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Discontinuous and impulsive excitation

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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, then we derive the equation of x 1 (t) and x 2 (t) by terms of property of distribution, and by solving x 1 (t) and x 2 (t) we obtain x(t); finally, we make a thorough investigation about periodic impulsive parametric excitation.

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References

  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.

    Google Scholar 

  2. Hsu, C.S., On nonlinear parametric excitation problem,J. Appl. Mech.,39, (1972), 551–559.

    Google Scholar 

  3. Hsu, C.S., Impulsive parametric excitation, theory,Adv. Appl. Mech.,17 (1977), 245–301.

    Google Scholar 

  4. Hsu, C.S., Nonlinear behaviour of multibody systems under impulsive parametric excitation.Dynamics of Multibody System, Magnus K. Springer, Berlin (1977), 63–74.

    Google Scholar 

  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.

    Google Scholar 

  6. You, Bingli,Complement Lectures of Ordinary Differential Equation, People's Education Press (1981). (in Chinese)

  7. Gerfangde, et al,Distribution, Scientific Press (1965). (Chinese Translation)

  8. Nayfeh, A.H.,Perturbation Methods, Wiley-Insterscience (1973).

  9. Ting, L.,Perturbation Methods and Its Application in Mechanics, Beijing (1981).

  10. Liu, Zheng-rong and Wei Xi-rong, Perturbation solution of weakly nonlinear differential equation with Dirac function,Appl. Math.and Mech., 5, (1984).

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Communicated by Li Li

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Zheng-rong, L. Discontinuous and impulsive excitation. Appl Math Mech 8, 31–35 (1987). https://doi.org/10.1007/BF02014496

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  • DOI: https://doi.org/10.1007/BF02014496

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