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A homotopy perturbation analysis of nonlinear free vibration of Timoshenko microbeams

Moeenfard, H ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1007/s12206-011-0130-8
  3. Abstract:
  4. This paper uses Hes Homotopy Perturbation Method (HPM) to analyze the nonlinear free vibrational behavior of clamped-clamped and clamped-free microbeams considering the effects of rotary inertia and shear deformation. Galerkins projection method is used to reduce the governing nonlinear partial differential equation. to a nonlinear ordinary differential equation. HPM is used to find analytic expressions for nonlinear natural frequencies of the pre-stretched microbeam. A parametric study investigated the effects of design parameters such as applied axial loads and slenderness ratio. The effect of rotary inertia and shear deformation on the nonlinear natural frequency was investigated. For verification, a numerical approach was implemented to solve the nonlinear equation. of vibration. A comparison between analytical and numerical results shows that HPM can predict system nonlinear vibrational behavior significantly more accurately than previously used methods in the literature
  5. Keywords:
  6. Homotopy perturbation method ; Microbeam ; Modified lindstedt-poincare method ; Nonlinear free vibration ; Rotary inertia ; Shear deformation ; Lindstedt-Poincare method ; Microbeam ; Non-linear free vibration ; Natural frequencies ; Nonlinear equations ; Numerical methods ; Ordinary differential equations ; Partial differential equations ; Perturbation techniques ; Shear flow ; Vibration analysis
  7. Source: Journal of Mechanical Science and Technology ; Volume 25, Issue 3 , 2011 , Pages 557-565 ; 1738494X (ISSN)
  8. URL: http://link.springer.com/article/10.1007%2Fs12206-011-0130-8