Review of the Nonlinear Vibration Analysis of Simply Supported Beams

The research of large amplitude vibration of simply supported beams can be dated back to 1950; many achievements and some evolution were accomplished by many researchers over hundred and fifty years. The development of nonlinear vibration formulations for beams has gone through distinct phases–earlier continuum solutions, development of appropriate forms, extra-variational simplifications, debate and discussions, variationally correct formulations and finally applications. A review of work in each of these phases is very necessary in order to have a complete understanding of the process of evolution of this field. This paper attempts to achieve precisely this objective.

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