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Structural Engineering and Mechanics
  Volume 50, Number 6, June25 2014 , pages 853-862

Forced nonlinear vibration by means of two approximate analytical solutions
Mahmoud Bayat, Mahdi Bayat and Iman Pakar

    In this paper, two approximate analytical methods have been applied to forced nonlinear vibration problems to assess a high accurate analytical solution. Variational Iteration Method (VIM) and Perturbation Method (PM) are proposed and their applications are presented. The main objective of this paper is to introduce an alternative method, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Some patterns are illustrated and compared with numerical solutions to show their accuracy. The results show the proposed methods are very efficient and simple and also very accurate for solving nonlinear vibration equations.
Key Words
    Variational Iteration Method (VIM); Perturbation Method (PM); nonlinear oscillators; nonlinear spring
Mahmoud Bayat, Mahdi Bayat : Department of Civil Engineering, College of Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
Iman Pakar : Young Researchers and Elites Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran

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