MODAL IDENTIFICATION OF WEAKLY NON-LINEAR MULTIDIMENSIONAL DYNAMICAL SYSTEMS USING A STOCHASTIC LINEARISATION METHOD WITH RANDOM COEFFICIENTS

Abstract

It is known that an efficient approach for modal identification of a weakly non-linear multidimensional second-order dynamical system consists of using a model based on equivalent stochastic linearisation with constant coefficients. Such a model leads to a good identification of the total power of the stationary response but can give an incorrect identification of the matrix-valued spectral density functions. The objective of this paper is to present an identification procedure which is based on the use of a stochastic linearisation method with random coefficients. The model is then defined as a multidimensional linear second-order dynamical system with random coefficients. An optimisation 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.