Abstract
A clasical representation in seismic response analizes its that of a single or multidegree- of-nonlinear oscillator subjected to earthuake ground motion at its support. An approximate method is presented for estimating the power spectral density of the response of multi-degree-of nonlinear random structure under white noise excitations. The non-linearities are assumed to be single-valued functions of accelerations, velocities and displacements. Using a property of gaussian vector processes, the closed forms of the coefficients of the equivalent linear system are obtained by the direct application of partial differentiation and expectation operators to the non-linear terms. The efficiency of the method is checked by comparing results with those numerical simulations.
Keywords: nonlinear vibration, probability distribution, random vibration, nonlinear structures.