Abstract
A chain of N identical oscillators (spring-mass-damper systems) coupled to a nonlinear oscillator (a pendulum) is studied in this work. More specifically, the interesting case of 1:2 subharmonic internal resonance between the pendulum and some kth mode of the system, when there is also an external resonance with some rth harmonic excitation, is studied. It is found that for these conditions, the first-order approximation to the response of this N+1 degree-of-freedom system is ultimately governed by a system of four first-order equations. The method of harmonic balance is used to obtain these four first-order amplitude equations. The stability of the steady-state response, their bifurcation behavior and resonant dynamics are described. These responses can be used to evaluate the effectiveness of the pendulum as a vibration limiting device.
