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Application of Recent Powerful Analytical Approaches on the Non-Linear Vibration of Cantilever Beams
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Hamid M. Sedighi
,
Kourosh H. Shirazi
Published/Copyright:
December 15, 2012
Abstract
This paper presents the advantages of some effective analytical approaches applied on the governing equation of transversely vibrating cantilever beams. Six studied methods are Min-Max Approach, Parameter Expansion Method, Hamiltonian Approach, Variational Iteration Method, Bubnov-Galerkin and Energy Balance Method. The powerful analytical approaches are used to obtain frequency-amplitude relationship for dynamic behavior of nonlinear vibration of cantilever beams. It is demonstrated that one term in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a numerical example is conducted to verify the accuracy of these methods.
Keywords: Min-Max Approach; parameter expansion method; hamiltonian approach; variational iteration method; Bubnov-Galerkin method; energy balance method; non-linear vibration of beam
Received: 2012-1-28
Accepted: 2012-10-25
Published Online: 2012-12-15
Published in Print: 2012-12-14
©2012 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Boiling Shocks and Self-Oscillations in Critical Nozzle Flow
- Method of Taylor Expansion Moment Incorporating Fractal Theories for Brownian Coagulation of Fine Particles
- Complex Hybrid Synchronization in Drive-Response Complex-Variable Chaotic Systems
- Numerical Solution of Nonlinear Kaup-Kupershmit Equation, KdV-KdV and Hirota-Satsuma Systems
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