In this paper, a modified harmonic balance method is presented to solve nonlinear forced vibration problems. A set of nonlinear algebraic equations appears among the unknown coefficients of harmonic terms and the frequency of the forcing term. Usually a numerical method is used to solve them. In this article, a set of linear algebraic equations is solved together with a nonlinear one. The solution obtained by the proposed method has been compared to those obtained by variational and numerical methods. The results show good agreement with the results obtained by both methods mentioned above.

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In this paper, He's homotopy perturbation method has been extended for obtaining the analytical approximate solution of second order strongly nonlinear generalized duffing oscillators with damping based on the extended form of the Krylov-Bogoliubov-Mitropolskii (KBM) method.Accuracy and validity of the solutions obtained by the presented method are compared with the corresponding numerical solutions obtained by the well-known fourth order Rangue-Kutta method.The method has been illustrated by examples.

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