Geometrical non-linear, steady state, forced, periodic vibration of plates, part II: stability study and analysis of multi-modal response

摘要

The steady state, geometrically non-linear, periodic vibration of rectangular thin plates under harmonic external excitations, is analyzed using the hierarchical finite element and the harmonic balance methods. Modal coupling due to internal resonance is detected and the consequent multi-modal and multi-frequency response is demonstrated. The stability of the obtained solutions is investigated by studying the evolution of perturbations to the solutions and using Floquet's theory.