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Structural Engineering and Mechanics
  Volume 43, Number 3, August10 2012 , pages 337-347
DOI: https://doi.org/10.12989/sem.2012.43.3.337
 


Accurate analytical solution for nonlinear free vibration of beams
M. Bayat and I. Pakar

 
Abstract
    In this study, Hamiltonian Approach (HA) is applied to analysis the nonlinear free vibration of beams. Two well-known examples are illustrated to show the efficiency of this method. One of them deals with the Nonlinear vibration of an electrostatically actuated microbeam and the other is the nonlinear vibrations of tapered beams. This new approach prepares us to achieve the beam\'s natural frequencies and mode shapes easily and a rapidly convergent sequence is obtained during the solution. The effects of the small parameters on the frequency of the beams are discussed. Some comparisons are conducted between the results obtained by the Hamiltonian Approach (HA) and numerical solutions using to illustrate the effectiveness and convenience of the proposed methods.
 
Key Words
    non-linear vibration; hamiltonian approach; electrostatically actuated microbeam; tapered beams
 
Address
M. Bayat and I. Pakar: Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
 

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