Forced resonance vibrations of the dissipative spring-pendulum system

Abstract

Resonance dynamics of the dissipative spring-pendulum system under periodic external excitation is studied. Analysis is based on the generalized concept of nonlinear normal vibration modes by Kauderer and Rosenberg. The 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 in the resonance vicinity is applied. New vibration regimes, transient nonlinear normal modes, which are realized only for the separate energy levels, are selected. New results, which are actual for vibration absorption, concerning stability and bifurcations of nonlinear normal modes and their interaction in the resonance vicinity are obtained. Numerical simulations confirm reliability of obtained analytical results.