Stationary response of states-constrained nonlinear systems under stochastic parametric and external excitations

A Fourier-series closure scheme is developed for the prediction of the stationary stochastic response of a stochastic parametrically and externally excited oscillator with a nonpolynomial type nonlinearity and under states constraint. The technique is implemented by deriving the moment relations and employing the Fourier series as the expansion of a non-Gaussian density for constructing and solving a set of algebraic equations with unknown Fourier coefficients. A single-arm robot manipulator operated in a constrained working space and subjected to parametric and/or external noise excitations is selected to illustrate the present approach. The validity of the present scheme is further supported by some exact solutions and Monte Carlo simulations.