Response to arbitrary force 12 闺 土本程李悦
Response to arbitrary force
Response of SDOF to special excitation Step force Ramp or linearly increasing force Step force with finite rise time ·Impulsive Force Response of SDOF to pulse excitation Rectangular pulse ·Half cycle sine pulse Triangular pulse force 目 主京2相季院
Response of SDOF to special excitation • Step force • Ramp or linearly increasing force • Step force with finite rise time • Impulsive Force Response of SDOF to pulse excitation • Rectangular pulse • Half cycle sine pulse • Triangular pulse force
Step force A step force jumps suddenly from zero to its amplitude po and stays constant at that value. p(t)=Po 5=0 g=0.05 p() =0.2 0 0 t/Tn (a) (b) A suddenly applied force produces twice the deformation it would have caused as a static force P(i)=Po 闺 土本程李悦
Step force • A step force jumps suddenly from zero to its amplitude p0 and stays constant at that value. • A suddenly applied force produces twice the deformation it would have caused as a static force 0 p t p 0 p t p
Response of SDOF to step force ·Non-damping case u(0=朵（1-cos04） Under-damped case a-aw产m个 A suddenly applied force produces twice the deformation it would have caused as a static force max(u(o)=22=2(u,)。 k 目 土本2程学院
Response of SDOF to step force • Non-damping case • Under-damped case A suddenly applied force produces twice the deformation it would have caused as a static force 0 1 cos n p u t t k 0 2 1 cos sin 1 n t D D P u t e t t k 0 max 2 2 st 0 p u t u k