Approximate analytical solution of nonlinear systems using homotopy perturbation method. (February 2016)

• Record Type: Journal Article
• Authors: Bayat, Mahmoud; Pakar, Iman; Bayat, Mahdi
• Is Part Of: Proceedings of the Institution of Mechanical Engineers. Volume 230:Number 1(2016)
• Page Start: 10
• Page End: 17
• Publication Date: 2016-02
• Subjects: Homotopy perturbation method -- nonlinear vibration -- analytical method; Mechanical engineering -- Periodicals; Production engineering -- Periodicals; Manufacturing processes -- Periodicals; 621.05
• DOI: 10.1177/0954408914533104
• Languages: English
• ISSNs: 0954-4089

Abstract

In this paper, we present a new approximate method called homotopy perturbation method to achieve an accurate analytical solution for strong nonlinear problems. Two different examples are studied to show the application of the proposed method. The results are compared with the numerical solution using Runge–Kutta algorithm and also another analytical method, namely energy balance method for these certain examples. It has been shown that only one iteration of the method prepares high accurate solutions for large amplitude of the vibrations. The homotopy perturbation method does not require any linearization or small perturbation and overcomes the limitations of the traditional methods. The obtained results show that the homotopy perturbation method could be easily extended to nonlinear problems as indicated in the following examples.