A Galerkin approach for power spectrum determination of nonlinear oscillators (Q1868311)

The authors construct an approximate procedure to estimate spectral properties of nonlinear single-degree-of-freedom systems with random perturbations. The procedure is based on Galerkin method. Firstly, the system response is expanded into Fourier series with random coefficients. Next, a set of nonlinear equations containing the unknown parameters of response is derived. In doing so, the authors assume that the nonlinearity is given by a cubic polynomial. The desired estimates are obtained by averaging the square modulus of Fourier coefficients over various excitation processes. A few numerical examples exhibit the capacities of the proposed algorithm in comparison with other computational methods.