About the Vibrations of the Mechanical Systems with Non-Linear Damping

Abstract

This work will analyze the non-linear vibrations of the mechanical systems, actually the ones with non-linear damping. If we consider damping F( x,x ) x( k k x );k1,k2 R 2 = − 1 − 2 Î & & & then the differential equation that characterizes the movement of the system is a Rayleigh one. Using a derivation and a substitution, the differential equation becomes a Van der Pol one, for which we find the analytical approximate solution.