Resonances in a kinematically driven nonlinear system - asymptotic analysis

Abstract

The dynamic response of a harmonically and kinematically excited spring pendulum is studied. The investigated two-degree-of-freedom system may serve as a paradigm example for various engineering applications. The applied multiple scale (MS) method allows us to solve analytically the equations of motion and to detect and study the system resonances. In addition, stability of steady state solutions is analytically estimated and numerically validated, and transfer of energy from one to another mode of oscillations is illustrated and discussed.