Analytical evaluation of dynamic responses of time-varying systems

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Original languageEnglish
Pages (from-to)1123-1142
Journal / PublicationJVC/Journal of Vibration and Control
Issue number8
Publication statusPublished - Aug 2009


An analytical approach for forced vibration of single-degree-of-freedom (SDOF) systems with arbitrary time-dependent parameters is presented. Unlike most of the previous studies on this topic, the function for describing the variation of mass of a SDOF system with time is an arbitrary continuous or piecewise real-valued function, and the variation of stiffness with time is expressed as a functional relation with the variation of mass and vice versa. Using appropriate functional transformation, the closed-form homogeneous solutions of the governing differential equations for forced vibrations of such a SDOF system with continuous time variable parameters (mass and stiffness) are derived for 10 important cases. The particular solutions of the non-homogeneous differential equations are determined based on the Lagrange method. Furthermore, the proposed exact method and solutions are developed to analyze the forced vibration of SDOF systems with multi-step (piecewise) non-periodical variable parameters. A numerical example illustrating the application of the proposed method shows that the proposed exact procedure is an efficient method. © 2009 SAGE.

Research Area(s)

  • Dynamic., Time-varying systems, Vibration