The Electro-Mechanical Coupling Surface Waves In A Triangular-Crystal Piezoelectric Half-Space And Layered Half-Space

The propagation of surface waves in triangular structures is of great practical significance and has attracted more and more attention.However,it is complicated because the three displacement directions are not coupled.In this paper,the electro-mechanical coupling surface waves of triangular-crystal piezoelectric half-space and layered half-space in three displacement directions are considered.The main research content of this paper includes the following aspects:(1)The propagation of surface-coupled waves in half-space structures of piezoelectric triangular crystal system is studied,and the piezoelectric triangle is considered.Under the influence of material parameters C14 and e22,a model of the half-space structure of piezoelectric triangular crystal system is established.Based on the basic equations of elastic dynamic theory and piezoelectric theory,a system of partial differential equations expressed by three displacement functions and potential functions is obtained.By substituting the trial solution,the system of partial differential equations is transformed into ordinary differential equations,and the displacement component and potential function are rewritten from the solution of ordinary differential equations.Then the dispersion equation is obtained through the constraint of stress freedom,continuous boundary condition and attenuation condition.The surface wave of piezoelectric triangle crystal in half-space structure is decoupled by three displacement components,and the velocity is constant.The numerical examples show that the material parameters C14 and e22 have influence on the surface coupling wave propagation characteristics of the piezoelectric triangular crystal in the half-space structure and cannot be ignored.If the material parameter C14 of triangular crystal system is ignored,the lithium niobate phase velocity and electro-mechanical coupling coefficient will be underestimated,and the lithium tantalate phase velocity and electromechanical coupling coefficient will be overestimated.If the material parameter e22 of triangular crystal system is ignored,the phase velocity of lithium niobate will be underestimated,the electro-mechanical coupling coefficient will be overestimated,and the phase velocity and electromechanical coupling coefficient of lithium tantalate will be overestimated.In the half-space structure of piezoelectric triangular crystal system,the coupling wave is dispersion-free,and the attenuation of surface coupling wave tends to zero at the depth of 1.5λ.(2)Considering that the material parameters of the triangular crystal system are not consistent with the structure axis,that is,the surface coupling wave propagation characteristics in the halfspace structure of the piezoelectric triangular crystal system are present when the axis is rotated.The material parameter expressions of the axis rotated at different angles are obtained,and the wave equation and dispersion equation of the electro-mechanical coupling are derived.The phase velocity,electromechanical coupling coefficient and wave structure of surface coupled wave are analyzed by numerical examples under different rotation angles.The results show that when γ=0 and a is a constant value,the phase velocity decreases first and then increases with the increase of β,and the rotation angle corresponding to the minimum value of the phase velocity is around 700 or 110°.β=0,α is a constant value,and the maximum phase velocity of β changes around 60° and 120°.α=0,α is a constant value,and γ changes phase velocity at a maximum value around 90°.The rotation angle can slow down the attenuation of the wave.At the depth of 1.5λ～2.5λ,the attenuation of the coupled wave tends to zero.(3)The coupled surface waves in a layered half-space composed of lithium niobate and silicon are studied.The thickness of silicon is much greater than the thickness and wavelength of lithium niobate.The dispersion equation related to wave number and phase velocity is derived.Based on the basic equations of elastic dynamic theory and piezoelectric theory,a system of partial differential equations expressed by three displacement functions and potential functions is obtained.By substituting the trial solution,the system of partial differential equations is transformed into ordinary differential equations,and the solutions of ordinary differential equations are rewritten as displacement components and potential functions.Then the dispersion equation is obtained by free boundary condition,continuous boundary condition and attenuation condition.The results show that the phase velocity of the surface coupled wave decreases until it becomes stable with the increase of kh,and the surface coupled wave of the triangular crystal system is normally dispersed.When kh-1 and kh=10,the coupled surface wave is dominated by u3.At the sub-surface depth of 1.5～2.5λ,the attenuation of the coupled surface wave tends to zero.These conclusions can provide theoretical basis for the application of lithium niobate in surface acoustic wave devices.