Stochastic linearization of multi‐degree‐of‐freedom non‐linear systems

Abstract

AbstractAn equivalent linearization technique to obtain the response of non‐linear multi‐degree‐of‐freedom dynamic systems to stationary gaussian excitations is developed. 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. It is shown that when the non‐linearities possess potentials, the linear system has symmetric coefficient matrices. A geometrical interpretation of the linear coefficients, in connection with the original non‐linearities, is presented. The accuracy is investigated by means of examples.