Nonlinear vibration of mechanical systems by means of Homotopy perturbation method


  • MAHMOUD BAYAT Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
  • IMAN PAKAR Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran


Energy balance method, Homotopy perturbation method, nonlinear oscillators, Runge-Kutta algorithm.


In this study, it has been tried to present a new approximate method by usingHomotopy Perturbation Method (HPM) for high nonlinear problems. Three differentexamples are considered and the application of the Homotopy perturbation method isstudied. Runge-Kutta algorithm is used to obtain numerical results. Another analyticalmethod called Energy Balance Method (EBM) is applied to compare the results ofHPM and Runge-Kutta algorithm. It has been shown that only one iteration of themethod prepares high accurate solution for whole domain. It has been established thatHomotopy perturbation method does not need any linearization and overcome thelimitations of the perturbation methods.


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