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

Spanos, P. D.; Di Paola, M.; Failla, G.

Meccanica 37, No. 1-2, 51-65 (2002).

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.

Reviewer: Elena Ya. Gorelova (Samara)

MSC:

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

Keywords:

Fourier series; Galerkin method; cubic nonlinearity