梯度半空间梯度覆层中的Love波

对功能梯度弹性半空间上覆盖一层功能梯度材料中的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. 对功能梯度弹性半空间和功能梯度覆层的反平面剪切波的运 动控制方程进行了求解，给出了半空间和覆盖层的位移、应力解析解，给出了Love波在该解析 解下的频散方程. 以覆盖层的剪切弹性模量和质量密度均呈指数函数变化，半空间的剪切弹 性模量和质量密度均呈抛物线变化为例，利用迭代方法对频散方程进行了求解，给出了频散 曲线. 结果显示：在最低阶振型频散曲线中出现截止频率.     

功能梯度材料板中Lamb波传播特性研究

对材料性能参数沿厚度连续变化的横观各向同性热应力缓和型功能梯度材料板中Lamb波的传播问题,采用幂级数法,求得其相速度方程.借助数值算例,分析了参数梯度变化对Lamb波频散曲线的影响,并与相应陶瓷板和金属板中的频散曲线进行了对比.进一步研究了参数梯度变化对波结构的影响,揭示了Lamb波在这种非均质板中的传播行为,所得结果可以为功能梯度材料及结构的超声表征与检测提供理论依据.     

功能梯度圆柱板中的周向衰逝导波

与传播波模态不同,衰逝波模态波数为纯虚数或复数,它们随传播距离呈指数或阻尼式衰减。复数根描述的衰逝波对结构缺陷形状和尺寸的导波检测具有重要作用,但其求解却是非常困难的,通常要借助于各种迭代技术。本文提出一种计算求解衰逝波问题的改进的Legendre正交多项式方法,该方法可将复杂的变系数微分方程组计算转换为特征值求解问题,无需迭代便能计算得到包含实波数域、虚波数域和复波数域的完整的频散曲线。通过具体算例验证了提出方法的正确性。应用提出方法计算了不同梯度圆柱板中的衰逝导波,绘制了三维频散曲线,研究了不同径厚比和梯度场对衰逝导波频散的影响,分析了衰逝导波的位移和应力分布,讨论了衰逝导波的传播特性。     

功能梯度压电夹层结构中SH波的传播

研究了功能梯度压电上、下半空间和均匀压电层组成的夹层结构中SH波的传播性能,上、下功能梯度半空间的材料性能沿垂直于界面方向以指数函数形式变化。首先推导了SH传播时电弹场的解析解,然后利用界面条件得到了行列式形式的频散方程。基于推导的频散方程,通过数值算例表明了材料性能梯度变化、压电层厚度和材料组合方式对相速度的影响,结果对功能梯度压电材料在声波器件中的应用有参考价值。     

SH波在局部非均匀声子晶体中的传播

使用传输矩阵法,研究了水平剪切波(SH波)在一维局部材料非均匀声子晶体中的传播。首先使用皮亚诺方程给出了SH波在特定非均匀梯度介质声场的传输矩阵。然后使用传输矩阵和布洛赫定律给出了该声子晶体的禁带结构和传输系数。通过具体计算,发现这种非均匀性能明显影响声子晶体的频散曲线和禁带结构。然后比较了幂指数取不同值时,禁带结构与归一化频率和填充比的关系。发现幂指数不同,声子晶体的禁带不同。     

多层圆柱体锚固结构中超声导波频散特征的研究

超声导波无损检测技术因其高效和快捷的优点成为检测锚杆锚固质量的有效方法。但锚固锚杆结构中超声导波的多模态性、频散性与能量泄露导致完整的锚杆底端反射信号的获得具有不确定性。应用弹性动力学理论并采用全局矩阵法建立超声导波在多层圆柱体锚固结构中的频散方程的通用表达式,然后通过非线性外推法和二分法两步算法求解频散方程的精确解,解决了频散曲线的分类和相交等难题,获得了具有自主知识产权的求解多层圆柱体锚固结构频散曲线的程序。利用该程序计算了不同锚固锚杆结构的频散曲线,并与商用软件Disperse计算的结果吻合较好。同时用本程序计算了实验室有限锚固结构中的频散曲线,验证了低频导波在有限与无限结构中的巨大差异,而这一结构特征的频散特性Disperse并未给出相关算例。     

高频纵向导波在钢杆中传播特性的研究

计算了钢杆中纵向轴对称导波模态的衰减频散曲线和群 速度频散曲线. 分析了1~3MHz范围内高频纵向轴对称超声导波在钢杆中的传播特 性. 理论分析表明，各高阶纵向模态都存在一个衰减最小值，在此衰减最小值所对应频率下 的高阶模态能传播较远距离，可用于钢杆导波检测. 建立实验系统，采用轴对称同端激 励接收的方法，根据第1次端面回波做出群速度和端面回波幅值随频率变化曲线，实验结 果与理论分析基本吻合. 表明考虑材料衰减特性的钢杆频散曲线可以作为实验指导依据.     

功能梯度磁电弹耦合结构中的间隙波

研究了由均匀磁电弹半空间和功能梯度磁电弹层组成的耦合结构中间隙波的传播特性.假定功能梯度层的材料性能沿厚度方向呈指数变化,且其表面机械自由,但承受两种电磁边界条件.首先推导了频散方程,然后结合数值算例分析了功能梯度层材料性能的梯度变化、厚度及电磁边界条件对相速度的影响,结果对功能梯度磁电弹材料在声波器件中的应用具有参考价值.      

GAS WAVE IN FUNCTIONALLY GRADED MAGNETO-ELECTRO-ELASTIC COUPLED STRUCTURE

研究了由均匀磁电弹半空间和功能梯度磁电弹层组成的耦合结构中间隙波的传播特性.假定功能梯度层的材料性能沿厚度方向呈指数变化,且其表面机械自由,但承受两种电磁边界条件.首先推导了频散方程,然后结合数值算例分析了功能梯度层材料性能的梯度变化、厚度及电磁边界条件对相速度的影响,结果对功能梯度磁电弹材料在声波器件中的应用具有参考价值.     

圆柱结构中的环向SH波及洞体内表面波不存在性讨论

目前有关圆柱结构中的环向SH波研究仅限于实心柱体与圆柱壳体结构。由于无法直接获得圆柱洞体中传播的SH表面波的解析解,对比研究了实心柱体和多种不同类型的圆柱壳体中的环向SH波,从波结构、应变能密度幅值分布与壳体厚度的关系讨论洞体内SH表面波的存在性。建立柱坐标系下均匀弹性材料与功能梯度材料环向SH波的波动方程;分别求得方程的贝塞尔函数解和幂级数渐近解;进一步计算得到其频散曲线、波结构与应变能密度幅值。结果表明：幂级数方法可用于计算圆柱型结构中的变系数波动方程,且具有较高的精度;圆柱型结构中环向SH波的能量集中在外表面或次外表面,并随着壳体厚度的增加,能量集中现象更为明显;通过应变能密度幅值分布规律推论出圆柱洞体内表面无法传播环向SH表面波。最后,针对均质结构和梯度结构,采用反证法证明了无法得到满足洞体内SH表面波衰减条件的解析解,从而证明了该推论。     

Characteristics of guided waves in graded spherical curved plates

An elastodynamic solution for the stress wave propagation in spherical curved plates composed of functionally graded materials (FGM) is presented. Properties of materials are assumed to vary in the direction of the thickness according to a known radial variation law (gradient field). The formulation is based on the linear three-dimensional elasticity. The Legendre orthogonal polynomial series expansion approach is used for determining the guided waves dispersion curves in functionally graded spherical curved plates. Our results from a homogeneous anisotropic spherical curved plate are compared with those published earlier to confirm the accuracy and range of applicability of this polynomial approach. Guided wave dispersion curves for graded spherical curved plates with different gradient fields are calculated, and the effects of the gradient field on the characteristics of guided waves are illustrated. Finally, dispersion curves for graded spherical curved plates at different ratios of inner radius to thickness are calculated to discover the influences of that ratio on the wave characteristics.     

Wave characteristics in functionally graded piezoelectric hollow cylinders

Based on linear three-dimensional piezoelasticity, the Legendre orthogonal polynomial series expansion approach is used for determining the wave characteristics in hollow cylinders composed of the functionally graded piezoelectric materials (FGPM) with open circuit. The displacement and electric potential components, expanded in a series of Legendre polynomials, are introduced into the governing equations along with position-dependent material constants so that the solution of the wave equation is reduced to an eigenvalue problem. Dispersion curves for FGPM and the corresponding non-piezoelectric hollow cylinders are calculated to show the piezoelectric effect. The influence of the ratio of radius to thickness is discussed. Electric potential and displacement distributions are used to show the piezoelectric effect on the flexural torsional mode. The influence of the polarizing direction on the piezoelectric effect is illustrated. For the radial and axial polarization, the piezoelectric effect reacts mostly on the longitudinal mode. For circumferential polarization, the piezoelectric effect reacts mostly on the torsional mode. In the FGPM hollow cylinder, piezoelectricity can weaken the guided wave dispersion.     

Wave propagation in graded rings with rectangular cross-sections

In this paper, a double orthogonal polynomial series method is proposed to investigate the guided wave propagation in a two-dimensional (2-D) structure, namely, a FGM ring with a rectangular cross-section. Two kinds of graded rings are considered: material gradient directions being in the radial direction and in the axial direction respectively. Numerical comparison with available reference results for a straightly homogeneous rectangular bar illustrates the validity of the proposed method. The dispersion curves and displacement distributions of various FGM rings, which have different radius to thickness ratios, different material gradient directions and different thickness to height ratios, are calculated to reveal the guided wave characteristics.     

厚壁管道周向超声导波缺陷检测研究

厚壁管道在特种承压设备领域中广泛使用,常规无损检测技术难以实现其快速有效地检测。本文采用数值模拟与实验相结合来研究周向导波快速检测厚壁管道的方法。首先,利用有限差分软件研究了不同角度激励下外径269mm、壁厚32mm的厚壁管道中周向导波的传播特性,优化了探头激励角度范围;然后分别制作了55°和45°的斜楔,并搭建了实验系统,研究了周向导波与厚壁管道壁厚方向不同位置缺陷的相互作用规律。研究结果表明,周向导波适用于厚壁管道快速检测。检测时需选择角度适中的探头。激发角度过小时,厚壁管中形成的周向导波模式较多,使得波包宽度较大,影响检测分辨率;而角度过大时,会使得盲区增大,导致靠近内壁区域缺陷漏检。本文的研究结论为厚壁管道缺陷周向导波的实际检测应用提供了指导。     

Characteristics of elastic waves in FGM spherical shells,an analytical solution

In this paper, we investigate the propagation characteristics of elastic guided waves in FGM spherical shells with exponentially graded material in the radial direction. A new separation of variables technique to displacements is proposed to convert the governing equations of the wave motion to the second-order ordinary differential equations with variable coefficients. By further a variables transform technique, these equations are transformed to the Whittaker equations so that analytic solutions can be obtained. For the spherical shell case, by satisfying the traction-free boundary conditions on both the inner and outer surfaces of the shell, we obtain the dispersion equations, which show that both the SH and Lamb-type wave modes are generated in the structure. The calculated dispersion curves in the functionally graded shell demonstrate a clear influence of the gradient coefficient as compared to those of the homogeneous shell, with the Lamb-type waves more sensitive to the gradient coefficient. The mode shapes and the distributions of stresses in the shells for various gradient coefficients are also presented to illustrate their dependence on the gradient coefficient.     

厚壁管道周向导波检测技术实验研究

厚壁管道是火电机组四大管道系统的核心部件,将超声导波技术应用于厚壁管道的无损检测显得十分重要.首先确定厚壁管道检测的激励方式,优化选取适合厚壁管道检测的0.5MHz探头和楔形块角度为60°的斜探头组合.通过改变斜探头与外壁轴向缺陷之间周向距离,在一定范围内仍可检测到缺陷回波,且接收到的周向回波幅值变化不大,表明周向导波...     

Evanescent waves in FGM spherical curved plates: an analytical treatment

A deep understanding of both guided propagating and evanescent waves is very essential for non-destructive evaluation. Guided propagating waves have received considerable attention, but the research on guided evanescent waves is quite limited, especially for functionally graded structures. This paper presents an analytical approach, based on the orthogonal function technique, to solve the evanescent waves in a spherical curved plate with functionally graded material in the radial direction. The proposed approach can obtain all the real, imaginary and complex solutions but without iterative process. The validity of the proposed approach is illustrated by comparison with available results. The convergence of the approach is also discussed through a numerical example. Dispersion characteristics of the guided waves in various graded spherical curved plates are studied and three dimensional dispersion curves are plotted in frequency-complex wavenumber space. The effects of different radius-thickness ratios and graded fields on the dispersion curves of the guided evanescent waves are illustrated. The displacement distributions are also discussed to analyze the characteristics of the guided evanescent waves.     

GUIDED CIRCUMFERENTIAL WAVES IN DOUBLE-WALLED CARBON NANOTUBES

A model of guided circumferential waves propagating in double-walled carbon nan- otubes is built by the theory of wave propagation in continuum mechanics,while the van der Waals force between the inner and outer nanotube has been taken into account in the model.The dispersion curves of the guided circumferential wave propagation are studied,and some dispersion characteristics are illustrated by comparing with those of single-walled carbon nanotubes.It is found that in double-walled carbon nanotubes,the guided circumferential waves will propagate in more dispersive ways.More interactions between neighboring wave modes may take place.In particular,it has been found that a couple of wave modes may disappear at a certain frequency and that,while a couple of wave modes disappear,another new couple of wave modes are excited at the same wave number.     

Circumferential wave in magneto-electro-elastic functionally graded cylindrical curved plates

Piezoelectric-piezomagnetic functionally graded materials (FGM), with a gradual change of the mechanical and electromagnetic properties, have greatly applying promises. Based on Legendre orthogonal polynomial series expansion approach, a dynamic solution is presented for the propagation of circumferential harmonic waves in piezoelectric-piezomagnetic FGM cylindrical curved plates. The materials properties are assumed to vary in the direction of the thickness according to a known variation law. The dispersion curves of the piezoelectric-piezomagnetic FGM cylindrical curved plate and the corresponding non-piezoelectric and non-piezomagnetic cylindrical curved plates are calculated to show the influences of the piezoelectricity and piezomagnetism. Electric potential and magnetic potential distributions are also obtained to illustrate the different influences of the piezoelectricity and piezomagnetism. Finally, a cylindrical curved plate at a different ratio of radius to thickness is calculated to show the influence of the ratio on the piezoelectric effect and piezomagnetic effect.