Approximate potentials with applications to strongly nonlinear oscillators with slowly varying parameters

Article type: Research Article

Authors: Cai, Jianping | Li, Y.P.

Affiliations: Department of Mathematics, Zhangzhou Teachers College, Fujian 363000, P. R. China. E-mail: zsucjp@sina.com | Department of Mathematics, Zhongshan University, Guangzhou 510275, P.R. China. E-mail: ypli@umac.mo

Abstract: A method of approximate potential is presented for the study of certain kinds of strongly nonlinear oscillators. This method is to express the potential for an oscillatory system by a polynomial of degree four such that the leading approximation may be derived in terms of elliptic functions. The advantage of present method is that it is valid for relatively large oscillations. As an application, the elapsed time of periodic motion of a strongly nonlinear oscillator with slowly varying parameters is studied in detail. Comparisons are made with other methods to assess the accuracy of the present method.

Keywords: strongly nonlinear oscillator, approximate potential, slowly varying parameter

Journal: Shock and Vibration, vol. 10, no. 5-6, pp. 379-386, 2003