A SIMPLE ANALYTICAL TECHNIQUE TO SOLVE HIGHER-ORDER APPROXIMATIONS OF A NONLINEAR OSCILLATOR WITH DISCONTINUITIES

Alal Hosen

Abstract


In this paper, a simple analytical technique has been developed to determine higher-order approximate periodic solutions of a nonlinear oscillator with discontinuities for which the elastic force term is proportional to $sgn(x)$. The classical harmonic balance method cannot be applied directly for such nonlinear problems. It is very difficult to solve nonlinear problems and in general, it is often more difficult to get an analytic approximation than a numerical one for such nonlinear problems. Analytical solutions of algebraic equations are not always possible, especially in the case of a large oscillation. In this article different parameters of the same nonlinear problems are found, for which the simple analytical solution produces desired results even for the large oscillation. We have been found out that a simple analytical principle which works very well for the excellent agreement of the approximate frequencies and period with the exact ones.

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