Large-Amplitude Free Vibrations of Uniform Timoshenko Beams: A Novel Formulation

摘要

The efficacy of the proposed novel formulation for studying the large-amplitude free vibration behavior of uniform Timoshenko beams, with hinged-hinged, clamped-clamped, and hinged-clamped boundary conditions, has been demonstrated in this note. The authors are of the opinion that the simplicity of the present formulation attracts both the analysts and researchers belonging to the basic field of nonlinear structural mechanics. In this note, the single-term admissible functions with one undetermined coefficient are used to represent the lateral displacement, corresponding to the boundary conditions considered, as most of the researchers on this topic concentrated on the first mode of vibration of slender beams using single-term admissible functions. The perfect match of the ratios of the nonlinear to linear radian frequencies obtained, through the rigorous coupled displacement field concept and the present novel formulations, shows that the present logically dominant formulation based on the physical concepts of the problem works beyond doubt for the Timoshenko beams. The formula derived for obtaining the frequency parameters of the initial axially loaded structural members is general, with an assumption on the mode shapes only. The present novel formulation which is developed for predicting the large-amplitude free vibrations, can be effectively applied to isotropic and composite beams and other structural members like circular (axisymmetric modes) and rectangular plates. However, proper values of the tension parameters developed due to large deflections along with the corresponding buckling load parameters are to be used in the formula developed.