Non-linear vibration analyses of beams resting on-elastic foundations using Fourier p-element

A Fourier P-element is presented for determining the geometrically non-linear free and forced vibration characteristics of Timoshenko beams resting on two-parameter elastic foundations. The harmonic balance method is applied in the analyses, and the arc-length continuation method is adopted to solve the resulting non-linear eigenvalue problem. Numerical results compared with available results validate the accuracy of the proposed method. It should be paid attention to that the axial tensile stress of the beams in non-linear vibration is of considerable large.