A theorem on the exact nonsimilar steadystate motions of a nonlinear oscillator
Abstract
In this work the steadystate motions of a nonlinear, discrete, undamped oscillator are examined. This is achieved by using the notion of exact steady state, i.e., a motion where all coordinates of the system oscillate equiperiodically, with a period equal to that of the excitation. Special forcing functions that are periodic but not necessarily harmonic are applied to the system, and its steady response is approximately computed by an asymptotic methodology. For a system with cubic nonlinearity, a general theorem is given on the necessary and sufficient conditions that an excitation should satisfy in order to lead to an exact steady motion. As a result of this theorem, a whole class of admissible periodic functions capable of producing steady motions is identified. An analytic expression for the modal curve describing the steady motion of the system in the configuration space is derived and numerical simulations of the steadystate motions of a strongly nonlinear oscillator excited by two different forcing functions are presented.
 Publication:

ASME Journal of Applied Mechanics
 Pub Date:
 June 1992
 Bibcode:
 1992ATJAM..59..418V
 Keywords:

 Asymptotic Methods;
 Forced Vibration;
 Harmonic Oscillators;
 Steady State;
 Vibration Mode;
 Degrees Of Freedom;
 Nonlinear Equations;
 Structural Vibration;
 Engineering (General)