Limit Cycles and Stability of a Nonlinear Two-Degree-of-Freedom Autonomous Vibratory System

Abstract

A perturbation technique based on small reciprocal of rotational inertia is used to find limit cycles for a system consisting of a spring, dashpot, and mass upon which is mounted an eccentric driven by a motor with a linear torque-speed characteristic. This technique, which is carried to second order, gives significantly different results from those of previous investigators using averaging techniques and is not limited to small eccentric mass, departure from resonant speed, and translational damping as they are. The linearized variational equations which govern stability are of fourth order with periodic coefficients. Instead of working with these equations, a modified averaging technique is developed which predicts limit cycles that agree with those of the zeroth-order perturbation solution and which allows a simpler stability determination to be made. The predicted limit cycles and their stability are verified by an analog computer simulation of the system.