Bending Edge Waves In Semi-infinitely Orthotropic Piezoelectric Plates

Piezoelectric materials are widely used to fabricate various devices such as sensing,energy conversion,filtering and frequency control because they can convert mechanical energy to electrical energy,vice versa.The propagation property of elastic waves in piezoelectric materials and structures is an important scientific problem related to device design and application.The edge wave is a kind of elastic guided wave with special dynamic properties.Its vibration energy is mainly concentrated near the edge of a semi-infinite structure and decays rapidly in the direction perpendicular to the wave propagation.This unique characteristic makes the piezoelectric acoustic wave device based on edge mode has more advantages in device miniaturization.In this dissertation,the propagation characteristics of bending edge waves in semi-infinitely orthotropic piezoelectric plate and sandwich plate are studied.The main contents and results are as follows:1.Based on the two-variable refined plate theory,the first-order Reissner-Mindlin plate theory and the classical plate theory,the propagation characteristics of bending edge waves in a semi-infinitely orthotropic piezoelectric plate are studied.The governing equations of the problem are derived by Hamilton principle,and the dispersion relation of the bending edge waves are obtained by using the mechanical and electrical boundary conditions applied to the plate edge.The applicability of different plate theories to bending edge wave is revealed.The effects of electrical boundary conditions,material properties and applied voltage on the phase velocity and group velocity of bending edge waves are numerically discussed.The results show that the classical plate theory is only applicable to the range of relatively small wavenumber,and the phase velocity is seriously overestimated when the wavenumber is large.The phase velocities calculated by the first-order Reissner-Mindlin plate theory and the twovariable refined plate theory are very close in the whole wavenumber range.The electrical boundary condition at the plate edge has nearly no effect on the phase velocity and group velocity,and the influence of the electrical boundary conditions of the plate edge can be ignored in practical applications.The phase velocity of the bending edge waves is positively related to the Rayleigh surface wave velocity in the piezoelectric half space.The larger the Rayleigh surface wave velocity,the faster the bending edge waves propagates.The phase velocity of the bending edge waves in the piezoelectric plate with stronger anisotropy is lower than that of weaker anisotropy.The influence of applied voltage on the phase velocity of bending edge wave is mainly concentrated in the range of small wavenumber.The positive voltage leads to the decrease of wave velocity,while the negative voltage increases the wave velocity.2.Based on the two-variable refined plate theory,the propagation characteristics of bending edge waves in a semi-infinitely orthotropic piezoelectric sandwich plate are studied.Two configurations are considered: elastic/piezoelectric/elastic and piezoelectric/elastic/piezoelectric sandwich plates.The governing equations of the problem are derived by Hamilton principle.According to the mechanical and electrical boundary conditions at the edge of the sandwich plate,the dispersion relations of the bending edge waves are obtained.The effects of electrical boundary conditions,thickness ratio and constituent material properties on the dispersion characteristics of the bending edge waves are discussed through some numerical examples.It is shown that the electrical boundary conditions applied at the plate edge have very small effect on the phase velocity of the bending edge waves in the two configurations.The propagation velocity of the bending edge waves in the elastic/piezoelectric/elastic sandwich plate is much higher than that in the piezoelectric/elastic/piezoelectric sandwich plate with the same constituents.When the Rayleigh surface wave velocity of the elastic layer is higher than that of the piezoelectric layer,the phase velocity of the bending edge waves increases with the increase of the thickness ratio.The larger the Rayleigh surface wave velocity of the constituent material in the sandwich plate,the faster the propagation speed of the bending edge wave along the edge of the plate.