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ANSYS . .1 ALPHADBETAfDMPRATjjMP,DAMPCwhere: C = structure damping matrix = mass matrix multiplier (input on ALPHAD command)M = structure mass matrix = stiffness matrix multiplier (input on BETAD command)c = variable stiffness matrix multiplier (see Equation 15C23)K = structure stiffness matrixNm = number of materials with DAMP or DMPR input? ?= stiffness matrix multiplier for material j (input as DAMP on MP command)? ?= constant (frequency-independent) stiffness matrix coefficient for material j (input as? ?DMPR on MP command) = circular excitation frequencyKj = portion of structure stiffness matrix based on material jNe = number of elements with specified dampingCk = element damping matrixC = frequency-dependent damping matrix (see Equation 15C21)2 idmiijjEjsjANSYSfTKfMP,DAMPMXPANDQRCQRMOPT,QRDAMPANSYS MP,DAMP/fc/kjMSE url=3.8.3/urlANSYSAplhaBetaRayleighANSYS/ProfessionalC , ALPHAD,BETADMP,DAMPDMPRATMDAMP 3(COMBIN7)N/AN/AN/AN/AN/ANo5No5No5NoNoYesYesNoNoYesYesYesYesNoYesYesYesYesNoYesYes6Yes46Yes7Yes7Yes6YesYesNoNoYesYesYesNoNoYesYes6Yes46Yes7Yes7Yes6SPRS,MPRS2Yes1YesYesYesNoDDAM2Yes1YesYesYesNoPSD2YesNoYesYesNoN/AN/AN/AN/AN/AYesYesNoNoYesN/A123456QRMODOPT,QRDAMPANSYS7QRMODOPT,QRDAMPDMPARTMDAMP1. Alpha Beta AlphaBetaRayleighMK ALPHAD BETAD Rayleigh i iAlpha=0 5ij2011-12-15 23:32:07 (9.68 KB)5AlphaAlphaBetaBetaANSYS2. BetaMP,DAMPANTYPE,SPECTRMP,DAMPSOLID46,SOLID65,SHELL91SHELL99MATMAT3. DMPRATDMPRAT4. MDAMP5. COMBIN7,COMBIN14,COMBIN37,COMBIN40ANSYSANSYSANSYS1RayleighANSYS ALPHDBETAD 5.1.15.1.1 ALPHDBETADfull 2ANSYSALPHAD BETAD DMPRAT MDAMP MPDAMP ?ANSYSC5.1.2ANSYSmn Rayleigh 35.1.3cCCCANSYSDMPRATMDAMPANSYSMDAMPDMPRATDMPRATMDAMPC C5.1.4 i 3ANSYSFullfull0.0050.05 5.1 ALPHDBETAD 1ALPHDBETAD4MP,DAMP5.2 k m c 5.1.5 ANSYS5.1.6ANSYSCfullANSYSFullfullMPDAMP c5.1 0.000020.002 0.0010.008 0.0080.014 0.0030.03 0.10.3 1.0 0.00060.002 0.010.06, C.F.5ANSYSANSYSi5.1.7ANSYS M j?FullANSYSfullANSYSANSYS1MP,dampDAMPRATO=0.025 ! LOSSMODM=2*DAMPRATO ! 2(!)CRITFREQ=2.6 ! MP_BETAD=DAMPRATO/(acos(-1)*CRITFREQ) ! /prep7mp,damp,1,MP_BETAD !iscous damping/soluantype,modalmodopt,lanb,1! ! mxpand,yes,! ansysCmxpand,1,yes,sole,2MP,DampDAMPRATO=0.025LOSSMODM=2*DAMPRATO ! LOSSMODM/prep7mp,damp,1,DAMPRATO !LOSSMODM2/soluantype,modal ! modopt,lanb,1! importantmxpand,1,yes,sole3BETAD! MSUP method with BETAD! BETAD is damping_ratio/pi*f, een for MSUPDAMPRATO=0.025 ! LOSSMODM=2*DAMPRATO !/prep7! mp,damp,1,DAMPRATOBETAD,DAMPRATO/(acos(-1)*442) ! 442/soluantype,modal !modopt,lanb,1! importantmxpand,1,yeslumpm,on,sole/soluantype,harmic !hropt, msuphrout, on, offharfrq, FREQBEGN, FREQENDG,sole4DMPRAT! MSUP method with DMPRAT! shows that DMPRAT is damping ratioDAMPRATO=0.025 0.025LOSSMODM=2*DAMPRATO/prep7!mp,damp,1,DAMPRATO/soluantype,modal ! sole/soluantype,harmichropt,msuphrout,on,offharfrq,FREQBEGN,FREQENDGnsubst,NUM_STEPkbc,1dmprat,DAMPRATO ! ,sole5MPDAMPFULL! ! Full method with MP,DAMP! shows that MP,DAMP with FULL is damping_ratio/pi*f! As freq increases, damping is hugeDAMPRATO=0.025LOSSMODM=2*DAMPRATOCRITFREQ=480MP_BETAD=DAMPRATO/(acos(-1)*CRITFREQ) ! /prep7mp,damp,1,MP_BETAD6DMPRAT! Full method with DMPRATDAMPRATO=0.025LOSSMODM=2*DAMPRATOCRITFREQ=480MP_BETAD=DAMPRATO/(acos(-1)*CRITFREQ)/prep7et,1,1! mp,damp,1,MP_BETAD ! dmprat,DAMPRATO /soluantype,modal !modopt,lanb,3! importantmxpand,3,yeslumpm,on,sole/soluantype,harmichropt,full ! full harmonic analysis6AnsysBeam4, Combin7, Link11, Combin14, Pipe16, C

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