An efficient approach for predicting the nonlinear vibrations of a beam system subjected to multipoint correlated random excitation

Abstract

In linear vibration studies, the statistical description of multipoint random excitations is sufficient to calculate the vibration response of a structure. For nonlinear vibrations, it is necessary to model each excitation point separately, taking into account the correlation between each excitation point. The objective of this paper is to show how to reduce the number of excitation terms while remaining in a formalism compatible with nonlinear vibration studies.The reduction of the number of stochastic excitation terms can be achieved by Galerkin methods (such as the Karhunen–Loève decomposition). This paper presents an original method which consists of projecting the excitation terms on the eigenmodes of the structure. These two methods are illustrated in the concrete case of a benchmark structure developed by the Commissariat à l’Energie Atomique (CEA), i.e., the mechanical beam system called the CEA-beam benchmark structure, previously studied in Talik et al. (2022), restrained to its first vibration mode and seen as a Duffing oscillator. A random excitation, composed of a consequent number of points of excitation distributed spatially along the structure (more exactly 101 points) and partially correlated, is used to illustrate the effectiveness of the proposed methodology. The proposed method makes it possible to reduce the number of random excitation signals to a single modal excitation term.