EQUIVALENT STATISTICAL QUADRATIZATION AND CUBICIZATION FOR NONLINEAR-SYSTEMS

A summary is given of the development of two techniques for handling s ystem and excitation nonlinearities: equivalent statistical quadratiza tion and equivalent statistical cubicization. Depending upon the natur e of a given nonlinearity, one of these procedures may be employed to approximate it by a quadratic or cubic polynomial. In this manner, the nonlinearity is preserved and the response transfer functions are att ainable using a Volterra functional series approach. When the parent i nput processes are characterized by appropriate spectra, integration i n the frequency domain yields the desired spectra, bispectra or higher -order cumulants of the response. Using the system moment information corresponding to the response cumulants, a moment-based Hermite transf ormation yields probability density functions for the non-Gaussian pro cess. Also, the force and response spectra exhibit the appropriate sec ondary peaks corresponding to the particular system and excitation cha racteristics. The accurate prediction of both extremes and response po wer spectral densities is a notable improvement over equivalent statis tical linearization. All results compare well with those obtained usin g a time-domain simulation.