Shear excitation of a multilayered magneto-electro-elastic half-space considering a vast frequency content

The objective of this paper is to present dynamic responses of a multilayered magneto-electro-elastic half-space due to an external/internal time-harmonic shear mechanical loading. To do so, a concrete mathematical tool is applied to solve a set of complicated high-order coupled equations of motion for a layered magneto-electro-elastic structure. The mathematical tool is constructed based on a new infinite dimensional vector space utilizing multiplication of exponential functions as a base for Fourier series in the tangential direction and Bessel function as a base in the radial direction. A cylindrical coordinate system is attached to the multi-layered half-space with the depth axis oriented perpendicular to the surface. In this way, with the use of this vector space, the coupled governing partial differential equations are changed to two sets of ordinary first-order differential equations, where their unknown functions are the coefficients of base functions in the Hankel-Fourier domain. It should be noted that these two sets of equations are completely decoupled based on the decoupling of SH-wave from P- and SV-waves. The effect of the layering is considered with the use of the dual-variable-position method. A mechanically uniform surface/internal shear time-harmonic loading is applied as a common excitation in nature to pursue the pattern of energy transformation in multifunctional magneto-electro-elastic structures with different material properties. Also, the effects of loading frequency and resonance phenomena are investigated in this paper numerically. The results show clearly how the arrangement and the designing process of different layers with different material properties can change responses in smart devices.