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Smart Structures and Systems Volume 15, Number 5, May 2015 , pages 1311-1327 DOI: https://doi.org/10.12989/sss.2015.15.5.1311 |
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Mathematical solution for nonlinear vibration equations using variational approach |
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M. Bayat and I. Pakar
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| Abstract | ||
| In this paper, we have applied a new class of approximate analytical methods called Variational Approach (VA) for high nonlinear vibration equations. Three examples have been introduced and discussed. The effects of important parameters on the response of the problems have been considered. Runge-Kutta\'s algorithm has been used to prepare numerical solutions. The results of variational approach are compared with energy balance method and numerical and exact solutions. It has been established that the method is an easy mathematical tool for solving conservative nonlinear problems. The method doesn\'t need small perturbation and with only one iteration achieve us to a high accurate solution. | ||
| Key Words | ||
| Variational Approach (VA); nonlinear vibrations; energy balance method; numerical method | ||
| Address | ||
| M. Bayat: Department of Civil Engineering, Mashhad Branch,Islamic Azad University, Mashhad, Iran I. Pakar: Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran | ||