EQUIVALENT STATISTICAL CUBICIZATION FOR SYSTEM AND FORCING NONLINEARITIES

This technical note outlines the treatment of a single-degree-of-freed om (SDOF) system containing statistically symmetric nonlinearities in both its stiffness characteristics and its excitation, Via equivalent statistical cubicization, the nonlinearities that are not in polynomia l form are cast as polynomials containing first- and third-order terms , This allows the use of a Volterra series approach that yields a syst em of two differential equations for the first- acid third-order compo nents of the response. Transforming this system into the frequency dom ain produces transfer functions from which power spectral density and statistics up to the fourth order may be obtained for the system respo nse. Finally, using the statistics within the framework of a moment-ba sed Hermite transformation model yields an estimate of the non-Gaussia n probability-density function (PDF) for the system response.