Lamb波理论及层合板冲击损伤的实验研究

从理论上分析了板中Lamb波信号的传播特性,并给出Lamb波在板中传播的频散方程。理论分析及实验均表明,Lamb波的频散特性与复合材料结构损伤有着直接的联系,而且最低阶的对称和反对称Lamb波模态对层合板的损伤比较敏感,但应用Lamb波的频散效应监测结构的损伤在检测技术上还难以实现。根据板中导波形成Lamb波的共振原理,板中应力波的幅频特性很大程度上反映了Lamb波的谐振特征。因此,利用压电元件的压电阻抗谱分析应力波的各阶模态频率及振幅对结构损伤的变化,能够反映材料内部损伤与Lamb波的频散特性。文中针对表面粘贴压电元件的层合板智能结构,建立了包含Lamb波谐振模式的压电阻抗计算模型。冲击损伤试件的实验表明,由于结构损伤的出现压电阻抗谱中的模态频率及其阻抗幅值等特征信息将发生变化。因此,引入应力波损伤因子可以对结构冲击损伤的存在和程度进行初步评价。该方法基于结构的机-电动态阻抗特性,不受结构的几何形状限制,测试用的压电元件成本低,方法简单可行,有望在智能结构的健康诊断方面获得应用。     

PWAS激励Lamb波的谱有限元建模及参数研究

基于谱有限元法发展了一种由压电晶片主动传感器(PWAS)、胶层和主结构组成的三层模型,来模拟PWAS激励结构中Lamb波的传播。首先在各层使用不同的梁理论,推导PWAS-胶层-主结构三层模型的控制方程和力的边界条件,建立谱有限元模型。通过和传统的有限单元法进行比较,表明了在显著提高计算效率的同时,所发展谱有限元模型在分析结构中Lamb波传播上仍具有较高的精度。分析了激励频率、PWAS长度与厚度、胶层厚度等参数变化对输出电压信号的影响,可以为基于PWAS和Lamb波的主动健康监测技术提供参考。     

基于Legendre多项式的双压电层合板三维压电谱元法模拟

谱单元作为一种高阶单元具有计算效率高和精度高的特点。本文在基于Legendre正交多项式的三维谱单元基础上提出了三维压电谱单元模型,用于压电层合板静力和动力性能模拟研究。压电层合板结构中的位移和电势自由度均离散到三维压电谱单元Gauss-Lobatto-Legendre(GLL)配置节点上,并且未对电势沿压电层厚度方向上的变化做任何假定。通过提高谱单元中沿压电层合板厚度方向上的形函数阶数的方法,来削弱三维谱单元在模拟薄板结构中出现的剪切闭锁现象。为验证单元的计算精度,取双压电层合板结构进行静力和动力行为模拟验证,并将计算结果与现有文献中的其它单元模型及有限元结果进行对比。结果表明,压电谱单元可有效模拟压电层合板的静力和动力行为,且提高谱单元形函数阶数可提高数值模拟精度。     

磁场对电磁弹性板中Lamb波频散特性的影响

研究了静态磁场下电磁弹性结构中Lamb波的传播行为.在确定静态磁场下电磁弹性板中耦合初始广义应力(弹性应力、电位移和磁感应强度的基础上,推导了含初始广义应力时板中Lamb波传播的运动方程,并由此获得了对称模态和反对称模态时的频散方程.以由BaTiO3-CoFe2O4材料构成的电磁弹性板模型作为数值算例,绘制了Lamb波传播的对称模态和反对称模态频散曲线.计算结果表明磁场对Lamb波的频散特性有一定的影响.     

具有叉指式电极的1-3型压电复合材料层合板力电耦合行为的三维精确分析

基于三维弹性理论和压电理论,导出了含有1-3型压电复合材料层的有限长矩形层合简支板的静力平衡方程和边界条件,给出了该层合板在叉指式电极和外力共同作用下力电耦合特性的三维精确解.数值算例的计算结果与有限元解进行了对比,取得了很好的一致性.研究了压电矩阵各向异性和刚度矩阵各向异性以及电势等因素对其挠曲面扭率最大值的影响.数值结果表明层合板扭率最大值的绝对值随压电矩阵各向异性系数Rd的增大而增大并随刚度矩阵各向异性系数Rc的减小而增加.     

基于时间反转法的Lamb波检测技术的研究进展

Lamb波具有传播距离远、衰减小等特点,已被广泛应用于大型板类结构的损伤检测。时间反转是实现超声波聚焦的有效方法之一。本文回顾并总结了近20年来时间反转方法在Lamb波检测领域中的研究进展。针对Lamb波固有的频散和多模态等传播特性,详细论述了时间反转法在板结构Lamb波检测中的应用。最后对基于时间反转法的免基准信号Lamb波损伤检测方法进行了总结,分析其存在的问题并对其应用前景进行了展望。     

Lamb波稀疏阵列CFRP层合板损伤成像检测

针对Lamb波阵列成像方法检测复合材料板时存在偏斜效应、频散及密集阵列成像分辨率低的问题,本文采用引入偏斜角修正的相位延迟叠加方法结合最小冗余度线性阵列（MRLA）实现了碳纤维增强复合材料（CFRP）层合板损伤的准确成像检测。根据Lamb波单一模态的波数曲线计算各方向的偏斜角,确保成像中损伤所在方位角的准确性;在频域中对每个频率成分进行相位延迟以弥补频散,确保成像中损伤所在位置的精度;利用MRLA设计十字型稀疏阵列,既降低了阵列成本,又保证损了伤成像质量。数值模拟成像结果验证了本文提出方案的有效性,实验成像结果凸显了十字型稀疏阵列在节约阵列成本、提高损伤空间分辨率方面的优越性,对工程实践中CFRP板结构的损伤检测具有一定的指导意义。     

偏压电场对压电板中Lamb波相速度的影响

本文研究了偏压电场作用下,Lamb波在压电板中的传播行为，首先给出了偏压电场作用时压电板中的应力场及电位移场，然后通过求解含初应力及初电位移的小幅波动问题的耦合方程，分别给出了Lamb波的对称模态和反对称模态的相速度方程，以典型的PZT－5H压电陶瓷板为例进行了数值计算,并讨论了偏压电场对Lamb波相速度及频散曲线的影响，结果表明，偏压电场可以显著地改变Lamb波的传播速度，借此可使声波器件获得延时效果。     

复合材料大层数层合板热变形热应力有限元分析

研究复合材料大层数层合板结构承受热载荷或同时存在机械载荷作用下，由于层合板各单层间存在着剪切耦合和泊松比的不协调等因素引起的热应力、热变形和自由边缘效应，采用三维八节点等参有限单元法，其特点是在划分三维单元时，每一个单元内可包含多个具有不同铺设角、不同组分材料的铺层。该文导出了相应的三维有限元分析各表达式，进行了实例数值计算，得到了反映大层数层合板热变形、热应力特性的一些有价值的结果。     

正交各向异性板中非主轴方向的Lamb波

基于线性三维弹性理论,采用勒让德正交多项式展开法,推导了波沿正交各向异性材料非主轴方向传播时的Lamb波耦合波动方程,并对耦合波动方程进行了数值求解。为验证该方法的适用性和正确性,首先将此方法应用于各向同性材料,并与已知的数据结果进行了比较;然后以单向纤维增强复合材料为例,计算了耦合Lamb波沿不同的非主轴方向传播时的相速度频散曲线,并分别研究了传播方向改变时低阶模态Lamb波和高阶模态Lamb波频散特性的变化。最后,针对潜在用于各向异性复合材料结构健康监测的耦合Lamb波低阶模态,给出了其在不同传播方向时的相速度分布和群速度分布。同时,结合低阶模态Lamb波的位移分布特性和材料的各向异性特点,阐释了S0模态对波的传播方向变化最为敏感的原因。     

Numerical modeling of PZT-induced Lamb wave-based crack detection in plate-like structures

This paper presents the numerical modeling and simulations of PZT-induced Lamb wave propagation in plate-like structures by using the spectral finite element method. A novel spectral plate finite element, which can efficiently model the three-dimensional (3D) behavior of Lamb waves, is proposed. In the formulation, linear displacement distributions in the thickness direction are assumed for both the PZT layer and the base plate. A way to avoid the thickness locking is proposed and used in the formulations. Two examples, one for the validation of the proposed two-dimensional (2D) spectral finite element and the other for the demonstration of crack detection in plates, are presented and discussed. The contact between the two faces of crack is considered. Numerical results show that (1) only the anti-symmetric mode is prone to thickness locking thus remedy should be made only on this part, (2) the proposed 2D spectral finite element can adequately model the Lamb wave propagation in plate-like structures and the complex scattering for the crack, and (3) crack location can be well determined by a PZT-induced Lamb wave-based diagnosis algorithm.     

Spectrally formulated wavelet finite element for wave propagation and impact force identification in connected 1-D waveguides

In this paper, a novel wavelet based spectral finite element is developed for studying elastic wave propagation in 1-D connected waveguides. First the partial differential wave equation is converted to simultaneous ordinary differential equations (ODEs) using Daubechies wavelet approximation in time. These ODEs are then solved using finite element (FE) technique by deriving the exact interpolating function in the transformed domain. Spectral element captures the exact mass distribution and thus the system size required is very much smaller then conventional FE. The localized nature of the compactly supported Daubechies wavelet allows easy imposition of initial-boundary values. This circumvents several disadvantages of the conventional spectral element formulation using Fast Fourier Transforms (FFT) particularly in the study of transient dynamics. The proposed method is used to study longitudinal and flexural wave propagation in rods, beams and frame structures. Numerical experiments are performed to show the advantages over FFT-based spectral element methods. The efficiency of the spectral formulation for impact force identification is also demonstrated.     

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采用谱单元方法推导带阻尼梁的传递函数矩阵. 采用一维连续梁的解析解作为动力形状函 数. 与有限元法相比,谱单元方法的自由度和单元数目小且计算精度高. 传递函数表示为梁 的几何和物理参数的超越隐函数,不同于用模态参数表示的传统传递函数. 提出了采用遗传 算法的结构物理参数识别方法. 以变截面悬臂梁为数值算例,显示该方法的有效性.     

含高温度梯度及接触热阻非线性热力耦合问题的谱元法

建立了含高温度梯度及接触热阻的非线性热力耦合问题的谱元法格式, 考虑了温度相关的热导率、弹性模量、泊松比和热膨胀系数, 以及界面应力相关的接触热阻的影响. 谱元法的插值函数基于非等距分布的Lobatto结点集或第二类Chebyshev结点集, 兼具谱方法的高精度和有限元法的灵活性. 数值算例表明, 建立的谱元法计算格式可以高效高精度地求解域内高温度梯度以及含接触热阻的非线性热力耦合问题, 不仅收敛速度快于传统有限元法, 而且用较少的自由度和较短的计算时间即可得到比传统有限元法更高精度的计算结果, 在工程实际热力耦合问题中具有广阔的应用前景.      

基于观点法的谱随机有限元分析——随机响应面法

提出了一种基于配点法的谱随机有限元分析方法-随机响应面法(SRSM),这种方法与已有的谱随机有限元方法(SSFEM)类似,都用Karhunen-Loeve级数扩展式表示输入随机场而计算结果的输出用多项式混沌展式表达。然而这两种方法采用了不同的方法确定多项式混沌展式中的系数:SRSM利用概率最小二乘配点法而SSFEM利用概率Galerkin法。与解析的SSFEM相比,SRSM的优势在于有限元计算和随机分析计算不耦合,即可把通用有限元程序作为黑箱进行求解。与黑箱版的SSFEM相比,SRSM需要的样本计算更少。SRSM中的各配点来自高概率的区域并使均方差最小化,从而可用少量的样本计算获得较高的计算精度。算例突出了本文提出的方法的特点并显示此方法是有效的且有较高的计算精度。     

随机结构有限元分析的递推求解方法

提出了一种新的谱随机有限元分析方法——递推求解方法。该方法将随机结构的随机响应表示成非正交多项式展式,建立了和摄动法类似的一系列确定的递推方程,并通过确定性有限元方法对这些递推方程进行静力问题求解。算例表明,当随机量出现较大涨落时,计算结果相对于传统摄动法有不小的改进。     

Comparison of spectral and finite element methods applied to the study of the core‐annular flow in an undulating tube

A Galerkin/finite element and a pseudo‐spectral method, in conjunction with the primitive (velocity‐pressure) and streamfunction‐vorticity formulations, are tested for solving the two‐phase flow in a tube, which has a periodically varying, circular cross section. Two immiscible, incompressible, Newtonian fluids are arranged so that one of them is around the axis of the tube (core fluid) and the other one surrounds it (annular fluid). The physical and flow parameters are such that the interface between the two fluids remains continuous and single‐valued. This arrangement is usually referred to as Core‐Annular flow. A non‐orthogonal mapping is used to transform the uneven tube shape and the unknown, time dependent interface to fixed, cylindrical surfaces. With both methods and formulations, steady states are calculated first using the Newton–Raphson method. The most dangerous eigenvalues of the related linear stability problem are calculated using the Arnoldi method, and dynamic simulations are carried out using the implicit Euler method. It is shown that with a smooth tube shape the pseudo‐spectral method exhibits exponential convergence, whereas the finite element method exhibits algebraic convergence, albeit of higher order than expected from the relevant theory. Thus the former method, especially when coupled with the streamfunction‐vorticity formulation, is much more efficient. The finite element method becomes more advantageous when the tube shape contains a cusp, in which case the convergence rate of the pseudo‐spectral method deteriorates exhibiting algebraic convergence with the number of the axial spectral modes, whereas the convergence rate of the finite element method remains unaffected. Copyright © 2002 John Wiley & Sons, Ltd.     

Stress analysis of functionally graded shells using a 7-parameter shell element

In this paper, finite element stress analysis of functionally graded structures using a high-order spectral/hp shell finite element is presented. The shell element is based on a seven-parameter first-order shear deformation theory in which the seventh parameter, in addition to the usual six degrees of freedom, is the thickness stretch. The continuum shell element is utilized for the numerical simulations of the fully geometrically nonlinear response of functionally graded elastic shell structures. Several nontrivial shell problems are considered to report deflections and stresses, the latter being the main focus of the current paper. It is found that the stresses computed in the current study agree only in some cases with those of ANSYS and/or ABAQUS and thus requires additional study to determine the cause of the disagreement.     

谱元法和高阶时间分裂法求解方腔顶盖驱动流

详细推导了谱元方法的具体计算公式和时间分裂法的具体计算过程 ;对一般的时间分裂法进行了改进 ,即对非线性步分别用 3阶 Adams-Bashforth方法和 4阶显式 Runge-Kutta法 ,粘性步采用 3阶隐式 Adams-Moulton形式 ,提高了时间方向的离散精度 ,同时还改进了压力边界条件 ,采用 3阶的压力边界条件 ;利用改进的时间分裂方法分解不可压缩 Navier-Stokes方程 ,并结合谱元法计算了移动顶盖方腔驱动流 ,提高了方法可以计算的 Re数 ,缩短了达到收敛的时间 ,并将结果与基准解进行比较 ;分析了移动顶盖方腔驱动流中 Re数对流场分布的影响。     

Spectral/hp penalty least‐squares finite element formulation for unsteady incompressible flows

In this paper, we present spectral/hp penalty least‐squares finite element formulation for the numerical solution of unsteady incompressible Navier–Stokes equations. Pressure is eliminated from Navier–Stokes equations using penalty method, and finite element model is developed in terms of velocity, vorticity and dilatation. High‐order element expansions are used to construct discrete form. Unlike other penalty finite element formulations, equal‐order Gauss integration is used for both viscous and penalty terms of the coefficient matrix. For time integration, space–time decoupled schemes are implemented. Second‐order accuracy of the time integration scheme is established using the method of manufactured solution. Numerical results are presented for impulsively started lid‐driven cavity flow at Reynolds number of 5000 and transient flow over a backward‐facing step. The effect of penalty parameter on the accuracy is investigated thoroughly in this paper and results are presented for a range of penalty parameter. Present formulation produces very accurate results for even very low penalty parameters (10–50). Copyright © 2008 John Wiley & Sons, Ltd.