Accession Number : AD0604047

Title :   THE SPECTRUM OF RANDOM VIBRATION OF A NONLINEAR OSCILLATOR,

Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE

Personal Author(s) : Crandall,Stephen H.

Report Date : JUN 1964

Pagination or Media Count : 28

Abstract : When a linear vibratory system is excited by a stationary random process the most useful statistical description of the response is given by either the autocorrelation function or the spectral density. The exact calculation of these statistics for a nonlinear oscillator remains an unsolved problem although a general approach has been outlined. This paper describes three approximate procedures which apply to systems which are only slightly nonlinear. The procedures are perturbation, equivalent linearization, and a new heuristic method based on simply averaging the deteministic properties of the nonlinear system. This latter procedure is an extension of the heuristic method recently introduced for obtaining the expected frequency of the stationary response of a nonlinear oscillator. It is shown that for vibratory systems with small stiffness nonlinearities all three procedures give autocorrelations (and spectra) which are identical to first order in the nonlinearity parameter. (Author)

Descriptors :   (*VIBRATION, NONLINEAR SYSTEMS), STATISTICAL PROCESSES, STATISTICAL FUNCTIONS, PROBABILITY, MECHANICS, PERTURBATION THEORY, STATISTICAL ANALYSIS

Distribution Statement : APPROVED FOR PUBLIC RELEASE