Equivalent Statistical Cubicization for System and Forcing Nonlinearities

This technical note outlines the treatment of a single-degree-of-freedom (SDOF) system containing statistically symmetric nonlinearities in both its stiffness characteristics and its excitation. Via equivalent statistical cubicization, the nonlinearities that are not in polynomial form are cast as polynomials containing firstand third-order terms. This allows the use of a Volterra series approach that yields a system of two differential equations for the firstand third-order components of the response. Transforming this system into the frequency domain produces transfer functions from which power spectral density and statistics up to the fourth order may be obtained for the system response. Finally, using the statistics within the framework of a moment-based Hermite transformation model yields an estimate of the non-Gaussian probability-density function (PDF) for the system response.