上海交通大学：《复杂系统动力学计算机辅助分析》课程教学资源_Chapter 6_Char6.2 Virtual work and generalized force

6.2 Virtual work and generalized force =+A δr°=δr+δ0，Bs 1 The virtual work of force y F δw=(6ryF =6rF+δ4yPrB,F -w4者→e

6.2 Virtual work and generalized force y x i x  i y  ir P ir P i s P Fi  P i i i P ir  r  A s P i i i i P i  r   r  B s The virtual work of force                 P i T i TP i P i i T i P i T i TP i i P i T i P i T P W i s B F F r r F s B F r F               P i T i TP i P i s B F F Q

Translational Spring-damper-actuator d,=+A”-5-AsP The virtual work of spring force y W=-f61 P=d,dy l8l=d'&M,(≠0) X 64-6-B606-879） T δl1 f=k(I-lo)+cl+F k一Spring coefficient C F=F(L,l,t) Damping coefficient F Actuator force 1-4,(6+B,6,-元-B,s®）

Translational Spring-damper-actuator P i i i P ij j j j d  r  A s  r  A s x i x  i y  ir P i s j y  j x  P j s y j r c F k ij d  o The virtual work of spring force ij T ij l  d d 2 W   f l f  k(l  l0 )  cl F l l  (l  0) ij T  dij d  i P j i i i P j j j T ij ij T ij l l  l   r B s   r B s  d d d        k Spring coefficient c Damping coefficient F Actuator force F F(l,l,t)    i P j i i i P j j j T ij l l        r B s r B s d      

The virtual work of spring force -微mm8]g-因- a-4a北1ye的-r,'aowh δl1 d f=k(1-1)+cl+F Generalized force e-r4 y 下 e- X

x i x  i y  ir P i s j y  j x  P j s y j r c F k ij d  o            j T i j T i W f l Q Q    q  q The virtual work of spring force  i ij T i TP i T j i T j TP j T ij j T ij ij T ij l l l l d r s B r s B d d d d                1        i i i  r q        j j j  r q       ij T i TP i ij i l f s B d d Q Generalized force        ij T j TP j ij j l f s B d d Q f  k(l  l0 )  cl F

Rotational Spring-damper-actuator 0,=中-中 k The virtual work of spring torque δW=-nδ0， δ0，=8，-8 n=kg(0-0)+c0n+N X 0 N=N(020,t) Torsional spring coefficient Ce Torsional damping coefficient N Actuator torque

Rotational Spring-damper-actuator ij   j i The virtual work of spring torque W  nij n  k (ij  0 )  c  ij  N ij   j i  k Torsional spring coefficient  c Torsional damping coefficient N Actuator torque N N( , ,t) ij ij   x i x  i y  j y  j x  y c F k  ij o j x  i x 

The virtual work of spring torque δW=-no0,=-no冲，+no冲， n=kg(0,-8)+c0,+N k x Generalized force x 0 2 0 n X 0

The virtual work of spring torque W  nij  n j  ni n  k (ij  0 )  c  ij  N x i x  i y  j y  j x  y c F k  ij o j x  i x         n i 0 0 Q Generalized force        n j 0 0 Q