S9-1 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation SECTION 9 DAMPING OVERVIEW

S9-2 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation

S9-3 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN DYNAMIC ANALYSIS n n Section 1 included an overview of the basic damping theory for SDOF models n n Sections 10 and 11 include details of implementation of material damping in Transient and Frequency Response Analysis n n This section provides a review of the damping elements available in MSC.Nastran and discusses what physically produces damping

S9-4 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN DYNAMIC ANALYSIS (Cont.) n n Damping is present in all oscillatory systems n n Damping removes energy from a system n n Possible energy dissipation (loss of energy to another system) via u u Mechanical motion u u Heat u u Sound waves u u Fluid motion n n Resulting effect u u Free Vibration gives decay in amplitude u u Steady State gives energy loss = energy input n n Mechanisms include: u u Internal Molecular friction : raw material u u Sliding Friction : joints, plies u u Fluid Resistance : dampers, air or water environment

S9-5 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN DYNAMIC ANALYSIS (Cont.) n n What levels of damping should be used ? n n There is no one good answer to this question ! n n For a particular structural configuration and material look at u u Test results u u Industry standards u u Company experience n n Remember, in General, lowest levels of damping are most conservative u u Use a range of damping values in presenting results u u Peak response is difficult to capture n n Typical values (NOT TO BE QUOTED !) u u NC machined components : 2% to 5% of critical u u Fabricated metal components : 4% to 10% of critical u u Composites : 6% to 20% of critical

S9-6 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN DYNAMIC ANALYSIS (Cont.) n n Damping types in MSC.Nastran u u Viscous – damping force is proportional to velocity (e.g. frequency dependent) l l Typical Dashpot behavior u u Structural – damping force is proportional to displacement l l Typical Steel or Aluminum behavior u u Modal – mathematical representation l l Used to match test data u u Rayleigh damping – damping force is proportional to Stiffness and/or Mass l l Used to match test data n n A real structure could have any combination of these types

S9-7 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT n Scalar viscous damping CDAMPi -- scalar damper (i = 1,2,3,4,5) between two DOFs, with reference to a property entry (PDAMP) or enter value of B on CDAMPi entry CVISC -- element damper between two grid points; references a property entry (PVISC) CBUSHi -- generalized spring and damper element that may be defined as nonlinear or frequency dependent. Damping values are assigned via physical property input on a PBUSHi entry. l PBUSH n Viscous damping n Structural damping n PBUSH1D n Viscous damping n Linear or nonlinear properties

S9-8 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.) n Scalar damping CDAMP1 Element n There are two forms Grounded Damper– only one grid is connected Scalar Damper – both grids are connected CDAMP1 (Grounded) Element CDAMP1 Element

S9-9 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.)

S9-10 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.)

S9-11 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.) n Viscous damping CVISC Element CVISC Element

S9-12 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.)

S9-13 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.)

S9-14 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.) n CBUSH Element

S9-15 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.)

S9-16 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.)

S9-17 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.)

S9-18 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.)

S9-19 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.)

S9-20 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.)

S9-21 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.)

S9-22 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.)

S9-23 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation VISCOUS DAMPING INPUT (Cont.)

S9-24 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation FREQUENCY DEPENDENT IMPEDANCE SAMPLE 1.0*K(f), PARAM,WTMASS, $ = 1.0/(2 ) 2,1.0*B(f) X f (f 2 ) (f/ ) (f 2 )

S9-25 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation SAMPLE USING CBUSH ELEMENT $ $cbush1. dat $ TIME 10 SOL 108 CEND TITLE = VERIFICATION PROBLEM, FREQ. DEP. IMPEDANCE BUSHVER SUBTITLE = SINGLE DOF, CRITICAL DAMPING, 3 EXCITATION FREQUENCIES ECHO = BOTH SPC = 1002 DLOAD = 1 DISP = ALL FREQ = 10 ELFO = ALL BEGIN BULK $ CONVENTIONAL INPUT FOR MOUNT GRDSET,,,,,,,23456 $ PS $ TIE DOWN EVERYTHING BUT THE 1 DOF GRID,11,,0.,0.,0.0 $ GROUND =,12,=,=,=,,$ ISOLATED DOF SPC1, $ GROUND CONM2,12,12,,1.0$ THE ISOLATED MASS $ $EIDPIDGAGBGO/X1X2X3CID $ CBUSH $ PBUSH2000K1.0 B1.0 $ PBUSHT2000K2001 B2002 $ TABLED1, 2001 $ STIFFNESS TABLE, ,1.0,1.0,1.1,1.21ENDT TABLED $ DAMPING TABLE, , 1.0, , 1.1, ENDT $CONVENTIONAL INPUT FOR FREQUENCY RESPONSE PARAM,WTMASS, $ 1/(2*PI)**2. GIVES FN=1.0 DAREA,1,12,1,2. $CAUSES UNIT DEFLECTION FREQ,10,0.9,1.0,1.1 $ BRACKET THE NATURAL FREQUENCY RLOAD1,1,1,,,3 TABLED1,3 $ TABLE FOR FORCE VS. FREQUENCY,0.9,0.81,1.,1.,1.1,1.21,ENDT $ P = K ENDDATA

S9-26 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation DISPLACEMENT OUTPUT FOR CBUSH FREQUENCY = E-01 C O M P L E X D I S P L A C E M E N T (REAL/IMAGINARY) POINT ID. TYPE T1 T2 T3 R1 R2 R3 011G G E E VERIFICATION PROBLEM, FREQ. DEP. IMPEDANCEBUSHVERMARCH 20,1997 MSC.Nastran 1/23/97 PAGE 8 SINGLE DOF, CRITICAL DAMPING, 3 EXCITATION FREQUENCIES 0 FREQUENCY = E+00 C O M P L E X D I S P L A C E M E N T (REAL/IMAGINARY) POINT ID. TYPE T1 T2 T3 R1 R2 R3 011G G E E VERIFICATION PROBLEM, FREQ. DEP. IMPEDANCEBUSHVERMARCH 20,1997 MSC.Nastran 1/23/97 PAGE 9 SINGLE DOF, CRITICAL DAMPING, 3 EXCITATION FREQUENCIES 0 FREQUENCY = E+00 C O M P L E X D I S P L A C E M E N T (REAL/IMAGINARY) POINT ID. TYPE T1 T2 T3 R1 R2 R3 011G G E E VERIFICATION PROBLEM, FREQ. DEP. IMPEDANCEBUSHVERMARCH 20,1997 MSC.Nastran 1/23/97 PAGE 10 SINGLE DOF, CRITICAL DAMPING, 3 EXCITATION FREQUENCIES

S9-27 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation FORCE OUTPUT FOR CBUSH ELEMENT FREQUENCY = E-01 C O M P L E X F O R C E S I N B U S H E L E M E N T S ( C B U S H ) (REAL/IMAGINARY) ELEMENT-ID. FORCE-X FORCE-Y FORCE-Z MOMENT-X MOMENT-Y MOMENT-Z E E VERIFICATION PROBLEM, FREQ. DEP. IMPEDANCEBUSHVERMARCH 20,1997 MSC.Nastran 1/23/97 PAGE 11 SINGLE DOF, CRITICAL DAMPING, 3 EXCITATION FREQUENCIES 0 FREQUENCY = E+00 C O M P L E X F O R C E S I N B U S H E L E M E N T S ( C B U S H ) (REAL/IMAGINARY) ELEMENT-ID. FORCE-X FORCE-Y FORCE-Z MOMENT-X MOMENT-Y MOMENT-Z E E VERIFICATION PROBLEM, FREQ. DEP. IMPEDANCEBUSHVERMARCH 20,1997 MSC.Nastran 1/23/97 PAGE 12 SINGLE DOF, CRITICAL DAMPING, 3 EXCITATION FREQUENCIES 0 FREQUENCY = E+00 C O M P L E X F O R C E S I N B U S H E L E M E N T S ( C B U S H ) (REAL/IMAGINARY) ELEMENT-ID. FORCE-X FORCE-Y FORCE-Z MOMENT-X MOMENT-Y MOMENT-Z E E VERIFICATION PROBLEM, FREQ. DEP. IMPEDANCEBUSHVERMARCH 20,1997 MSC.Nastran 1/23/97 PAGE 13 SINGLE DOF, CRITICAL DAMPING, 3 EXCITATION FREQUENCIES 0

S9-28 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation STRUCTURAL DAMPING INPUT n n Uniform and element/material based structural damping Depends on the type of excitation, e.g. transient or frequency l l Example, direct transient l l where l l is defined by previously described viscous elements, e.g. CVISC l l occurs because of the equivalence between structural and viscous damping n n This is discussed in detail in subsequent sections (chapters)

S9-29 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation STRUCTURAL DAMPING INPUT (Cont.) MSC.Patran forms for specifying G (g), W3 ( 3 ), and W4 ( 4 )

S9-30 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation STRUCTURAL DAMPING INPUT (Cont.) n n Material from MSC.Nastran QRG for the PARAMs G, W3, and W4.

S9-31 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation STRUCTURAL DAMPING INPUT (Cont.) n n MSC.Patran forms for specifying GE (g e ), the structural element damping coefficient.

S9-32 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation STRUCTURAL DAMPING INPUT (Cont.) n n Material from MSC.Nastran QRG for specifying GE.

S9-33 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation MODAL DAMPING INPUT n n Modal damping is used to represent any source of system damping Depends on the type of excitation, e.g. transient or frequency l l Example, modal transient analysis with just modal damping; there are no viscous elements, e.g. CVISC, and no structural damping. n n where n n is defined using the MSC.Nastran TABDMP1 Bulk Data entry n n This is discussed in detail in subsequent sections (chapters)

S9-34 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation MODAL DAMPING INPUT (Cont.) MSC.Patran forms for specifying G (g), W3 ( 3 ), and W4 ( 4 ) u u Possible to specify the value for these parameters for modal transient

S9-35 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation MODAL DAMPING INPUT (Cont.) n n MSC.Patran forms for specifying modal damping using structural (G), fraction of critical (CRIT), or dynamic amplification (Q) damping measures.

S9-36 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation MODAL DAMPING INPUT (Cont.) n n Material from MSC.Nastran QRG for TABDMP1 Bulk Data entry for specifying modal damping.

S9-37 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation MODAL DAMPING INPUT (Cont.) n n Modal damping is used to represent any source of system damping (continued) Depends on the type of excitation, e.g. transient or frequency (continued) l l Example, modal transient analysis with just structural damping; a table for modal damping, TABDMP1, is not specified. n n This is discussed in detail in subsequent sections (chapters)

S9-38 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation RAYLEIGH DAMPING INPUT n Rayleigh damping is proportional to either the mass or stiffness matrix It is also known as proportional damping n Available in transient and frequency response analysis n The scale factors are applied to the d-set (direct) or h-set (modal) matrices n If damping is proportional to the mass matrix use PARAM,ALPHA1,x n If damping is proportional to stiffness matrix use PARAM,ALPHA2,y n If damping is proportional to both mass and stiffness matrix, and want to include both of them, use both PARAMs n It is added to the viscous damping matrix, [B 1 ], as follows n Not Supported in MSC.Patran; requires Direct Text Input

S9-39 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation n ALPHA1 and ALPHA2 are real valued parameters, however the programming treats them as complex valued variables, e.g. PARAM, ALPHA2, 1.25E-4, 0.0 n Relationship of modal damping to Rayleigh damping Modal damping Rayleigh damping Solution of the equations is equal for the following damping relationship RAYLEIGH DAMPING INPUT (Cont.)

S9-40 NAS122, Section 9, August 2005 Copyright 2005 MSC.Software Corporation RAYLEIGH DAMPING INPUT (Cont.) The relationship between modal and rayleigh damping is obtained i i ( 1, 2 )