Dispersion relations for SH wave in magneto-electro-elastic heterostructures

Abstract

a b s t r a c tIn the present work the dispersion relations of stationary SH waves in a heteroestructure with magneto-electro-elastic properties have been obtained. The calculations were done taking into consideration the symmetry of the system and separating the solutions in symmetric and anti-symmetric parts. Different limit cases are presented. The dispersion curves and amplitudes of vibration are shown for different configurations.

Transient-state response of wave propagation in magneto-electro-elastic square column

“…Furthermore, there is rare research on three-dimensional body-wave propagating in a magneto-electro-elastic structure. Although some conclusions about SH wave [6][7][8] propagation through piezoelectric plate or magneto-electro-elastic materials were reported, they cannot reflect the whole feature we considered. In general, the Bessel-Fourier expansion method [9] and the Stroh method [10] can be applied in studying the body-wave problem of a magneto-electro-elastic structure.…”

General form of the Green’s function regular at infinity for the homogeneous Sturm–Liouville matrix operator

“…As we know the eigenvalues can be real or complex numbers. From expression (15), the following situations were analyzed considering P + Y = 0 (C = 0):…”

“…[15] for an homogeneous material that exhibits magneto-electro-elastic properties with 6 mm symmetry. The system consists of five coupled partial differential equations whose unknowns are the three elastic displacement components: (u x , u y , u z ), the electric potential function (ϕ) and the magnetic potential function (ψ ).…”

“…The following analysis is valid for any N ≥ 1. Since our secular matrix Q (k j ) is self-adjoint we can use the expression (15) to analyze the eigenvalue k j corresponding to our QEP, namely:…”

“…As mentioned earlier, magneto-electro-elastic modes were studied for an homogeneous material with 6 mm symmetry. In this case, constitutive equations were expressed in matrix form [15] and clearly showed the reduction in the number of independent coefficients: only 5 elastic, 3 piezoelectric, 2 dielectric, 3 piezomagnetic, 2 magnetic permeabilities and 2 magnetoelectric coefficients.…”