间断和脉冲激励

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Discontinuous and Impulsive Excitation

摘要: 本文讨论由于脉冲和间断激励所引起的含有Dirac函数和Heavisde函数微分方程的求解问题。首先,按照微分方程理论,我们建议把方程解表达为x(t)=x₁(t)+x₂(t)H(t-a);然后,利用广义函数性质,导出x₁(t)和x₂(t)方程,通过求解x₁(t)和x₂(t)来得到原来方程解x(t)。最后,对周期脉冲参数激励问题进行了深入讨论。

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.

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