Resonances in Non-Linear Structural Vibrations Involving Two External Periodic Excitations.

摘要

Multi-degree of freedom structural or mechanical systems with weak quadratic and cubic non-linearities are considered. They are subjected to an external excitation with two harmonic components, having frequencies Omega 1 and Omega 2. Attention is focused on the resonances Omega 2 + or - Omega 1 approximately equals 2 omega q, where omega 2 is one of the natural frequencies of the system. Solutions are obtained by using the method of multiple scales. Steady state response amplitudes are determined and are plotted as a function of a detuning parameter, the excitation amplitudes, and measures of the relative values of Omega 1 and Omega 2.