Modal identification of weakly nonlinear multidimensional dynamical systems using a stochastic linearization method with random coefficients

Christian Soize (1) , O. Le Fur (1)

1 ONERA - The French Aerospace Lab [Châtillon]

It is known that an efficient approach for modal identification of a weakly nonlinear multidimensional second-order dynamical system consists in using a model based on equivalent stochastic linearization with constant coefficients. Such a model leads us to a good identification of the total power of the stationary response but can give an incorrect identification of the matrixvalued spectral density functions. The objective of this paper is to present an identification procedure which is based on the use of a stochastic linearization method with random coefficients. The model is then defined as a multidimensional linear second-order dynamical system with random coefficients. An optimization procedure is developed to identify the parameters of the probability law of the random coefficients. The identification procedure is described step by step. Finally, an example is presented and shows the interest of the method proposed.

Mots clés: Modal identification; nonlinear dynamical systems; stochastic linearization; random coefficients

Domaines: Mécanique [physics.med-ph]; Vibrations [physics.class-ph]; Probabilités [math.PR]; Statistiques [math.ST]

Christian Soize, O. Le Fur. Modal identification of weakly nonlinear multidimensional dynamical systems using a stochastic linearization method with random coefficients. Mechanical Systems and Signal Processing, 1997, 11 (1), pp.37-49. ⟨10.1006/mssp.1996.0085⟩. ⟨hal-00770020⟩