Vibration and stability of angle-ply laminated composite plates subjected to in-plane stresses

Natural frequencies and buckling stresses of angle-ply laminated composite plates are analyzed by taking into account the effects of shear deformation, thickness change and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for thick rectangular laminates subjected to in-plane stresses is derived through Hamilton's principle. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported thick laminated plate. In order to assure the accuracy of the present theory, convergence properties of the fundamental natural frequency are examined in detail. Numerical results are compared with those of the published existing theories. The modal displacement and stress distributions in the thickness direction are obtained and plotted in figures. The present global higher-order approximate theories can predict the natural frequencies, buckling stresses and modal stresses of thick multilayered angle-ply composite laminates accurately within small number of unknowns which is not dependent on the number of layers.     

Natural frequencies of symmetrically laminated elliptical and circular plates

Elliptical and circular fibre reinforced composite plates are important structural elements in modern engineering structures. Vibration analysis of these elements are of interest to structural designers. The present paper deals with the free transverse vibration analysis of symmetrically laminated solid and annular elliptic and circular plates with several complicating effects.The approach developed is based on the Rayleigh–Ritz method where the deflection of the plate is approximated by a general shape function of polynomial type.The analysis includes several complicating effects, such as the presence of an internal hole, an internal ring support, several concentrated masses and the boundary elastically restrained against rotation and translation.Several examples are solved and some results which correspond to particular cases are compared with existing values in the literature. New results are also presented for cross-ply and angle-ply elliptical and circular laminates with different boundary conditions.The algorithm developed can be applied to a wide range of elastic restraint conditions, to any aspect ratio and to higher modes. The effect of the restraint parameters along the boundary on the natural frequencies for plates with these complicating effects is considered.     

基于高阶改进方法的层合板固有频率分析

针对一般的计算层合板振动特性的方法过于繁复的问题,采用了一种高阶改进方法来计算复合材料层合板的固有频率。建立了高阶改进方法的层合板动能和势能表达式,利用哈密顿原理构建了层合板的自由振动方程并计算了层合板的固有频率。在此基础上,通过该方法计算了铺设角度、跨厚比和弹性模量比对层合板固有频率的影响。结果表明：该算法可以有效地计算出反对称铺设层合板和正交铺设层合板的固有频率,同时也可以计算任意形式铺设的层合板的固有频率。     

Vibration of circular Mindlin plates with concentric elastic ring supports

This paper studies the vibration behaviour of circular Mindlin plates with multiple concentric elastic ring supports. Utilizing the domain decomposition technique, a circular plate is divided into several annular segments and one core circular segment at the locations of the elastic ring supports. The governing differential equations and the solutions of these equations are presented for the annular and circular segments based on the Mindlin-plate theory. A homogenous equation system that governs the vibration of circular Mindlin plates with elastic ring supports is derived by imposing the essential and natural boundary and segment interface conditions. The first-known exact vibration frequencies for circular Mindlin plates with multiple concentric elastic ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented. The influence of the elastic ring support stiffness, locations, plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed.     

Determination of material properties of orthotropic plates with general boundary conditions using Inverse method and Fourier series

Determination of material properties of orthotropic plates with general elastic boundary supports using the Inverse method is presented in this paper. The material properties were identified through updating four parameters in the governing equation of a symmetrically laminated thin plate. The sum of the squared difference of the natural frequencies obtained from modal testing was minimized using the Forward method. The displacement function was expressed as a 2-D Fourier cosine series supplemented with several terms in the form of 1-D series. A classical solution was derived by letting the series exactly satisfy the governing differential equation and all the boundary conditions at every field and boundary point. In the Inverse method, the series expansions for all the relevant derivatives of the eigen frequencies were obtained through term-by-term differentiations of the displacements. Many simulations were done but one numerical example is presented to demonstrate the accuracy and convergence of the solutions.     

含智能流变材料铝合金夹层板结构的动力学特性研究

通过对一种含电流变液铝合金夹层板智能结构的动力学实验与仿真，分析和研究该结构在外电场作用下的动力特性变化。实验发现，利用外部控制条件(电场强度)的变化，可以改变结构的固有特性，如自然频率、结构阻尼等，可实现对结构的主动控制。数值分析时采用粘弹性材料等效处理方法模拟电流变材料，计算得到的结构振动特性与实验结果吻合较好。实验与仿真计算结果均表明，随着电场强度的增大，结构固有频率也随之出现上升，且增幅与场强有关；同时，电流变材料对结构振动所产生的阻尼效应不仅受外加电场影响，还与外加激励频率有关，响应控制实验结果说明电流变材料对结构在固有频率附近所产生响应的控制效果要更为明显一些。     

复合材料层合板阻尼特性有限元数值模拟

应用耗散能原理建立了复合材料层合板的阻尼预测分析模型,对复合材料层合板进行三维有限元模态分析,求出各个模态下的应力、应变分量。根据模态分析结果,从单向复合材料的阻尼性能参数出发,利用层合板应变能、耗散能和结构模态阻尼的关系求出各个模态对应的模态阻尼损耗因子。利用该方法,分别计算了单向层合板和对称层合板的结构模态阻尼损耗因子。数值计算结果与已有的理论分析和试验结果相比吻合较好,从而验证了该方法的合理性,该方法还可以比较三维应力分量对阻尼的贡献。     

Vibration and buckling of cross-ply laminated composite circular cylindrical shells according to a global higher-order theory

Natural frequencies and buckling stresses of cross-ply laminated composite circular cylindrical shells are analyzed by taking into account the effects of higher-order deformations such as transverse shear and normal deformations, and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for laminated composite circular cylindrical shells made of elastic and orthotropic materials is derived through Hamilton's principle. Several sets of truncated approximate higher-order theories are applied to solve the vibration and buckling problems of laminated composite circular cylindrical shells subjected to axial stresses. The total number of unknowns does not depend on the number of layers in any multilayered shells. In order to assure the accuracy of the present theory, convergence properties of the first natural frequency and corresponding buckling stress for the fundamental mode r=s=1 are examined in detail. The internal and external works are calculated and compared to prove the numerical accuracy of solutions. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. It is noticed that the present global higher-order approximate theories can predict accurately the natural frequencies and buckling stresses of simply supported laminated composite circular cylindrical shells within small number of unknowns.     

复合材料板与金属板榫槽粘接结合有限元分析

榫槽连接是航空结构中常用的一种连接形式。通过对金属板和复合材料板的榫槽粘接部位进行有限元计算，分析简单拉力作用下连接部位的应力分布以及金属板和复合材料板尺寸对最大等效应力的影响。通过比较发现，在所考察范围内榫槽长度、粘接层厚度和板宽度等因素对模型等效应力的影响并不十分显著，而两种材料板之间的相对厚度对最大等效应力影响较大，随着金属板厚度的增大，整个榫槽连接结构的最大等效应力有所减小。     

Maximizing the fundamental frequency of laminated cylindrical panels using layerwise optimization

A method of analysis is presented for determining the free vibration frequencies of cylindrically curved laminated panels under general edge conditions, and is implemented in a layerwise optimization (LO) scheme to determine the optimum fiber orientation angles for the maximum fundamental frequency. Based on the classical lamination theory applicable to thin panels, a method of Ritz is used to derive a frequency equation wherein the displacement functions are modified to accommodate arbitrary sets of edge conditions for both in-plane and out-of-plane motions. The LO approach, a recently developed scheme for laminated plates, is extended for the first time to the optimum design of curved panels. In a number of numerical examples, the accuracy of the analysis and the effectiveness of the LO approach are demonstrated.     

Nonlinear free vibration of laminated composite plates on elastic foundation with random system properties

The present investigation is concerned with free vibration analysis of laminated composite plates resting on elastic foundation undergoing large amplitude oscillation with random system properties. The lamina material properties and foundation stiffness parameters are modeled as basic random variables for accurate prediction of the system behavior. The basic formulation of the problem is based on higher-order shear displacement theory including rotatory inertia effects and von Karman-type nonlinear strain displacement relations. A C⁰ finite element is used for descretization of the laminate. A direct iterative method in conjunction with first-order Taylor series based perturbation technique procedure is developed to solve random nonlinear generalized eigenvalue problem. The developed probabilistic procedure is successfully used for the nonlinear free vibration problem with a reasonable accuracy. Typical numerical results (second-order statistics) are obtained for the composite plates resting on Winkler and Pasternak elastic foundations with different support conditions, side-to-thickness ratio, aspect ratio, oscillation amplitude ratio, stacking sequences and foundation parameters for symmetric and anti-symmetric cross-ply and angle-ply laminates. The results are validated with existing available results and independent Monte Carlo simulation.     

Dynamic finite element method for generally laminated composite beams

A dynamic finite element method for free vibration analysis of generally laminated composite beams is introduced on the basis of first-order shear deformation theory. The influences of Poisson effect, couplings among extensional, bending and torsional deformations, shear deformation and rotary inertia are incorporated in the formulation. The dynamic stiffness matrix is formulated based on the exact solutions of the differential equations of motion governing the free vibration of generally laminated composite beam. The effects of Poisson effect, material anisotropy, slender ratio, shear deformation and boundary condition on the natural frequencies of the composite beams are studied in detail by particular carefully selected examples. The numerical results of natural frequencies and mode shapes are presented and, whenever possible, compared to those previously published solutions in order to demonstrate the correctness and accuracy of the present method.     

螺栓松动边界下纤维增强复合薄板固有特性分析

通过人工弹簧刚度法对螺栓松动边界下纤维增强复合薄板的固有特性进行了分析。首先，为了研究螺栓松动边界的影响，人为地在复合薄板的约束端引入多组弹簧来模拟不同程度的螺栓松动边界，并建立了此类型边界下复合薄板的理论模型。然后，采用正交多项式法建立薄板自由振动的振型函数，并通过Ritz法对方程进行求解，计算此边界下薄板的固有频率和模态振型，给出具体的计算流程。最后，设计并组配了带有预埋压力传感器的螺栓松动边界下复合薄板的振动测试系统，准确测试了螺栓松动不同程度边界下对应的固有频率和模态振型，将实验结果与理论分析结果进行对比，发现两者的振型形态基本一致，其固有频率的误差在0.08%~7.54%之间，属于误差允许的范围，从而验证了所提出方法的可行性。     

基于重构核粒子法的带孔薄板模态分析研究

无网格法是一种新颖的工程数值计算方法,与有限元法相比,具有很多独特的优势。重构核粒子法具有变时-频特性和多分辨率特性等优点,在结构动力学中有广泛的应用。本文针对带孔薄板这一不连续问题,根据无网格法和板壳振动的基本理论,采用了可视性准则处理场函数的不连续性,编写了基于重构核粒子法的模态分析程序,得到了不同边界条件下带孔薄板的前五阶固有频率和模态,并和有限元分析结果进行了比较。算例表明该方法收敛性好、精度高,为带孔薄板的模态分析提供了一种新的求解方法。     

Dynamic instability characteristics of laminated composite plates subjected to partial follower edge load with damping

The study of vibration and dynamic instability behaviour of laminated composite plates subjected to partially distributed non-conservative follower forces is presented by using the finite element technique. The first-order shear deformation theory is used to model the plate, considering the effects of shear deformation and rotary inertia. The modal transformation technique is employed to the resulting equilibrium equation for subsequent analysis. Structural damping is introduced into the system in terms of equivalent viscous damping to study the significance of damping on stability characteristics. The effects of load width, boundary condition, aspect ratio, ply orientation, direction control of the load and damping parameters are considered for the stability behaviour of the plates. The results show that under follower loading, the system is susceptible to instability due to flutter alone or due to both flutter and divergence, depending on system parameters.     

Air damping influence on dynamic parameters of laminated composite plates

Damping performance of lightweight composite structures, like fibre reinforced plastics (FRPs) is more efficient than the conventional materials. This phenomena was found valuable in the aerospace and transport industries. For this reason accurate material properties of FRPs are required for precise prediction of dynamic response. However, the given properties are often burden with a significant uncertainty level due to environment influence which includes air damping, temperature changes, humidity, etc. The present study concerns with the air damping influence on the dynamic behaviour of laminated composites plates with moderate damping level. The effect on dynamic characteristics is evaluated experimentally using a vacuum chamber and a laser vibrometer. Resonant frequencies and modal loss factors changes are investigated in terms of material type, sample size and excitation amplitude. A semi-automatic and time efficient two-step testing procedure is developed for a precise measurement of loss factors of laminated composite plates.     

Stability behaviour of arbitrarily laminated composite plates with free and elastically restrained unloaded edges

In this paper, the initial buckling loads and the corresponding buckling modes of symmetric rectangular laminated plates are investigated. The considered laminates are supposed to have a uniform thickness, are subjected to a linearly distributed inplane compressive normal load and are simply supported at the two loaded edges with one free unloaded plate edge and with one simply supported unloaded edge where elastic rotational restraints are considered. Unlike in many other investigations, the composite laminates presently under consideration may have arbitrary yet symmetric lamination schemes with bending–torsion coupling. The initial buckling loads of such plates are calculated using the RITZ-method for which some especially adjusted displacement shape functions are employed. Since a series expansion of the buckling shape is performed in the load direction only while in the perpendicular direction one single displacement function can be shown to be sufficient, the present approach is numerically very efficient when compared to approaches in which a series representation is chosen with respect to both inplane directions. Comparison with reference results and with finite element computations leads to an excellent agreement. Some new findings on the general stability behaviour of this class of laminated plates are presented as a closure.     

基于材料-结构协同设计的层合板多级优化方法

提出一种以材料参数与结构参数为变量的复合材料层合板多级优化设计新方法。以单层纤维含量、层厚和铺层角为设计参数,建立了刚度和强度约束下的结构减重设计模型,基于有限元分析,运用所提出的三级优化策略完成结构轻量化设计。本文给出了不同载荷类型和位移边界条件下层合板优化算例,设计结果验证了方法的有效性。     

无网格法在固有频率分析中的应用

针对复合材料层合板的固有频率问题,结合径向基插值函数和修正后的H-R变分原理,推导了Hamilton正则方程的无网格列式,使得无网格法的优越性与弹性力学Hamilton正则方程的半解析法得到了有机的结合,为Hamilton正则方程提出了一种无网格半解析方法。     

弹性关节柔性操作臂的频率及振型特性分析

为了研究柔性操作臂关节弹性对频率及振型的作用机理,建立了柔性操作臂的弹性约束模型。根据弹性约束模型,得到了弹性关节柔性操作臂的频率方程及振型函数。采用数值方法,对弹性关节柔性操作臂的前三阶频率及振型特性进行了分析。结果表明：关节的弹性对柔性操作臂的频率及振型具有明显的影响,将关节视为理想刚性约束会产生明显的误差;由灵敏度分析可知,线性约束对频率的影响大于扭转约束,且高阶频率段表现较为明显;扭转约束对振型的影响比线性约束更为显著,随着扭转约束的增大,振型发生改变,且高阶振型表现较为明显。通过实验对建立的弹性约束模型进行验证,实验结果表明,所建立的弹性约束模型能够合理地表征关节的弹性约束作用,分析结果更接近实际情况,误差较小。