Nonlinear dynamic response of piezoelastic laminated plates considering interfacial damage effects

This paper presents a nonlinear model for cross-ply piezoelastic laminated plates containing the damage effect of the intralayer materials and interlaminar interfaces. The model is based on the general six-degrees-of-freedom plate theory, the discontinuity of displacement, and electric potential on the interfaces are depicted by three shape functions, which are formulated according to solutions about three equilibrium equations and conservation of charge. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage are presented. Then using the finite difference method and the Newmark scheme, an analytical solution is presented. In numerical examples, the effects of different damage models, damage evolution, amplitude and frequency of electric loads on the nonlinear dynamic response of piezoelectric laminated plate with interfacial imperfections are investigated.     

具损伤压电智能层合板的动力分析

基于应变能等效原理、高阶剪切变形理论和Hamilton变分原理,考虑复合材料铺设层内的损伤效应,建立了具损伤压电智能层合板的运动控制方程,并运用Galerkin方法进行求解.数值算例中,讨论了损伤效应、厚跨比及压电层厚度与层合板总厚度之比对四边简支压电智能层合板自由振动频率的影响和外部控制电压对其动力响应的影响.     

ANALYSIS OF INTER-LAMINAR STRESSES FOR COMPOSITE LAMINATED PLATE WITH INTERFACIAL DAMAGE

A constitutive model for composite laminated plates with the damage effect of the intra-layers and inter-laminar interface is presented. The model is based on the general six-degrees-of-freedom plate theory, the discontinuity of displacement on the interfaces are depicted by three shape functions, which are formulated according to solutions satisfying three equilibrium equations, By using the variation principle, the three-dimensional non-linear equilibrium differential equations of the laminated plates with two different damage models are derived. Then, considering a simply supported laminated plate with damage, an analytical solution is presented using finite difference method to obtain the inter-laminar stresses.     

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.     

局部损伤复合材料层合板的振动分析

本文采用了一种改进方法对局部损伤复合材料层合板进行了振动分析,将复合材料板中的损伤模拟为局部刚度的削减,并取三个损伤因子来刻画损伤的特性．利用高阶摄动法对其自由振动方程进行求解,主要计算了损伤板的自然振动频率和振动模态．相较于一阶摄动展开法,该方法在计算局部较大损伤问题中具有更高的准确度和敏感度．最后对损伤问题进行了参数研究,分析了不同的损伤因子（包括局部损伤程度、方向、面积大小）对板自由振动频率的影响．该方法为二维板局部损伤检测提供了有效精确的理论依据,并为损伤的定量评价提供了一种思路．     

Nonlinear dynamic response and fatigue damage evolution for piezoelectric laminated plates with matrix cracks

Based on the Talreja’s damage model with tensor valued internal state variables, considering the effects of piezoelectricity, geometrical nonlinearity and the constitutive relations of the composite uni-ply plate with matrix cracks, the nonlinear dynamic equations of piezoelectric laminated plates with damage are established and the problems are solved by using the finite difference method. In numerical calculating examples, the nonlinear dynamics responses and the fatigue damage evolution curves of the plates are obtained, and the effects of piezoelectric materials, damage and external load on the nonlinear dynamic response and fatigue damage evolution of the plates are discussed.     

ACTIVE CONTROL OF THE PIEZOELASTIC LAMINATED CYLINDRICAL SHELL''''S VIBRATION UNDER HYDROSTATIC PRESSURE

IntroductionDuetotheintrinsicdirectandconversepiezoelectriceffects,piezoelectricmaterialscanbeeffectivelyusedtoproducesensorsoractuatorsfortheactiveshapeorvibrationcontrolostructures.Therefore,theuseofpiezoelectricmaterialsinintelligentstructuresattractedmanyattentionsinrecentyears.Thedesignofsuchactivesystemsrequiresgoodunderstandingofthemechanical_electricinteractionbetweenthestructuresandpiezoelectricmaterials.Manyinvestigationshavebeendoneinthisfield[1].However,mostofthesestudiesarebasedo…     

具损伤压电智能层合中厚板的非线性动力稳定性分析

基于各向异性损伤理论和压电理论，采用能量法和Lagrange方程，建立了具损伤压电智能层合中厚板在参数激励下的非线性运动控制方程，应用增量谐波平衡法，求解了具损伤压电智能层合中厚板的非线性动力稳定性问题。算例中，分析了损伤参数和压电效应对压电智能层合板非线性动力稳定性的影响，揭示了力电耦合效应的内在特征，并与有关文献的结果进行了比较。     

Nonlinear active control of damaged piezoelectric smart laminated plates and damage detection

Considering mass and stiffness of piezoelectric layers and damage effects of composite layers, nonlinear dynamic equations of damaged piezoelectric smart laminated plates are derived. The derivation is based on the Hamilton＇s principle, the higher- order shear deformation plate theory, von Karman type geometrically nonlinear straindisplacement relations, and the strain energy equivalence theory. A negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects is used to realize the active control and damage detection with a closed control loop. Simply supported rectangular laminated plates with immovable edges are used in numerical computation. Influence of the piezoelectric layers＇ location on the vibration control is in- vestigated. In addition, effects of the degree and location of damage on the sensor output voltage are discussed. A method for damage detection is introduced.     

考虑界面损伤层合梁板的层间应力分析

基于精确应力分析的广义六自由度板理论，应用变分原理和损伤力学中 的应变等效原理，考虑复合材料铺设层内和层间界面处的损伤效应，建立了具两种损伤模式 的复合材料层合板的三维非线性平衡微分方程，且运用有限差分法对考虑损伤简支层合梁板 的层间应力进行了求解.     

复合材料层合板的二次屈曲和二次分枝点分析

为了研究复合材料层合板的二次分叉特性 ,利用能量变分原理和非线性几何方程建立了具有弹性约束的复合材料层合板在面内载荷作用下的非线性稳定性控制方程组。控制方程组用广义傅立叶级数法进行求解 ,并得到载荷 -挠度曲线。基于分叉理论中的 Lerray-Schaulder定理 ,采用小挠动法 ,直接导出了复合材料层合板的二次失稳方程。研究结果表明 ,非对称层板也可能存在分叉 ,弹性转动支持系数和铺层等因素对二次分叉有很重要的影响。随着弹性系数的增大 ,二次失稳载荷值与初次失稳载荷值之比下降     

含基体横向损伤的黏弹性板的蠕变后屈曲分析

基于Schapery三维黏弹性损伤本构关系，引入沈为和Kachanov损伤演化方程，建立了基体横向损伤的纤维单一方向铺设黏弹性板的损伤模型；应用von Karman板理论，导出了考虑损伤效应的具初始挠度的纤维单一方向铺设黏弹性矩形板的非线性压屈平衡方程. 对未知变量在空间上采用差分法离散，时间上采用增量算法和Newton-Cotes积分法离散，控制方程被迭代求解. 算例中讨论了损伤以及有关参数对黏弹性复合材料板后屈曲行为的影响，且与已有文献的结果进行了比较. 数值结果表明：随着外载荷或者初始挠度的增大，板后屈曲趋于稳定时的挠度就愈大，损伤的影响愈明显；而随着长宽比的增大，板后屈曲趋于稳定时的挠度愈小，损伤的影响却随之增大.     

金属板结构疲劳损伤二倍频兰姆波检测方法研究

针对重大基础设施安全运行需要,本文进行了金属板结构疲劳损伤非线性兰姆波检测方法研究。基于兰姆波二次谐波产生条件,确定了产生二次谐波积累增长效应的两种兰姆波模态及对应的激励频率。通过有限元仿真,研究了材料性能改变对兰姆波非线性效应的影响,证明了二倍频兰姆波非线性系数对材料性能退化表征的有效性。在此基础上,开展了金属板结构疲劳损伤非线性兰姆波检测实验研究。将极性反转方法应用于疲劳试件检测实验中,有效提高了检测信号中二倍频兰姆波的幅值和信噪比。实验结果表明,两种兰姆波模态对的二次谐波非线性系数均随疲劳损伤增加呈线性增长趋势,但基频S(0,2)模态和二倍频S(0,4)模态对对疲劳损伤检测的灵敏度更高,更适合金属板结构疲劳损伤检测。     

复合材料层压板低速冲击响应尺度效应数值模拟研究

为了研究尺度效应对于复合材料层压板在低速冲击作用下的动态响应和冲击损伤的影响,基于相似理论,建立了三种不同尺寸的层压板受冲击的三维有限元模型。在该模型中,针对层压板的面内损伤,采用改进的Chang-Chang准则进行预测;针对层压板内层间分层损伤,则使用Cohesive界面单元进行模拟。一旦复合材料层压板在低速冲击作用下产生损伤,则对出现损伤的区域进行材料参数退化。采用该模型对三种不同尺寸的层压板的冲击过程进行有限元分析,并将不同冲击速度下的冲击响应进行比较,得出了如下结论：在层压板内未发生冲击损伤时,冲击产生的挠度和冲击力与相似理论解十分吻合,一旦出现冲击损伤,则冲击力的变化与相似理论解有所差别;如果两个缩放模型的冲击速度之比等于缩放比例的平方根,则两个模型中的相对分层尺寸基本是相同的,这个结果与已有的实验结果吻合;而对冲击后面内损伤的分析表明,其损伤尺寸不符合这一相似规律。     

复合材料结构内埋光纤网络测试其内部损伤试验研究

本文介绍了在复合材料层板内埋入光纤网络，用于测试层板冲击损伤的试验方法和结果。试验表明该法探测损伤是有效的，具有广阔的发展前途。     

具有分层损伤的不同加筋形式复合材料层合板的后屈曲性态研究

基于板的一阶剪切理论和V on-K arm an大挠度理论,分别推导了复合材料层合板和层合梁的几何非线性有限元列式,提出了含嵌入分层的复合材料加筋层合板在受压缩载荷作用下的后屈曲有限元分析方法,对在板厚方向具有不同分层位置的加筋板结构进行了有限元数值分析,研究了不同的加筋方式及筋的分布对具有分层损伤的复合材料加筋层合板的后屈曲性态的影响,所得结果对确定在压缩载荷作用下含损伤复合材料加筋层合板的剩余承载能力具有参考价值。     

含有分层损伤的复合材料加筋层合板的屈曲性态研究

基于Ｍｉｎｄｉｎ假定推导了考虑剪切的复合材料加筋层板的有限元列式,并在此基础上计算出筋间基板含嵌入分层以及筋与基板连接处含穿透分层的加筋层合板在受压缩载荷情况下的屈曲模式和临界力。本文所给出的有限元方法及结论对从事复合材料结构设计的工程人员具有参考价值。     

矩形板非线性蠕变损伤屈曲特性分析

基于Von Karman非线性板理论和Kachanov-Rabotnov损伤理论,建立了在横向和面内载荷共同作用下考虑蠕变损伤效应的矩形板的非线性控制平衡方程,采用有限差分法和时间增量算法对未知变量进行离散,对整个问题进行迭代求解,分析了几何非线性、荷载等因素对板非线性蠕变损伤特性的影响。     

两级载荷下复合材料层板疲劳与寿命预测

研究了复合材料层板疲劳过程中的累积应变演化规律，建立了以累积应变为基础的非线性积累损伤法则，实验结果表明：文中提出的累积应变方法能够较好地反映加载次序效应，准确地预测了复合材料层板在两级载荷下的疲劳寿命。     

Elasto-plastic postbuckling of damaged orthotropic plates

Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.