RESPONSE SPECTRAL DENSITIES OF SYSTEMS UNDER BOTH ADDITIVE AND MULTIPLICATIVE EXCITATIONS

摘要

Solution techniques are developed to obtain the response spectral densities for systems under both additive and multiplicative random excitations, where the multiplicative excitations appear in the linear terms. For the case of a quasi-linear system, in which the damping and stiffness forces are linear, exact solutions for the stationary moments and response spectral densities are obtained from sets of linear algebraic equations. When the damping forces and/or the stiffness forces are nonlinear, the system can be replaced by an equivalent quasi-linear system for which exact solutions are available. A numerical example shows that the procedure yields quite accurate results when compared with those obtained from Monte Carlo simulations even for the case of strong nonlinear-ity.