期刊
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
卷 13, 期 7-8, 页码 487-494出版社
WALTER DE GRUYTER GMBH
DOI: 10.1515/ijnsns-2012-0030
关键词
Min-Max Approach; parameter expansion method; hamiltonian approach; variational iteration method; Bubnov-Galerkin method; energy balance method; non-linear vibration of beam
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.
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