Monofrequent oscillations in mechanical systems governed by second order hyperbolic differential equations with small non-linearities

Abstract

The solution to certain second order hyperbolic differential equations with weak non-linearities is found by using the Krylov Bogoliubov-Mitropolskii method. Both autonomous and non-autonomous equations are considered, and in the latter case, both the non-resonant and resonant problems are solved. The general methods are applied to the case of the longitudinal vibrations of a rod in which non-linear elastic behavior, nonlinear viscoelastic behavior, and viscous damping occur.