that the excitation (with frequency, e ) is quasi-static compared with the time scale of the truncated modes (with frequency, t ). n An approximate solution to the previous equation is static. RESIDUAL VECTOR METHOD (Cont.)

S12-6 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation The quality of a modal solution depends on how well the linear combination [ k ]{ k } represents the response due to the applied loads. n Using the residual vector approach improves the quality of modal solutions. n This is recommended to be used for all response analyses using the modal approach. n Superelements are supported n Residual vectors associated to inertia relief, applied loads, adjoint load vectors, viscous damping, etc. RESIDUAL VECTOR METHOD (Cont.)

S12-7 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation n Selecting Residual Vector Computation causes PARAM,RESVEC,YES to be written to the.bdf file in the Bulk Data section. n It is preferable to enter a RESVEC command in the.bdf file in the Case Control section RESIDUAL VECTOR METHOD (Cont.)

S12-8 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation RESIDUAL VECTOR METHOD (Cont.) n RESVEC, Case Control section

S12-9 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation RESIDUAL VECTOR METHOD (Cont.) n RESVEC, Case Control section (continued)

S12-10 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation RESIDUAL VECTOR METHOD (Cont.) n RESVEC, Case Control section (continued)

S12-11 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation RESIDUAL VECTOR METHOD (Cont.) n RESVEC processing in MSC.Nastran u Ensures loads are linearly independent of modal inertial forces. u Determines base vectors from static response. u Ensures base vectors are linearly independent. l Independent of modal vectors. l Independent of other base vectors. u Orthogonalize base vectors with respect to the modal vectors to create residual vectors.

S12-12 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESIDUAL VECTOR Apply a one cycle sine load at a corner of the free edge, opposite the constrained edge, of a 5 x 2 plate. The thickness of the plate is 0.1. The load is 1.0 lbf, 250 Hz, and in the Y-direction. The material properties are E = 10x10 6 psi, = 0.3, and = 0.282*

S12-13 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESIDUAL VECTOR (Cont.) n Applied load

S12-14 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESIDUAL VECTOR (Cont.) n Transient analyses to be performed u Modal analysis using RESVEC l Under the Case Control section set RESVEC to YES (BOTH is the default for most modal solution sequences, e.g. SOL 112, modal transient response) l Use just the first four modes l Use modal damping of 3% of critical u Modal analysis not using RESVEC l Under the Case Control section set RESVEC to NO l Use just the first four modes l Use modal damping of 3% of critical u Direct analysis l The effect is to include all modes Damping of g (G) = 0.06, and 3 (W3) = rad/sec (250.0 Hz)

S12-15 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESIDUAL VECTOR (Cont.) n Specify time step and modal damping data for modal analysis

S12-16 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESIDUAL VECTOR (Cont.) n.bdf file for transient modal analysis w/ RESVEC = YES u File name is tran_modal_resvec_yes.bdf

S12-17 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESIDUAL VECTOR (Cont.) n.bdf file for transient modal analysis w/ RESVEC = YES (continued)

S12-18 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESIDUAL VECTOR (Cont.) n.bdf file for transient modal analysis w/ RESVEC = YES (continued)

S12-19 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESIDUAL VECTOR (Cont.) n.bdf file for plate elements and nodes u File name is plate.bdf

S12-20 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESIDUAL VECTOR (Cont.) n.bdf file for plate elements and nodes (continued)

S12-21 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESIDUAL VECTOR (Cont.) n Transient modal analysis w/ first four modes and RESVEC = YES.

S12-22 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESIDUAL VECTOR (Cont.) n.bdf file for transient modal analysis w/ RESVEC = NO u File name is tran_modal_resvec_no.bdf

S12-23 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation n Transient modal analysis w/ first four modes and RESVEC = NO. CASE STUDY: RESIDUAL VECTOR (Cont.)

S12-24 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESIDUAL VECTOR (Cont.) n.bdf file for transient direct analysis u File name is transient_direct.bdf

S12-25 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation n Transient direct analysis, in effect using all modes, and no residual vectors used. CASE STUDY: RESIDUAL VECTOR (Cont.)

S12-26 NAS122, Section 12, August 2005 Copyright 2005 MSC.Software Corporation n Results comparison u The first four modes involve out-of-plane deformation u A linear combination of these four modes cannot represent in-plane deformation due to in-plane loading u The transient modal method using just the first four modes, without using residual vectors, produces unacceptable results u The transient modal method using just the first four modes, and using residual vectors, produces acceptable results. This is seen by comparing the results with those from the transient direct method. u The difference between the transient modal, with the residual vectors, and the transient direct methods is due to the damping that was used for the two methods. Modal and viscous equivalent of structural damping was used for the modal and direct methods, respectively. CASE STUDY: RESIDUAL VECTOR (Cont.)