Influence of shear deformation and rotary inertia on nonlinear free vibration of a beam with pinned ends

The method of multiple scales is used to analyze the nonlinear vibrations of a beam with pinned ends. The formulation incorporates the effects of the transverse shear deformation as well as the rotary inertia on the large amplitude vibration behaviour. A uniformly valid higher second-order perturbation solution is obtained. The predictions of nonlinear frequencies at different beam parameters are given. The influences of shear and rotary inertia are significant in the case of moderately thick and short beams undergoing large amplitude vibrations.