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The purpose of this paper is to highlight the implementation of a recently developed weak form quadrature element method for nonlinear free vibrations of Timoshenko beams subjected to three different boundary conditions.

The design of the paper is based on considering the geometrically nonlinear effects of axial strain, bending curvature, and shear strain. Then the quadrature element formulation of the beam is introduced.

The efficiency of the method is demonstrated by a convergence study. Ratios of the nonlinear fundamental frequencies to the corresponding linear frequencies are extracted. Their variations with the ratio of amplitude to radius of gyration and the slenderness ratio are examined. The effects of the nonlinearity on higher order frequencies and mode shapes are also investigated.

The computed results show fast convergence and compare well with available literature results.