Stochastic analysis of nonlinear vehicle systems using a generalized harmonic linearization technique

The discrete harmonic linearization method which is applicable to stochastic systems could not provide an equivalent stiffness coefficient for a nonlinear restoring element. In this paper, this technique is generalized to obtain linear representations of both nonlinear restoring and damping elements, based on a principle of energy similarity of dynamic elements. A numerical iterative procedure is presented to compute the local linear coefficients of nonlinear dynamic elements. A nonlinear system is then represented by a set of its complex frequency response function matrices, as functions of the excitation frequency. Stochastic analysis of general multi-DOF nonlinear vehicle systems is established in terms of response PSD characteristics.