Three-Dimensional Multiferroic Structures under Time-Harmonic Loading

Magneto-electro-elastic (MEE) materials are a specific class of advanced smart materials that simultaneously manifest the coupling behavior under electric, magnetic, and mechanical loads. This unique combination of properties allows MEE materials to respond to mechanical, electric, and magnetic stimuli, making them versatile for various applications. This paper investigates the static and time-harmonic field solutions induced by the surface load in a three-dimensional (3D) multilayered transversally isotropic (TI) linear MEE layered solid. Green & scaron;functions corresponding to the applied uniform load (in both horizontal and vertical directions) are derived using the FourierBessel series (FBS) system of vector functions. By virtue of this FBS method, two sets of first-order ordinary differential equations (i.e., N-type and LM-type) are obtained, with the expansion coefficients being Love numbers. It is noted that the LM-type system corresponds to the MEE-coupled P-, SV-, and Rayleigh waves, while the N-type corresponds to the purely elastic SH- and Love waves. By applying the continuity conditions across interfaces, the solutions for each layer of the structure (from the bottom to the top) are derived using the dual-variable and position (DVP) method. This method (i.e., DVP) is unconditionally stable when propagating solutions through different layers. Numerical examples illustrate the impact of load types, layering, and frequency on the response of the structure, as well as the accuracy and convergence of the proposed approach. The numerical results are useful in designing smart devices made of MEE solids, which are applicable to engineering fields like renewable energy.