Wuhan University of Technology3.2 System with viscous dampingThe SteadyState Harmonic Response isPop(0)=(1-β2)sinot-2=βcosotkβ2)+(2EB)二TheSteadyStateResponseis inotherformy,(t)=psin(at-0)4-16
4-16 Wuhan University of Technology vt t p ( ) sin 3.2 System with viscous damping 0 2 2 2 2 1 ( ) 1 sin 2 cos 1 2 p P vt t t k The SteadyState Harmonic Response is The SteadyState Response is in other form
Wuhan University of Technology3.2 System with viscous dampingImReO+2P(1-β3)P-exp(iot))[-iexp(iot)]-B3)2+(25β）1-(1-β3)2+(25β）0piexp[i(ot-e)]Steady-statedisplacementresponse.4-17
4-17 Wuhan University of Technology 3.2 System with viscous damping Steady-state displacement response
Wuhan Universityof Technology3.2 System with viscous dampingThe amplitude isp=[(1- β-) +(25P) ]20=tan1-β2Theratiooftheresultantharmonicresponseamplitudetothestaticdisplacement which would be produced by the force Pwill be calledthedynamicmagnificationfactorD;thus[(1-β) +(25B)4-18
4-18 Wuhan University of Technology 3.2 System with viscous damping 1/2 2 2 2 1 2 P k 。 The amplitude is The ratio of the resultant harmonic response amplitude to the static displacement which would be produced by the force p o will be called the dynamic magnification factor D; thus 1 2 2 tan 1 1/2 2 2 2 0 1 2 / D p k
Wuhan University of Technology3.2 System with viscous damping4E=03E = 0.22D=0.55= 0.7=1.002301BVariation of dynamic magnification factorwith damping and natural frequency4-19
4-19 Wuhan University of Technology 3.2 System with viscous damping Variation of dynamic magnification factor with damping and natural frequency
Wuhan University of Technology3.2 System with viscous damping180°5=05=0.055=0.20E= 0.5e5= 1.090023(Frequency ratio, βVariation of phase angle with damping andnatural frequency.4-20
4-20 Wuhan University of Technology 3.2 System with viscous damping Variation of phase angle with damping and natural frequency