EQUIVALENT NONLINEAR-SYSTEM METHOD FOR STOCHASTICALLY EXCITED HAMILTONIAN-SYSTEMS

An equivalent nonlinear system method is presented to obtain the appro ximate probability density for the stationary response of multi-degree -of-freedom nonlinear Hamiltonian systems to Gaussian white noise para metric and/or external excitations. The equivalent nonlinear systems a re obtained on the basis of one of the following three criteria: least mean-squared deficiency of damping forces, dissipation energy balanci ng, and least mean-squared deficiency of dissipation energies. An exam ple is given to illustrate the application and validity of the method and the differences in the three equivalence criteria.