Recherche numérique d'oscillations composées du type additif dans un système oscillant non-linéaire amorti à deux degrés de liberté

Abstract

The combination tones of summed type are studied in a non-linear damped vibratory system of two degrees of freedom with spring characteristics of second and third order and excited by two external harmonic forces of different frequencies. A modified Galerkin method is presented, based on the replacement of some integrals by their Simpson approximations instead of using the formulae given by M. Urabe. For some systems this modified method has the advantage to ameliorate the precision of the Galerkin approximations and to diminish considerably the error of these approximations. The existence and stability of an exact periodic solution is discussed and the error bound of the Galerkin approxi¬ mations is given. The modified Galerkin method is compared to other approximation methods for two numerical examples.