Edge Waves And Edge Modes In Semi-infinite Piezoelectric Plates

Piezoelectric materials can realize the mutual conversion between mechanical energy and electrical energy,and have great potential in the fields of sensing,energy conversion,actuator,energy harvesting and communication.The design and application of many piezoelectric components are based on the mechanical analysis of wave motion and vibration.Therefore,it is of great scientific significance and application value to study the wave propagation and vibration characteristics of piezoelectric materials.Edge phenomena include edge waves and edge resonance,which mean that the vibration is mainly concentrated at the edges of the structure,and there is almost no vibration in the area far from the edge.The special properties of edge mode of the piezoelectric structure can provide theoretical guidance for the miniaturization and performance improvement of piezoelectric acoustic wave devices.However,compared to other dynamics,the study of edge problems,especially for piezoelectric structures,is very limited.The objective of this dissertation is to study the edge waves and edge resonance in semi-infinite piezoelectric plates and to reveal the characteristics of edge dynamics.Based on the first-order Reissner-Mindlin plate theory,the propagation characteristic of edge bending waves in semi-infinite transversely isotropic piezoelectric plates is studied.The dispersion relation of edge bending waves is obtained by employing the electro-mechanical boundary conditions of the upper and lower surfaces as well as the end of the traction-free plate.The effects of electrical boundary conditions,electrical potential distribution along the thickness of the plate,and the properties of piezoelectric material on the phase velocity,attenuation,and modes of the edge wave are analyzed through numerical computations.The results show that the electrical boundary conditions applied on the free end have great effect on the property of edge wave when the upper and lower surfaces of the piezoelectric plate are subjected to electrically open circuit,while has nearly no effect when upper and lower surfaces are electrically shorted.And then we can discard the electrical constraint applied on the end in case of electrically shorted surfaces.The phase velocity of edge waves in a semi-infinite piezoelectric plate is related to the Rayleigh surface wave velocity in piezoelectric half-space.The larger the Rayleigh wave velocity,the larger the edge wave velocity.The influence of distribution of electrical potential along the thickness of plate on the edge wave dispersion can be ignored due to its very few variation.The classical Kirchhoff theory may significantly overestimate the frequencies of localized edge waves compared with Reissner-Mindlin plate theory.Consider a semi-infinite piezoelectric plate consists of a semi-infinite piezoelectric plate and a thin elastic strip.The thickness of the thin elastic strip is same as the thickness of the piezoelectric plate.The interface is perfectly bonding and the electrical potential at the interface is taken to be zero.Propagation behavior of edge bending waves in such edge-reinforced piezoelectric plate is theoretically investigated.The influences of thin elastic strip on the propagation characteristics of edge waves are analyzed.The results show that the thin strip has strong effect on phase velocity of edge wave,but the width-thickness ratio has less effect on dispersion property.The higher modes which have their cut-off frequencies occur when the width-thickness ratio becomes larger.Moreover,the magnitude of higher modes increases as the width-thickness ratio increasing.The case of electrically shorted surfaces can produce a high frequency of edge bending wave.The thickness-twist edge mode in a semi-infinite piezoelectric plate is studied.The piezoelectric material is considered as orthorhombic crystal with mm2 symmetry.The exact solution for certainly electro-mechanical boundary condition is obtained and the resonant frequencies of three piezoelectric crystals are calculated numerically.It is shown that the upper and lower surfaces and free ends should be both electrically open in order to inspire the edge thickness-twist resonance in a semi-infinite piezoelectric plate while no edge mode can be found for any other boundary conditions.The obtained results provide the possibility of new thickness-twist plate edge modes for piezoelectric resonators and acoustic wave sensors.