Non-linear multi-degree-of-freedom system random vibration by equivalent statistical quadratization (Q1202859)

The method of statistical quadratization is generalized to multi-degree- of-freedom systems. The statistical quadratization solution procedure involves replacing the nonlinear system by an ``equivalent'' system with polynomial nonlinearities up to quadratic order. The nonlinear equivalent system has a form whose solutions can be approximated by using the Volterra series method. The non-Gaussian joint response probability distribution is approximated by a third-order Gram-Charlier expansion. The method is formulated for systems with general nonlinearities and with nonlinearities of a special form. To demonstrate the usefulness of the method, solutions are obtained for a specific system.