Summary
In the present work nonlinear vibrations of a circular plate under dynamic and thermal loading are investigated. The model of the plate is based on the geometrically nonlinear Mindlin plate theory. It is accepted that the plate gets elevated temperature instantaneously and it is subjected to harmonic loading. The theoretical model is represented by a set of partial differential equations and is reduced consecutively to one and to three degrees of freedom system by Galerkin method based on the first vibration mode or on the first three vibration modes. The obtained reduced nonlinear ordinary differential equations with cubic non-linearity and temperature influence is studied analytically by harmonic balance method. The influence of the amplitude of the loading and the elevated temperature on the frequency response functions is studied and selected bifurcation diagrams are computed. The analytical results are compared with numerical solutions obtained by the one-mode reduction model.
