Prediction of thermal post buckling and deduction of large amplitude vibration behavior of spring–hinged beams

Abstract

A general energy formulation to predict the thermal post buckling behavior of uniform isotropic beams is presented in this paper. The hinged ends of the beam contain elastic rotational restraints to represent the actual practical support situation. The large amplitude vibration behavior of beams is deduced from the post buckling results. The classical hinged and clamped conditions can be obtained as the limiting cases of the rotational spring stiffness. The numerical results, in the form of the ratios of the post buckling to buckling loads for various maximum deflection ratios, are presented in the digital form. An alternate independent formulation, based on the nonlinear finite element formulation, is also used in this paper to validate the numerical results of the present work. Further, the results for the large amplitude vibrations, deduced from the thermal post buckling results are also presented and these results compare very well with the finite element results, available in the literature, for the large amplitude vibration problem. These comparisons show an excellent agreement not only for the present work on the proposed thermal post buckling formulation but also on the deduced results for the large amplitude vibration of beams with the ends elastically restrained against rotation (spring–hinged beams). The numerical results presented confirm the efficacy of the proposed methodology used for predicting the post buckling behavior and deducing the large amplitude vibration behavior of the spring–hinged beams.