压电层合梁静动力学分析的高精度梁单元

给出了一个对复合材料压电层合梁进行数值分析的高精度压电层合梁单元。基于Shi三阶剪切变形板理论的位移场和Layer-wise理论的电势场,用力-电耦合的变分原理及Hamilton原理推导了压电层合梁单元列式。采用拟协调元方法推导了一个可显式给出单元刚度矩阵的两节点压电层合梁单元,并应用于压电层合梁的力-电耦合弯曲和自由振动分析。计算结果表明,该梁单元给出的梁挠度和固有频率与解析解吻合良好,并优于其它梁单元的计算结果,说明了本文所给压电层合梁单元的可靠性和准确性。研究结果可为力-电耦合作用下压电层合梁的力学分析提供一个简单、精确且高效的压电层合梁单元。     

复合材料层合厚板锯齿理论及有限元分析

对于较厚复合材料弯曲问题,已有锯齿型厚板理论最大误差超过35%。为了合理地分析较厚复合材料弯曲问题,发展了准确高效的锯齿型厚板理论。此理论位移变量个数独立于层合板层数,其面内位移不含有横向位移一阶导数,构造有限元时仅需C0插值函数,故称此理论为C0型锯齿厚板理论。基于发展的锯齿理论,构造了六节点三角形单元并推导了复合材料层合/夹层板弯曲问题有限元列式。为验证C0型锯齿厚板理论性能,分析了复合材料层合/夹层厚板弯曲问题,并与已有C1型锯齿理论对比。结果表明,本文的C0型锯齿厚板理论最大误差15%,比已有锯齿型厚板理论准确高效。     

压电复合材料层合梁非线性模糊滤波振动控制

在振动主动前馈控制中通常采用的自适应滤波-XLMS算法只限定于线性主动控制问题.由于在振动主动控制中各种非线性因素的存在,使得非线性控制方法成为必需.本文利用模糊逻辑系统能够逼近任何非线性系统的特性,提出了一种非线性模糊滤波振动控制方法,解决了由于传感通道的非线性使得参考信号与外扰间呈非线性函数关系的主动控制问题.针对具有压电作动器的复合材料层合梁进行了振动主动控制的数值仿真计算,结果表明该非线性模糊自适应控制方法优于线性滤波-XLMS方法.     

相似电路耦合模型及其在压电—梁结构分析中的应用

根据线性系统微分方程的相拟性确定机械系统的相似电路,由压电材料的本构和动力方法确定压电材料作为电耦合的变压器,从而用一具耦合的电路系统模拟智能结构的电学和力学行为,通过一个压电－梁智能结构的分析,证明了模型的可用性。     

强电场作用下简支压电层合梁的非线性动力分析

研究可移简支压电弯曲层合梁在交变强电场作用下的非线性动力学行为.考虑材料的电致伸缩和电致弹性压电效应以及几何非线性导出压电层合梁的数学模型.导出简支压电执行器的弯曲振动控制方程,并得到它的刚度是关于时间的慢变函数关系.利用非定常振动的渐近理论和Galerkin方法对具有慢变系数的非线性动力方程进行求解.得到了可移简支压电层合梁的动力特征.最后得到了可移压电简支梁的共振频率、固有频率和电场频率三者之间的变化关系以及谐振幅度与作用电场强度的关系.     

压电智能梁的阻抗分析与损伤识别

压电陶瓷具有正、逆压电效应,可以用作自驱动传感器.该文对表面粘贴有单片压电陶瓷的压电智能钢梁进行了阻抗分析.讨论了单压电片驱动下钢梁的纵向振动和弯曲振动,得到了压电智能梁的机械阻抗.介绍了压电片与基梁的机电耦合作用及基于压电阻抗技术的结构损伤识别机理.以两端自由钢梁为例对压电智能梁的压电阻抗进行了数值与实验验证,结果表明数值计算结果与实验结果基本相符.利用压电阻抗技术对两端自由的裂纹钢梁进行了损伤识别实验研究,实验结果发现,裂纹的出现引起高频段压电阻抗实部和虚部曲线出现了明显的变化;随着裂纹尺寸的增大,曲线谐振频率和反谐振频率逐渐减小.由此可见,通过测量钢梁损伤前后压电陶瓷片的电阻抗变化能够识别梁中的裂纹损伤.     

复合材料厚梁精化锯齿理论及有限元分析

由于具有预先满足层间应力连续的优点,锯齿理论被广泛研究和应用.然而,至今锯齿理论仍然存在如下难题:基于锯齿理论构造单元时,需使用满足单元间C1连续的插值函数,难于构造多节点高阶单元,而且精度较低.如果这些问题不被重视和解决,应用此类理论分析复合材料力学问题可能得出不恰当的结论.通过发展高精度的考虑横法向应变的C0型锯齿理论,论文将克服已有锯齿理论遇到的上述难题.基于发展的锯齿理论,构造三节点梁单元验证发展理论模型的性能.     

压电-弹性层合梁自由振动分析的新方法

将状态空间法和微分求积法相结合,分析了压电-弹性层合梁的自由振动. 通过微分求积把状态方程在每一个节点处离散,进而求得解答. 选用不同的节点数目, 分析了方法的收敛性. 计算结果与相关文献的结果能较好地符合. 该方法 对于分析压电-弹性层合梁的工程振动问题非常方便.     

含压电片层合壳的有限元分析与控制仿真

本文首先针对含压电材料的一般结构，推导了按位移和电位移求解时的混合变分原理，在此基础上，通过对面电荷取变分，直接得到了含按电压驱动压电片层合壳的有限元方程，最后给出了利用压电片进行静变形和振动控制的仿真算例，并进行了分析。结果表明，本文建立的有限元方程准确、可靠。     

C~0型高阶锯齿理论及复合材料厚梁热应力分析

基于已有锯齿理论构造单元时,需使用满足单元间C1连续的插值函数,难于构造多节点高阶单元,而且精度较低。针对已有锯齿理论存在的问题,本文首先发展了C0型锯齿理论。通过虚位移原理推导出在热载荷作用下复合材料梁的平衡方程,并给出了简支复合材料层合梁解析解。基于发展的锯齿理论分析了复合材料夹层梁和层合梁热膨胀问题,并与其他理论结果对比。数值结果表明,发展的C0型锯齿理论能克服已有锯齿理论的难题。     

层合结构压电器件的机电耦合响应

压电传感嚣和致动器都可以看成是由压电材料层和非压电(弹性)材料层交替铺设而成。对于这类任意铺设的层合板悬臂梁结构,推导出了表示力学变形与外加电场之间耦合效应的解析表达式。进而,又推导出了两类(一类为单层压电-弹性层。另一类为双层压电-弹性层)层合型悬臂梁结构机电耦合性能的解析公式。在该机电耦合模型中,包括了两个压电常数d211和d222。最后。通过比较解析解、实验值以及有限元计算结果,发现它们吻合得很好。     

Steady-state responses of forced laminated piezoelectric composite beams

The steady-state responses of laminated piezoelectric composite beams subjected to a uniformly distributed load and an electrical potential are investigated by using the state-space-based differential quadrature method. The constraints of the beam considered in the present paper can be any combination of four different kinds of end geometric boundary conditions and two kinds of end electrical boundary conditions. The influence of some material and geometrical parameters such as the thickness ratio and the number of layers on the responses of the beams is discussed. The present solutions are also compared with the numerical results, and a good agreement is found. The static solutions of laminated piezoelectric composite beams can be degenerated from the present steady-state solutions. The results obtained in the present paper are useful and can be applied to design the piezoelectric sensors and actuators in practical applications.     

Stress and strain analysis in elastic laminated composite beams

A detailed theoretical analysis of stress and strain in fiber-reinforced, laminated composite beams is presented within the framework of three-dimensional theory of thermo-elastodynamics. Each of reinforcing and matrix layers is made of different anisotropic material and is of different constant thickness. By the use of a variational theorem, the fully non-linear governing equations are consistently obtained for the case when the displacement components of each layer are taken to vary linearly over the cross-section of the layer. Then the linear version of the resulting equations, including the uniqueness of its solution is given, and the general results are briefly discussed.

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Zusammenfassung In der vorliegenden Abhandlung wird eine detaillierte Spannungs-und Verzerrungsuntersuchung von faserverstärkten laminierten Balken innerhalb der dreidimensionalen thermo-elastodynamischen Theorie durchgeführt. Für jede Verstärkungs-und Bindeschicht wird unterschiedliches anisotropes Verhalten und unterschiedliche Schichtstärke vorausgesetzt. Unter Annahme eines linearen Verlaufs der im Querschnitt liegenden Verformungskomponenten über jede einzelne Schicht werden mit Hilfe eines Satzes der Variationsrechnung die vollständigen nichtlinearen Grundgleichungen abgeleitet. Damit ist auch die linearisierte Form der Gleichungen mit eindeutiger Lösung bestimmt. Eine kurze Untersuchung der Ergebnisse in ihrer allgemeinen Form ist angeschlossen.

     

Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.     

Coupled buckling and postbuckling analysis of active laminated piezoelectric composite plates

A theoretical framework for analyzing the pre- and postbuckling response of composite laminates and plates with piezoactuators and sensors is presented. The mechanics include nonlinear effects due to large rotations and stress stiffening, and are incorporated into a coupled mixed-field piezoelectric laminate theory. Using the previous mechanics, a nonlinear finite element method and an incremental-iterative solution are formulated for the analysis of nonlinear adaptive plate structures subject to in-plane electromechanical loading. A novel eight-node nonlinear plate finite element is also developed. Evaluation cases predict the buckling and postbuckling response of adaptive composite beams and plates with piezoelectric actuators and sensors. The case of piezoelectric buckling and postbuckling induced by the actuators is addressed and quantified. Finally, the possibility to actively mitigate the mechanical buckling and postbuckling response of adaptive piezocomposite plates is illustrated.     

Linear viscoelastic analysis of straight and curved thin-walled laminated composite beams

This paper is devoted to study the behavior, in the range of linear viscoelasticity, of shear flexible thin-walled beam members constructed with composite laminated fiber-reinforced plastics. This work appeals to the correspondence principle in order to incorporate in unified model the motion equations of a curved or straight shear-flexible thin-walled beam member developed by the authors, together with the micromechanics and macromechanics of the reinforced plastic panels. Then, the analysis is performed in the Laplace or Carson domains. That is, the expressions describing the micromechanics and macromechanics of a plastic laminated composites and motion equations of the structural member are transformed into the Laplace or Carson domains where the relaxation components of the beam structure (straight or curved) are obtained. The resulting equations are numerically solved by means of finite element approaches defined in the Laplace or Carson domains. The finite element results are adjusted with a polynomial fitting. Then the creep behavior is obtained by means of a numerical technique for the inverse Laplace transform. Predictions of the present methodology are compared with experimental data and other approaches. New studies are performed focusing attention in the flexural–torsional behavior of shear flexible thin-walled straight composite beams as well as for thin-walled curved beams and frames.     

Coupled refined layerwise theory for dynamic free and forced response of piezoelectric laminated composite and sandwich beams

This work extends a previously presented coupled refined layerwise theory to dynamic analysis of piezoelectric laminated composite and sandwich beams. Contrary to most of the available theories, all the kinematic and stress boundary conditions are satisfied at the interfaces of the piezoelectric layers with the non-zero longitudinal electric field. Moreover, both electrical transverse normal strains and transverse flexibility are taken into account for the first time in the present theory. In the presented formulation a high-order polynomial, an exponential expression and a layerwise term containing the electric field are included in the describing expression of the in-plane displacement of the beam. For the transverse displacement, the coupled refined model uses a combination of continuous piecewise fourth-order polynomials with a layerwise representation of electrical unknowns. The electric field is also approximated as linear across the thickness direction of piezoelectric layers. One of advantages of the present theory is that the mechanical number of the unknown parameters is very small and is independent of the number of the layers. For validation of the proposed model, various free and forced vibration tests for thin and thick laminated/sandwich piezoelectric beams are carried out. For various electrical and mechanical boundary conditions, excellent correlation has been found between the results obtained from the proposed formulation with those resulted from the three-dimensional theory of piezoelasticity.     

Vibration analysis of piezoelectric laminated slightly curved beams using distributed transfer function method

Piezoelectric laminated slightly curved beams (PLSCB) is currently one of the most popular actuators used in smart structure applications due to the fact that these actuators are small, lightweight, quick response and relatively high force output. This paper presents an analytical model of PLSCB, which includes the computation of natural frequencies, mode shapes and transfer function formulation using the distributed transfer function method (DTFM). By setting the radius of curvature of the proposed model to infinity, a piezoelectric laminated straight beams (PLSB) model can be obtained. The DTFM is applied and extended to carry out the transfer function formulation of the PLSCB and PLSB models. This method will be used to solve for the natural frequencies, mode shapes and transfer functions of the PLSCB and PLSB models in exact and closed form solution without using truncated series of particular comparison or admissible functions. The natural frequencies of the cantilevered PLSCB and PLSB are calculated by the DTFM and the Rayleigh–Ritz method. The analysis indicates that the stretching–bending coupling due to curvature has a considerable effect on the frequency parameters. Increasing the radius of curvature of the PLSCB has its largest effect on the natural frequencies. But the inhomogeneity of the boundary conditions does not have any effects on the natural frequencies or system spectrum due to the both receptance and boundary transfer functions have the same characteristic equations. The method can also be generalized to the vibration analysis of non-piezoelectric composite beams with arbitrary boundary conditions.