Determination of Response Statistics of Single Degree of Nonlinear Random Structure with Nonlinear Damping Characteristic and Nonlinear Elastic Characteristic

Abstract

The paper investigates the applicability of the path integral solution method for calculating the response statistics of nonlinear dynamic systems whose equations of motion can be modelled by the use linearization differential equations. The present paper consists of discussion on dynamic response of structures under random load. They are random processes and commonly described by spectral density functions. An identification technique is proposed for a nonlinear oscillator excited by response-dependent white noise. Stiffness, damping and excitation are estimated from records of the stationary stochastic response. Assume that a single-degree of freedom structure is excited by a force which is a random process described by the spectral density function. We present a method for estimating the power spectral density of the stationary response of oscillator with a nonlinear restoring force under external stochastic wide-band excitation. An equivalent linear system is derived, from which the power spectral density is deduced.