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Nonlinear free vibration of a symmetrically conservative two-mass system with cubic nonlinearity

Pirbodaghi, T ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1115/1.4000315
  3. Publisher: 2010
  4. Abstract:
  5. In this study, the nonlinear free vibration of conservative two degrees of freedom systems is analyzed using the homotopy analysis method (HAM). The mathematical model of such systems is described by two second-order coupled differential equations with cubic nonlinearities. First, novel approximate analytical solutions for displacements and frequencies are established using HAM. Then, the homotopy Padé technique is applied to accelerate the convergence rate of the solutions. Comparison between the obtained results and those available in the literature shows that the first-order approximation of homotopy Padé technique leads to accurate solutions with a maximum relative error less than 0.068 percent for all the considered cases. © 2010 by ASME
  6. Keywords:
  7. Analytical solution ; Homotopy analysis method ; Homotopy Padé technique ; Nonlinear vibration ; Two degrees of freedom ; Analytical solutions ; Homotopies ; Homotopy analysis methods ; Non-linear vibrations ; Two degrees of freedom ; Differential equations ; Mathematical models ; Mechanics ; Nonlinear analysis ; Vibration analysis
  8. Source: Journal of Computational and Nonlinear Dynamics ; Volume 5, Issue 1 , 2010 , Pages 1-6 ; 15551415 (ISSN)
  9. URL: http://computationalnonlinear.asmedigitalcollection.asme.org/article.aspx?articleid=1395675