Discontinuous and Impulsive Excitation

Abstract

In this paper,we study the solution of differential equation with Dirac function and Heaviside function,arising from discontinuous and impulsive excitation.Firstly,according to the theory of differential equation,we suggest x(t)=x₁(t)+x₂(t)H(t-a);then we derive the equation of x₁(t) and x₂(t) by terms of property of distribution,and by solving x₁(t) and x₂(t) we obtain x(t);finally,we make a thorough investigation about periodic impulsive parametric excitation.

[1]	Pan,H.H.and R.M.Hohenstein,A method of solution for an ordinary differential equation containing symbolic functions,Quart.Appl.Math.,39,(1981),131-137.
[2]	Hsu,C.S.,On nonlinear parametric excitation problem,J Appl.Mech.,39,(1972),551-559.
[3]	Hsu,C.S.,Impulsive parametric excitation,theory,Adv.Appl.Mech.,17(1977),245-301.
[4]	Hsu,C.S.,Nonlinear behaviour of multibody systems under impulsive parametric excitation,Dynamics of Multibody System,Magnus K.Springer,Berlin(1977),63-74.
[5]	Hsu,C.S.,W.H.Cheng and H.C.Yee,Steady-state response of a non-linear system under impulsive periodic parametric excitation,J.Sound.Vib.,50(1977),95-116.
[6]	尤秉礼,《常微分方程补充教程》,人民教育出版社(1981).
[7]	盖尔芳特等,《广义函数》,科学出版社(1965).
[8]	Nayfeh,A.H.,Perturbarion Methods,Wiley-Insterscience(1973).
[9]	Ting,L.,Perturbation Methods and Its Application in Mechanics,Bejing(1981).
[10]	刘曾荣、魏锡荣,含有δ函数的弱非线性微分方程的摄动解,应用数学和力学,5,5(1984)691-698.