Numerical Simulation of Elastic Wave Propagation in Composite Structure

This paper delves into the concept of multimodal waveguide structures and their modeling across a relatively wide frequency spectrum encompassing low and medium frequencies. The chosen methodology combines wave propagation with finite element modeling. The proposed wave/finite element (WFE) technique involves a post-processing step applied to the mass and stiffness matrices, which are initially obtained through finite element methods, for a specific substructure. To establish connections between degrees of freedom and node forces, periodicity conditions are implemented. Consequently, real, imaginary, or complex wave numbers and frequencies are derived from distinct eigenproblems that arise. The exact form of these eigenproblems hinges on the desired solution's nature and can take the shape of a linear, quadratic, or polynomial eigenproblem. The primary focus here is on determining guided multimodal dispersion curves. This propagative approach, grounded in a finite element model (WFE), offers an efficient means to compute dispersion curves for both straightforward and intricate guided structures. The paper also derives certain properties of guided waves through this formulation and provides a comprehensive account of its numerical implementation. Furthermore, the paper showcases the practicality of the Wave Finite Element (WFE) method in predicting wave propagation within single- and multilayer structures across various frequency ranges.