A Galerkin approach for power spectrum determination of nonlinear oscillators. (English) Zbl 1060.70031

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.


70L05 Random vibrations in mechanics of particles and systems
70K40 Forced motions for nonlinear problems in mechanics
Full Text: DOI