Stability and Bifurcation Analysis of Oscillators With Piecewise-Linear Characteristics: A General Approach

[+] Author and Article Information
Y. B. Kim, S. T. Noah

Mechanical Engineering Department, Texas A&M University, College Station, TX 77843-3123

J. Appl. Mech 58(2), 545-553 (Jun 01, 1991) (9 pages) doi:10.1115/1.2897218 History: Received August 24, 1989; Revised April 30, 1990; Online March 31, 2008


A general approach is developed for determining the periodic solutions and their stability of nonlinear oscillators with piecewise-smooth characteristics. A modified harmonic balance/Fourier transform procedure is devised for the analysis. The procedure avoids certain numerical differentiation employed previously in determining the periodic solutions, therefore enhancing the reliability and efficiency of the method. Stability of the solutions is determined via perturbations of their state variables. The method is applied to a forced oscillator interacting with a stop of finite stiffness. Flip and fold bifurcations are found to occur. This led to the identification of parameter ranges in which chaotic response occurred.

Copyright © 1991 by The American Society of Mechanical Engineers
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