Propagation of Lamb waves in transversely isotropic piezoelectric elastic plate

Abstract

The propagation of Lamb waves in a homogeneous, transversely isotropic, piezoelectric plate subjected to charge free and electrically shorted, stress free boundary conditions is investigated. Secular equations for the plate in closed form and isolated mathematical conditions for symmetric and anti symmetric wave mode propagation in completely separate terms are derived. It is shown that motion of purely transverse (SH) mode gets decoupled from rest of the motion and remains unaffected due to piezoelectric effects. At short wavelength limits the secular equation for symmetric and skew-symmetric waves in both charge free and electrically shorted, stress free plate reduce to Rayleigh surface wave frequency equations because a finite plate in such situation behave like a semi-infinite medium. The amplitudes of displacement and electrical potential have also been computed in case of symmetric and skew-symmetric motions of the plate. Finally, numerical solution is carried out for cadmium-selenide (6 mm class) material. The dispersion curves and amplitudes of displacements and electrical potential for symmetric and antisymmetric wave modes are presented graphically in order to illustrate and compare the analytical results. The theory and numerical computations is found to be in close agreement. The various wave

characteristics are found to be more stable and realistic in the presence of piezoelectric effects than in the absence of such a effect thereby making such materials more viable for practical importance and use.