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.