Forced Resonance Vibrations of the Dissipative Spring-Pendulum System

Abstract

Dynamics of the dissipative spring-pendulum system under periodic external excitation in the vicinity of external resonance and simultaneous external and internal resonances is studied. The concept of nonlinear normal vibration modes is used in this analysis. The multiple scales method and subsequent transformation to the reduced system with respect to the system energy, an arctangent of the amplitudes ratio and a difference of phases of required solutions are applied. Transient nonlinear normal modes, which exist only for some particular levels of the system energy, are obtained. In the vicinity of values of time, corresponding to these energy levels, the transient modes temporarily attract other system motions. Interaction of nonlinear vibration modes under resonance conditions is also analysed