An analytical approach for the nonlinear forced vibration of clamped-clamped buckled beam

Document Type : Research Article

Authors

1 Ph.D. student, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran.

2 Proffesor, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

3 MSc student, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

Abstract

Analytical solutions are attractive for parametric studies and consideration of the problems physics. In addition, analytical solutions can be employed as a reference framework for verification of numerical results. In this paper
Homotopy analysis method and Homotopy Pade technique which are approximate analytical methods, are used to obtain nonlinear forced vibration response of Euler-Bernoulli clamped-clamped buckled beam subjected to an axial force and transverse harmonic load for the first time. Analytical solutions for nonlinear frequency are derived via Homotopy analysis method, Homotopy Pade technique and Runge Kutta method and the results are compared with experimental results of literature. Also the time response of the beam is obtained for free and forced vibration via analytical and numerical methods. In addition, the frequency response is drawn. Comparison of analytical results with numerical results and literature results reveals that Homotopy analysis method and Homotopy Pade
technique have excellent accuracy for wide range of nonlinear parameters and predict system behavior precisely
.

Highlights

  • Two semi-analytical methods, HAM and Homotopy Pade techniques are used.
  • The methods are used to obtain nonlinear forced vibration response of a beam.
  • Beam is subjected to transverse harmonic load and axial force.
  • Analytical results are compared with experimental results of literature.
  • Excellent accuracy is found for wide range initial deflection and beam characeristics.

Keywords

Main Subjects


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