An analytical technique for handling forced Van der Pol vibration equation

Abstract

Based on the modified harmonic balance method, an analytical method has been developed for handling the forced Van der Pol vibration equation. Usually, a system of nonlinear algebraic equations arises within the unfamiliar coefficients in several harmonics terms and the frequency of the forcing term. A numerical technique has been applied to handle those nonlinear algebraic equations in the classical harmonic balance method. In our study, a system of linear algebraic equations is calculated with the aid of a single nonlinear one. The solutions attained by the suggested scheme have been likened to the results acquired by the well-known Runge-Kutta method, and these results display very nice harmony with the result obtained by the mentioned method. Also, it is noticed that the proposed technique is straightforward and gives the desired results in the whole solution domain.

J. Bangladesh Acad. Sci. 45(2); 231-240: December 2021