Guided waves propagation in multi-layered porous materials by the global matrix method and Biot theory

In this research, a numerical approach for analyzing the analytical solution of guided wave propagation characteristics in multilayer two-phased porous media is presented. Combing the global matrix method and Biot theory, and introducing the modulus-porosity-poisson’s ratio relation, the global dispersion equations of multi-layered porous materials are established. Also, the complex boundary conditions in multi-layered two-phase porous media are considered simultaneously. In order to confirm the feasibility and accuracy of the proposed method, the dispersion curves of the guided waves propagation in a single-layer porous graphite layer and a triple-layer graphite/copper/graphite model (porosity close to 0) were numerically calculated. The results were compared with the propagation characteristics of the guided waves in the corresponding stacked sequential laminates without porosity, which is done by the state-vector formalism and the Legendre polynomials method based on our previous work. Then, this approach is further applied to lithium ion battery. The change of porosity in graphite is used to simulate the state of charge of lithium-ion battery. The influence of porosity change on mode coupling effect of guided waves is analyzed, and the mapping relationship between porosity and corresponding dispersion curves is explored. Meanwhile, the research shows that, with the decrease of porosity (which means the state of charge increases), the phase velocity of the fundamental modes gradually increases, making the corresponding time of flight decrease gradually. Moreover, the theoretical model captures a meaningful relationship between state of charge and acoustic behavior. It gives theoretical support for nondestructive evaluation and quantitative estimation of the state characteristics of lithium-ion batteries.