Edge Waves In Semi-infinite Piezoelectric Plates

Edge wave is a type of elastic guided wave that propagates along the edge of a semi-infinite structure,and decays in the direction perpendicular to the propagation.This means that the energy is mainly concentrated on the edge of the structure,and there is almost no vibration in the area away from the edges.Because of its special properties,edge waves have been widely used in the fields of nondestructive testing of thin-walled structures and the measurement of material properties.Most of the reported work focuses on the edge dynamic characteristics of pure elastic structures.The wide application of piezoelectric materials and the performance monitoring of acoustic devices urgently need to carry out the related research work on edge problems.This paper studies the propagation characteristics of edge waves in a semi-infinite piezoelectric composite plate and a piezoelectric plate resting on a Pasternak foundation.The main contents and results are as follows:Based on the high-order Ambartsumian plate theory,the propagation characteristic of edge waves in a semi-infinite piezoelectric composite plate consisting of a piezoelectric strip plate and an elastic plate are studied.The governing equations of the edge wave are derived by using Hamiltonian principle.Considering the different electrical boundary conditions of the upper and lower surfaces as well as the end of the plate,the dispersion relations of the edge waves are obtained.The effects of the boundary conditions,the width-thickness ratio of the piezoelectric strip and the properties of the piezoelectric and elastic materials on the dispersion characteristics and modes of the edge wave are discussed and compared with Kirchhoff theory.The results showed that: When the upper and lower surfaces of the semi-infinite plate are under electrically shorted circuit,the influence of electrical conditions at the end can be ignored.When the upper and lower surfaces are electrically open,the electrical conditions at the ends have a great influence on the phase velocity of the edge waves.The phase velocity of the edge wave in the composite plate is lower than that of the semi-infinite pure elastic plate.The smaller the width to thickness ratio of the piezoelectric strip plate,the faster the propagation velocity of the edge wave,and the larger the corresponding mechanical displacements and electric potential responses.The phase velocities of the edge waves in the semi-infinite composite plate are positively correlated with the Rayleigh surface wave velocities of piezoelectric and elastic materials.Kirchhoff theory is only suitable for low frequency analysis of edge waves,and shear deformation should be considered for high frequency.The edge wave propagation characteristics of a semi-infinite piezoelectric plate supported by a Pasternak foundation are studied.The dispersion relations of edge waves for electrically open circuit and applied potential on the upper and lower surfaces of the plate are derived.The effects of stiffness coefficients of elastic foundation,boundary conditions,applied potential and piezoelectric material properties on phase velocity and mode of edge wave are analyzed.The results showed that: The effect of the stiffness coefficients of elastic foundation on the dispersion characteristics of edge waves is mainly concentrated in the range of small wave number.With dimensionless wavenumber increases,the influence of the stiffness coefficients gradually disappears.Within the scope of the small wavenumber,the larger the stiffness coefficients the larger the phase velocities of edge waves.Comparing with the electrically shorted condition,the effect of stiffness coefficients on dispersion curves of electrically open case is more significantly.The external potential has a great influence on the dispersion curve in the low frequency range.The phase velocity increases under positive potentials,and the reverse potential can reduce the propagation velocity of edge waves.The larger the velocity of the Rayleigh surface wave in the piezoelectric half-space,the faster the edge wave propagates.