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研究了间隙波在功能梯度压电板和压电半空间结构中的传播性质.功能梯度压电板的材料性能沿x2方向呈指数变化,首先推导了间隙波传播时的解析解,利用界面条件得到了间隙波的频散方程,基于推导的频散方程,结合数值算例分析了功能梯度压电材料的梯度、压电层厚度以及材料性能对间隙波相速度的影响,研究结果对功能梯度压电材料的覆层结构在声波器件中的应用具有重要的参考价值. 相似文献
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覆盖层为功能梯度材料弹性半平面中的Love波 总被引:1,自引:0,他引:1
对均匀各向同性弹性半平面上覆盖一层功能梯度材料中存在的Love波的频散问题进行了研究,给出了Love波频散方程的一般形式。利用WKBJ近似理论,给出了功能梯度材料层的位移、应力近似解析解,导出了Love波WKBJ近似频散方程的一般形式。该文以功能梯度材料层的剪切弹性模量和质量密度沿厚度方向均为指数函数变化为例,进行了实例计算和分析,给出了频散曲线,讨论了Love波在功能梯度材料覆盖层弹性半平面中传播的一般性质。这些结论对无损检测和反问题分析方法的改进提供理论依据。 相似文献
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利用积分方程方法,本文研究了夹在两个均匀压电半空间的功能梯度压电带界面共线双裂纹的反平面问题。在电渗透型边界条件下,通过Fourier余弦变换将所考虑的问题化为一对偶积分方程,再用Copson方法将该对偶积分方程转化为Fredholm方程进行数值求解,从而给出了裂纹尖端的应力强度因子,电位移强度因子的表达式。分析了裂纹长度,功能梯度非均匀参数以及材料的几何尺寸等对应力强度因子的影响。 相似文献
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研究了正交各向异性层与压电半空间非理想连接时Love波的传播特性。其中,界面条件由剪切滞后模型表征,正交各向异性层表面机械自由。首先,对压电材料和正交各向异性材料的波动方程进行求解,然后利用界面条件和边界条件推导了显函形式的频散方程,最后进行了数值计算,分析了界面性态、压电材料性能和正交各向异性程度对频散特性的影响。分析结果表明:Love波的传播速度随着界面约束强度的降低而减小;当不理想程度较高时,正交各向异性程度和压电材料性能对Love波的传播速度影响不大。 相似文献
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功能梯度材料在机械、光电、核能、生物工程领域的应用非常广泛.但由于生产技术及工作环境等方面的原因,功能梯度材料内部常常产生各种形式的裂纹并最终导致材料破坏,这将会给材料所处的整个系统带来巨大损失.因此研究功能梯度材料的断裂问题对于该种材料的设计,制备和合理、安全的应用具有极大的促进作用.本文在压电材料线性宏观理论下,研究了功能梯度压电带中偏心裂纹对SH波的散射问题.借助于积分变换方法,在电非渗透型边界条件的情况下,将所考虑的问题转化为奇异积分方程,运用Gauss-Chebyshev数值积分方法对奇异积分方程进行了数值求解,进而得到了裂纹尖端的应力和电位移强度因子. 相似文献
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针对压电功能梯度板的静力学问题,建立了一种基于三阶剪切变形理论的等几何分析求解方法。其中,定义功能梯度板的材料属性为板厚方向的幂函数分布,并假设压电功能梯度板中的机械位移场与电势场相互独立。利用压电材料的第二类本构方程以及哈密顿变分原理,推导出压电功能梯度板的相关等几何有限元方程。在压电功能梯度板的自由振动分析中,研究了各类机械边界条件的等几何数值方法的收敛性及精度问题。并分析了开短、路状电学边界条件、功能梯度指数n、功能梯度层的宽厚比、压电层与功能梯度层的厚度比对其固有频率的影响。分析了机械载荷、电载荷以及机电耦合情况下,压电功能梯度板的静态弯曲行为,并利用位移反馈控制规律实现了压电功能梯度板的闭环变形控制。通过算例及相关文献对比,表明了本文求解方法的精确性和可靠性。 相似文献
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The propagation of Love waves in a smart functionally graded piezoelectric structure is analyzed by applying elastic wave theory. There is an additional functionally graded layer between the piezoelectric layer and the substrate in this smart structure. When the piezoelectric and dielectric constants vary individually in a functionally graded layer, the asymptotic solutions of Love waves are obtained by applying the WKB method and solving the fourth order differential equation with variable coefficients. The effects of gradient variation on the phase velocity and the coupled electromechanical factor are discussed in detail. The analysis shows that the number of vibration modes is greater than that in the non-graded layer structure, and the coupled electromechanical factor increases with the increase of piezoelectric constant graded variation. Presented results are useful for the improvement of properties of surface acoustic wave (SAW) devices. 相似文献
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Summary. The propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress is studied. Solutions of the mechanical displacement and electrical potential function are obtained for the isotropic elastic layer and transversely isotropic piezoelectric substrate, respectively, by solving the coupled electromechanical field equations. Firstly, effects of the inhomogeneous initial stress on the dispersion relations and phase velocity of Love wave propagation are discussed. Then the influence of the initial stress gradient coefficient on the stress, mechanical displacement and electrical potential distribution in the layer and the substrate is investigated in detail. The results reported in this paper are not only meaningful for the design of surface acoustic wave (SAW) devices with high performance, but also effective for evaluating the residual stress distribution in the layered structures. 相似文献
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This paper proposes an improvement of the Legendre polynomial series method to solve the harmonic wave propagation in multilayered piezoelectric spherical plates, which are used in point-focusing transducers. The conventional Legendre polynomial method can deal with the multilayered structures only when the material properties of two adjacent layers do not change significantly and cannot obtain correctly normal stress and normal electric displacement shapes unlike the proposed improved orthogonal polynomial approach which overcomes these drawbacks. Detailed formulations are given to highlight its differences from the conventional Legendre polynomial approach. Through the comparisons of numerical results given by an exact solution (obtained from the reverberation-ray matrix method), and by the conventional polynomial approach and the improved polynomial approach, the validity of the proposed approach is illustrated. The influences of the radius-to-thickness ratio on dispersion curves, stress and electric displacement distributions are discussed. It is found that three factors determine the distribution of mechanical energy and electric energy at higher frequencies: radius-to-thickness ratio, wave speed, and position of the component material. 相似文献
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Three-dimensional nonlinear thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers under the effect of asymmetric thermo-electro-mechanical loads is carried out. The strain–displacement relations are based on the nonlinear Lagrangian strain–displacement relations; that is, nonlinear terms containing derivatives of the displacement in the radial direction are included. Material properties of the shell are assumed to be graded in the radial direction according to a power law but the Poisson’s ratio is assumed to be constant. Cylindrical shells are assumed to be under the effect of pressure loading in cosine form, ring pressure loads, electric and temperature fields. Numerical results of stress, displacement, electric and thermal fields are obtained by using two versions of the differential quadrature methods, namely polynomial and Fourier quadrature methods. The convergence of the solution is studied, and results of the axisymmetric loadings are verified with reported results for a cylindrical shell with material properties obeying a power law. Effects of the grading index of material properties, the temperature difference, the ratio of the mean radius to the thickness of the shell, boundary conditions, the thickness of piezoelectric layers and electric excitation on stress, displacement, electric and temperature fields are presented. 相似文献
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In the present paper, the dynamic behavior of a Griffth crack in the functionally graded piezoelectric material (FGPM) is investigated. It is assumed that the elastic stiffness, piezoelectric constant, dielectric permittivity and mass density of the FGPM vary continuously as an exponential function, and that FGPM is under the anti-plane mechanical loading and in-plane electrical loading. By using the Fourier transform and defining the jumps of displacement and electric potential components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement and electric potential components across the crack surface are expanded in a series of Jacobi polynomial. Numerical examples are provided to show the effects of material properties on the stress and the electric displacement intensity factors. 相似文献
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《International Journal of Engineering Science》2007,45(2-8):455-466
The propagation behavior of transverse surface waves (Love waves) in a piezoelectric half space of polarized ceramics carrying a functionally graded material layer is studied from the three-dimensional equations of linear piezoelectricity. The Wentzel–Kramers–Brillouin (WKB) asymptotic technique is adopted for the theoretical derivations of analytical solutions in the functionally graded layer. The dispersion relations of Love wave in the structure are obtained for both electrically open and shorted cases. Firstly, these solutions are used to study effect of the gradient coefficients on the dispersive relations and phase velocities of Love wave propagation. Then influence of the gradient coefficients on the electromechanical coupling factor is discussed in detail. The results reported are meaningful for the design of surface acoustic wave (SAW) devices with high performance. 相似文献
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The existence and propagation behavior of Love waves in a functionally graded material (FGM) layered structure are theoretically investigated in this paper based on the three-dimensional equations of linear electricity. The Wentzel–Kramers–Brillouin (WKB) method is applied to obtain the analytical solutions in the FGM layer. The dispersion equation for a Love surface wave in this kind of structure is obtained in a simple mathematical form, where the material property variation of the FGM layer is arbitrary. First, the solution is used to study the effect of the gradient coefficients on the dispersion curves and the phase velocities of Love waves. Then, the influence of gradient coefficients on the stress and displacement fields is discussed in detail. The reported results are important in the design of surface acoustic wave (SAW) devices with high performance. 相似文献
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The characteristics of the guided waves propagation in functionally graded rods with rectangular cross-section (finite width and height) under initial stress are investigated in this paper based on Biot’s theory of incremental deformation. An extended orthogonal polynomial approach is present to solve the coupled wave equations with variable coefficients. By comparisons with the available results of a rectangular aluminum rod, the validity of the present approach is illustrated. The dispersion curves and displacement profiles of various rectangular functionally graded rods are calculated to reveal the wave characteristics, and the effects of different width to height ratios and initial stress and gradient functions on the guided waves are discussed in detail. 相似文献