Nonlinear vibration of multi-body systems with linear and nonlinear springs

  • Bayat, Mahmoud (Young Researchers and Elite Club, Roudehen Branch, Islamic Azad University) ;
  • Pakar, Iman (Young Researchers and Elite club, Mashhad Branch, Islamic Azad University) ;
  • Bayat, Mahdi (Department of Civil Engineering, Roudehen Branch, Islamic Azad University)
  • Received : 2016.12.19
  • Accepted : 2017.09.20
  • Published : 2017.11.20


In this paper, nonlinear vibration of multi-degree of freedom systems are studied. It has been tried to develop the mathematical model of systems by second-order nonlinear partial differential equations. The masses are connected with linear and nonlinear springs in series. A great effort has been done to solve the nonlinear governing equations analytically. A new analytical method called Variational Iteration Method (VIM) is proposed and successfully applied to the problem. The linear and nonlinear frequencies are obtained and the results are compared with numerical solutions. The first order of Variational Iteration Method (VIM) leads us to high accurate solution.


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