Steel and Composite Structures

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Study of complex nonlinear vibrations by means of accurate analytical approach

  • Bayat, Mahmoud (Department of Civil Engineering, College of Engineering, Mashhad Branch, Islamic Azad University) ;
  • Pakar, Iman (Young Researchers and Elites Club, Mashhad Branch, Islamic Azad University) ;
  • Bayat, Mahdi (Department of Civil Engineering, College of Engineering, Mashhad Branch, Islamic Azad University)
  • Received : 2014.03.24
  • Accepted : 2014.08.22
  • Published : 2014.11.25
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Abstract

In the current study, we consider a new class of analytical periodic solution for free nonlinear vibration of mechanical systems. Hamiltonian approach is applied to analyze nonlinear problems which occur in dynamics. The proposed method doesn't have the limitations of the classical methods and leads us to a high accurate solution by only one iteration. Two well known examples are studied to show the convenience and effectiveness of this approach. Runge-Kutta's algorithm is also applied and the results of it are compared with the Hamiltonian approach. High accuracy of the proposed approach reveals that the Hamiltonian approach can be very useful for other nonlinear practical problems in engineering.

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References

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