共查询到16条相似文献,搜索用时 125 毫秒
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《应用力学学报》2020,(3)
研究含梯度残余应力的弹性半无限体的平面应变型表面波,即广义Rayleigh波。将该结构等效为含梯度初应力的弹性覆盖层和无初应力的弹性基底构成的半无限体结构。求得覆盖层中位移函数的幂级数解与均质基底位移函数的解析解,并代入边界条件,得到频散方程。针对拉、压残余应力,分别讨论了其随厚度方向均匀分布、线性变化和指数变化情况下广义Rayleigh波的一阶模态频散特性。数值结果表明:随着拉应力增大,广义Rayleigh波波速会增加,反之,压应力的增大会导致波速的降低;残余应力均匀分布时波速的改变量较大,线性变化次之;当残余应力按照指数函数变化时,梯度参数越趋近于零,其结果越趋近于线性变化情况,随着梯度参数的减小,波速改变量也随之减小。当使用广义Rayleigh波频散特性实现残余应力无损检测时,如果采用与实际梯度渐变残余应力不符的均匀残余应力模型将会低估表面残余应力。本文所得结论可为利用广义Rayleigh波实现梯度残余应力无损检测提供理论基础。 相似文献
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对剪切弹性模量沿深度以指数函数变化的非均质半空间,本文用摄动法得到了Rayleigh面波的波函数解答及相速度方程。以不同金属与陶瓷复合而成的几种梯度材料为例,用数值方法求解了相速度方程,给出了相应的波的弥散曲线,结果表明,梯度介质半空间自由表面附近的Rayleigh波通常有两种不同的弥散形式,即正常弥散和非正常弥散。 相似文献
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研究功能梯度Kelvin模型粘弹性板中Lamb波传播的频散和衰减特性,基于弹性力学理论,建立了以位移函数表示的功能梯度粘弹性板中Lamb波传播问题的控制方程;采用幂级数方法求得其渐近解,得到波速-波数方程的解析形式;采用最小模值逼近法求解复数域超越方程。通过对比均质粘弹性板和特殊梯度粘弹性板中Lamb波传播的精确解析解和幂级数渐近解,由此验证幂级数解的可靠性。研究结果表明:当梯度参数同时变化时,梯度板中的Lamb波波速的实部、虚部、减幅系数较均匀板中均无显著变化;仅密度梯度参数增大时波速实部和虚部绝对值都减小,减幅系数增大;仅弹性模量梯度参数增大时,波速实部和虚部绝对值都增大,减幅系数减小。准S0模态和准A0模态的减幅系数基本相同,而与准A1模态相差较大。在同模态下频率越高减幅系数越大,同频率下高模态对应的减幅系数较小。这些结论可为非均质粘弹性板结构无损检测提供理论依据。 相似文献
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利用应力函数半逆解法,研究了均布载荷作用下、材料属性在厚度上任意变化的功能梯度简支梁弯曲的解析解,给出了各向应力应变与位移的解析显式表达式.首先根据平面应力状态的基本方程,得出了功能梯度梁的应力函数应满足的偏微分方程,并根据应力边界条件得出了各应力分布的表达式;进而根据功能梯度材料的本构方程和位移边界条件,得出了应变和位移的分布.最后,通过将本文的解退化到均质各向同性梁并与经典弹性解比较,证明了本文理论的正确性,并求解了材料组分呈幂律分布的功能梯度梁的应力和位移分布,分析了上下表层材料的弹性模量比λ与组分材料体积分数指数n对应力和位移分布的影响. 相似文献
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《International Journal of Solids and Structures》2014,51(21-22):3689-3697
The paper investigates the existence of Love wave propagation in an initially stressed homogeneous layer over a porous half-space with irregular boundary surfaces. The method of separation of variables has been adopted to get an analytical solution for the dispersion equation and thus dispersion equations have been obtained in several particular cases. Propagation of Love wave is influenced by initial stress parameters, corrugation parameter and porosity of half-space. Velocity of Love waves have been plotted in several figures to study the effect of various parameters and found that the velocity of wave decreases with increases of non-dimensional wave number. It has been observed that the phase velocity decreases with increase of initial stress parameters and porosity of half-space. 相似文献
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Zheng-Hua Qian Feng Jin Kikuo Kishimoto Tianjian Lu 《International Journal of Solids and Structures》2009,46(6):1354-1361
The propagation behavior of Love waves in a functionally graded material layered non-piezoelectric half-space with initial stress is taken into account. The Wentzel–Kramers–Brillouin (WKB) technique is adopted for the theoretical derivations. The analytical solutions are obtained for the dispersion relations and the distributions of the mechanical displacement and stress along the thickness direction in the layered structure. First, these solutions are used to study the effects of the initial stress on the dispersion relations and the group and phase velocities, then the influences of the initial stress on the distributions of the mechanical displacement and shear stresses along the thickness direction are discussed in detail. Numerical results obtained indicate that the phase velocity of the Love waves increases with the increase in the magnitude of the initial tensile stress, while decreases with the increase in the magnitude of the initial compression stress. The effects on the dispersion relations of the Love wave propagation are negligible as the magnitudes of the initial stress are less than 100 MPa. Some other results are obtained for the distributions of field quantities along thickness direction. The results obtained are not only meaningful for the design of functionally graded structures with high performance but also effective for the evaluation of residual stress distribution in the layered structures. 相似文献
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The present paper framed to study the impact of heterogeneity on propagation of Love wave in a heterogeneous micropolar layer over an elastic inhomogeneous stratum, when both rigidity and density are assumed to vary linearly with depth. The equations of motion have been formulated separately for layer and half-space under suitable boundary conditions. Analytical solution for the dispersion equation has been obtained using method of separation of variables by means of the Airy function and Whittaker function. Some particular cases have also been investigated. Further, as a special case the velocity equation for isotropic layer over a homogeneous half-space coincides with the standard result of Love wave. Numerical calculations of frequency relation have been performed and depicted by means of graphs to exhibit the substantial impact of heterogeneity, micropolar parameters and wave number on the phase velocity of Love wave. The wave velocity is strongly influenced by these parameters. 相似文献
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X. Y. Li Z. K. Wang S. H. Huang 《International Journal of Solids and Structures》2004,41(26):310-7328
To investigate the features of Love waves in a layered functionally graded piezoelectric structure, the mathematical model is established on the basis of the elastic wave theory, and the WKB method is applied to solve the coupled electromechanical field differential equation. The solutions of the mechanical displacement and electrical potential function are obtained for the piezoelectric layer and elastic substrate. The dispersion relations of Love waves are deduced for electric open and short cases on the free surface respectively. The actual piezoelectric layer–elastic substrate systems are taken into account, and some corresponding numerical examples are proposed comparatively. Thus, the effects of the gradient variation about material constants on the phase velocity, the group velocity, the coupled electromechanical factor and the cutoff frequency are discussed in detail. So the propagation behaviors of Love waves in inhomogeneous medium is revealed, and the dispersion and the anti-dispersion are analyzed. The conclusions are significant both theoretically and practically for the surface acoustic wave devices. 相似文献
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Zheng-Hua Qian Feng Jin Sohichi Hirose 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(11):1743-1755
An analytical approach is used to investigate the effects of covering layer thickness on the propagation behavior of Love
waves in functionally graded piezoelectric materials (FGPMs) covered with a dielectric layer. The piezoelectric substrate
is polarized in the direction perpendicular to the wave propagation plane, and its material parameters change continuously
along the thickness direction. The dispersion equations for the existence of Love waves with respect to phase velocity are
obtained for electrically open and shorted cases, respectively. A detailed investigation of the effects of the covering dielectric
layer thickness on dispersion curve, phase velocity, group velocity, and electromechanical coupling factor is carried out.
Numerical results show that for a given FGPM, the covering dielectric layer thickness affects significantly the fundamental
mode of Love waves but has only negligible effects on the high-order modes. The changes in phase velocity, group velocity,
and electromechanical coupling factor due to the change of gradient coefficient of FGPMs could be approached approximately
by changing the thickness of the covering dielectric layer, which imply a potential factor for designing new-type surface
wave devices with FGPMs. 相似文献
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The stress fields are obtained for a functionally graded half-plane containing a Volterra screw dislocation.The elastic shear modulus of the medium is considered to vary exponentially.The dislocation s... 相似文献