变角度纤维复合材料环扇形层合板的自由振动分析

与传统的直线纤维增强复合材料相比，变角度纤维复合材料具有更强的可设计性，为改善结构性能提供了更大的可能．鉴于此，本文将研究纤维的变角度铺设对复合材料环扇形层合板的自振频率及振动模态的影响．假设纤维的方向角沿环扇形板的径向线性变化，基于经典的层合板理论，采用微分求积法获得了环扇形层合板自由振动问题的数值解．通过与现有文献及ABAQUS有限元结果的比较验证了本文模型及方法的正确性和收敛性，并详细分析了纤维起始角和终止角的变化对层合板的自振频率及振动模态的影响．研究结果表明：与常刚度层合板相比，变角度纤维复合材料层合板的基频具有更大的调整空间，通过合理选择纤维起始角和终止角可有效提高层合板的基频．研究结果可为该种新型复合材料结构的优化设计提供一定的参考．     

基于连续丝束剪切技术的变角度复合材料层合板的热屈曲分析

连续丝束剪切(Continuous Tow Shearing, CTS)铺放技术是一种新的变角度层合板制作技术，这种新技术能显著减少丝束铺放过程中产生的丝束重叠和间隙等缺陷，然而，采用CTS技术铺设时，层合板的厚度将随着纤维角度的变化而变化．本文基于一阶剪切变形理论并应用Chebyshev-Ritz法对这种变厚度的变角度复合材料层合板的热屈曲问题进行了研究．假设纤维方向角沿板的长度方向按照线性变化，获得了均匀温度变化时变厚度层合板的临界热屈曲荷载．通过与现有文献的比较验证了本文方法的正确性，并进一步讨论了纤维铺设技术、纤维方向角的变化以及边界条件的不同对变角度复合材料层合板的临界屈曲温度的影响．研究结果表明，在体积相同的情况下，采用CTS铺设较传统的自动丝束铺放(AFP)可以进一步提升变角度层合板的临界屈曲温度．本文的研究结果可为变角度复合材料的设计提供一定的参考．     

考虑制作缺陷的变角度纤维复合材料层合板的屈曲

假设纤维方向角沿层合板的长度方向线性变化,研究含丝束重叠、间隙等制作缺陷的变角度纤维复合材料层合板的屈曲问题．采用ABAQUS 有限元软件建立层合板的有限元模型,选用S4 壳单元计算四边简支层合板在两端压缩荷载作用下的屈曲临界荷载及屈曲模态,并进行详细的参数分析．研究结果表明：当起始角相同时,含或不含制作缺陷的层合板的屈曲临界荷载均随着终止角的增大而逐渐提高,说明纤维的不同铺设方式对层合板的屈曲性能有很大影响．含重叠缺陷的层合板的屈曲临界荷载均大于不含缺陷层合板的值,而含间隙缺陷的层合板的屈曲临界荷载均小于不含缺陷层合板的值．当层合板的重叠、间隙缺陷共存且面积相等时,层合板的屈曲临界荷载与不含缺陷时层合板的值接近,制作缺陷对变角度纤维复合材料层合板屈曲模态的影响较小．本文研究结果可为含缺陷的变角度纤维复合材料层合板设计提供一定参考．     

含椭圆孔的变角度复合材料层合板的屈曲性能研究

本文利用变角度复合材料的纤维方向角可沿平面位置任意连续变化的特点,提出在孔附近采用与孔同心的椭圆曲线作为纤维铺设路径的层合板铺层方案,以改善含椭圆孔的层合板的孔边应力集中,进而提高层合板的抗屈曲性能．主要研究内容有：利用ABAQUS软件分析本文提出的孔边特殊铺层方式下变角度复合材料层合板的面内应力分布及屈曲性能,通过与传统直线铺层方式以及线性变角度铺层方式进行比较,说明了本文提出的新铺层方式的优越性,并详细分析了椭圆孔的离心率、开孔尺寸及开孔方位对层合板的屈曲临界荷载的影响．研究结果可为含椭圆孔的变角度复合材料层合板的结构设计和优化提供一定的参考．     

含分层损伤的变角度纤维层合板后屈曲力学行为研究

变角度（Variable angle tow,简称VAT）纤维复合材料层合板的纤维方向能够连续变化．相较于传统的直线纤维层合板,此类层合板通过刚度变化,整体的屈曲性能可以得到很大的提升．本文利用ABAQUS 自带的粘结单元(Cohesive Element)对预制圆形分层的变角度纤维复合材料层合板进行了后屈曲力学行为研究,得出载荷位移曲线,以及分层裂纹萌生和扩展的情况．然后本文分析了预制分层尺寸对板的刚度、前后屈曲阶段和裂纹萌生及扩展的影响．最后通过变角度纤维层合板和直线纤维层合板的后屈曲力学行为进行对比,深入探索了变角度复合材料层合板在抵抗分层裂纹萌生和扩展方面的优势．     

纤维曲线铺放的复合材料层合板的自由振动分析

假设曲线纤维的方向角沿板的长度方向按照线性规律变化,导出了纤维曲线铺设时的参考路径,将参考路径沿板的宽度方向平移可得一种曲线纤维增强复合材料单层板,当这种纤维曲线铺设的单层板对称铺放时即可得相应的曲线纤维增强复合材料层合板．基于弹性薄板的小挠度理论,建立了曲线纤维增强复合材料层合板自由振动问题的基本方程,采用微分求积法进行数值求解,得到了层合板的自振频率及相应的振型．与已有文献计算结果的比较,验证了本文计算结果的正确性．通过数值算例分析了微分求积法求解本问题时的收敛性,研究了纤维铺放路径和边界条件的不同对曲线纤维增强复合材料层合板频率及振型的影响,研究结果可为该种结构的设计提供一定的参考．     

复合材料层合板的动力特性分析

本文采用渐近分析方法,研究了对称角铺设复合材料层合板的动力特性问题,并给出了层合板自振频率关于铺设角的一般渐近表达式。最后,文中对三种常用的纤维增强复合材料板,给出了具体的计算数值结果。本文的所有方法均可推广到各种复合材料层合板的静力和稳定性的问题分析中。     

变角度纤维复合材料圆柱壳的轴压屈曲

变角度纤维复合材料的纤维方向角可沿铺层面内连续变化,因此相应结构的性能具有更高的设计灵活性和更大的优化空间．本文假设纤维方向角沿圆柱壳的轴向呈正弦函数变化,对变角度纤维复合材料圆柱壳在两端简支边界条件下的轴压屈曲问题进行研究．基于Donnell经典壳体理论,推导变角度纤维复合材料圆柱壳的前屈曲控制方程并运用伽辽金法进行求解,然后采用瑞利里兹法求解屈曲问题．通过和现有文献及有限元数值结果的对比,验证了本文模型的收敛性和正确性,通过数值算例分析了纤维起始角和终止角的变化对圆柱壳的屈曲临界荷载的影响．本文的研究结果可为变角度纤维复合材料圆柱壳的分析和设计提供一定的参考．     

粘弹层合板的稳态振动和层间应力

应用混合分层理论和Ressiner混合变分原理，在板厚方向取二次位移插值函数和三次、四次横向应力插值函数推导出粘弹层合板的动力学方程，得出简支粘弹层合板稳态振动的解。不仅得出与三层弹性板精确的自振频率吻合良好的解，而且对于粘弹层合板，所计算的自振频率和结构损耗因子也与三维结果吻合较好。计算了自由阻尼层合板对应的低阶法向位移响应幅值和层问横向应力的幅值。结果表明，较高的层间横向正应力是低频稳态振动中引起粘弹层合板分层破坏的主要因素，采用适当模量和厚度的粘弹性材料将有效地降低粘弹层合板的层间横向正应力的幅值。     

基于各向异性修正偶应力理论的Reddy型层合板的自由振动

本文基于各向异性修正偶应力理论建立了只含一个尺度参数的Reddy型复合材料层合板的自由振动模型。同见诸于文献的细观尺度Kirchhoff薄板偶应力模型相比,本文提出的新模型能够更精确的预测细观尺度下的中、厚层合板的自振频率。基于Hamilton原理推导了细观尺度下Reddy型复合材料层合板的运动微分方程以及边界条件,并以正交铺设的四边简支复合材料层合方板为例进行了解析求解,分析了尺度参数对自振频率的影响并对比了Kirchhoff、Mindlin和Reddy等三种板模型计算结果的异同。算例结果表明本文所给出的模型能够捕捉到复合材料层合板自由振动问题的尺度效应。另外,在细观尺度下Kirchhoff板模型所预测的自振频率相对于Mindlin板模型和Reddy板模型总是过高,且越接近厚板三者的差别就越大,这与经典理论中三种板模型的对比情况是一致的。     

Nonlinear vibration of symmetrically laminated composite skew plates by finite element method

Here, the large amplitude free flexural vibration behavior of symmetrically laminated composite skew plates is investigated using the finite element method. The formulation includes the effects of shear deformation, in-plane and rotary inertia. The geometric non-linearity based on von Kármán's assumptions is introduced. The nonlinear matrix amplitude equation obtained by employing Galerkin's method is solved by direct iteration technique. Time history for the nonlinear free vibration of composite skew plate is also obtained using Newmark's time integration technique to examine the accuracy of matrix amplitude equation. The variation of nonlinear frequency ratios with amplitudes is brought out considering different parameters such as skew angle, fiber orientation and boundary condition.     

Large amplitude free flexural vibrations of laminated composite skew plates

Here, the large amplitude free flexural vibration behaviors of thin laminated composite skew plates are investigated using finite element approach. The formulation includes the effects of shear deformation, in-plane and rotary inertia. The geometric non-linearity based on von Karman's assumptions is introduced. The non-linear governing equations obtained employing Lagrange's equations of motion are solved using the direct iteration technique. The variation of non-linear frequency ratios with amplitudes is brought out considering different parameters such as skew angle, number of layers, fiber orientation, boundary condition and aspect ratio. The influence of higher vibration modes on the non-linear dynamic behavior of laminated skew plates is also highlighted. The present study reveals the redistribution of vibrating mode shape at certain amplitude of vibration depending on geometric and lamination parameters of the plate. Also, the degree of hardening behavior increases with the skew angle and its rate of change depends on the level of amplitude of vibration.     

Maximum frequency design of laminated plates with mixed boundary conditions

A layerwise optimization (LO) approach is extended to accommodate the finite element analysis for optimizing the free vibration behavior of laminated composite plates with discontinuities along the boundaries. The classical non-conforming finite element is modified to fit into the LO procedure and is used to calculate natural frequencies of symmetrically laminated plates. This combined LO-FEM approach is applied to laminated rectangular plates with combinations of free, simply supported and clamped edges along parts of the plate boundary. The fundamental frequency, an object function for the present study, is maximized by optimizing design variables that are a set of fiber orientation angles in the layers. For illustrative purpose nine examples of square and rectangular plates with various types of mixed boundary conditions are considered, and a comprehensive set of results are presented for the optimum fiber orientation angles and the maximum fundamental frequencies of the 8-layer and 24-layer plates.     

轴向运动层合圆柱壳体的振动特性

研究了轴向运动层合圆柱壳体的振动特性．基于Donnell壳体理论,建立了轴向运动层合圆柱壳体的横向振动方程,使用Galerkin方法求解该振动方程,得到其固有频率,通过与有限元结果对比说明方法的有效性．分析了轴向速度、纤维方向角、长径比和厚径比对壳体振动特性的影响．研究表明：当纤维方向角为 (15?/-15?)s时,轴向运动柱壳前3阶固有频率达到最大值．     

Parametric study on supersonic flutter of angle-ply laminated plates using shear deformable finite element method

The influence of fiber orientation,flow yaw angle and length-to-thickness ratio on flutter characteristics of angle-ply laminated plates in supersonic flow is studied by finite element approach.The structural model is established using the Reissner-Mindlin theory in which the transverse shear deformation is considered.The aerodynamic pressure is evaluated by the quasi-steady first-order piston theory.The equations of motion are formulated based on the principle of virtual work.With the harmonic motion assumption,the flutter boundary is determined by solving a series of complex eigenvalue problems.Numerical study shows that (1) The flutter dynamic pressure and the coalescence of flutter modes depend on fiber orientation,flow yaw angle and length-to-thickness ratio;(2) The laminated plate with all fibers aligned with the flow direction gives the highest flutter dynamic pressure,but a slight yawing of the flow from the fiber orientation results in a sharp decrease of the flutter dynamic pressure;(3) The angle-ply laminated plate with fiber orientation angle equal to flow yaw angle gives high flutter dynamic pressure,but not the maximum flutter dynamic pressure;(4) With the decrease of length-to-thickness ratio,an adverse effect due to mode transition on the flutter dynamic pressure is found.     

On bimodal flutter behavior of a flexible airfoil

The dynamic aeroelastic behavior of an elastically supported airfoil is studied in order to investigate the possibilities of increasing critical flutter speed by exploiting its chord-wise flexibility. The flexible airfoil concept is implemented using a rigid airfoil-shaped leading edge, and a flexible thin laminated composite plate conformally attached to its trailing edge. The flutter behavior is studied in terms of the number of laminate plies used in the composite plate for a given aeroelastic system configuration. The flutter behavior is predicted by using an eigenfunction expansion approach which is also used to design a laminated plate in order to attain superior flutter characteristics. Such an airfoil is characterized by two types of flutter responses, the classical airfoil flutter and the plate flutter. Analysis shows that a significant increase in the critical flutter speed can be achieved with high plunge and low pitch stiffness in the region where the aeroelastic system exhibits a bimodal flutter behavior, e.g., where the airfoil flutter and the plate flutter occur simultaneously. The predicted flutter behavior of a flexible airfoil is experimentally verified by conducting a series of systematic aeroelastic system configurations wind tunnel flutter campaigns. The experimental investigations provide, for each type of flutter, a measured flutter response, including the one with indicated bimodal behavior.     

Dynamic stability analysis of shear-flexible composite beams

Dynamic stability behavior of the shear-flexible composite beams subjected to the nonconservative force is intensively investigated based on the finite element model using the Hermitian beam elements. For this, a formal engineering approach of the mechanics of the laminated composite beam is presented based on kinematic assumptions consistent with the Timoshenko beam theory, and the shear stiffness of the thin-walled composite beam is explicitly derived from the energy equivalence. An extended Hamilton’s principle is employed to evaluate the mass-, elastic stiffness-, geometric stiffness-, damping-, and load correction stiffness matrices. Evaluation procedures for the critical values of divergence and flutter loads of the nonconservative system with and without damping effects are then briefly introduced. In order to verify the validity and the accuracy of this study, the divergence and flutter loads are presented and compared with the results from other references, and the influence of various parameters on the divergence and flutter behavior of the laminated composite beams is newly addressed: (1) variation of the divergence and flutter loads with or without the effects of shear deformation and rotary inertia with respect to the nonconservativeness parameter and the fiber angle change, (2) influence of the internal and external damping on flutter loads whether to consider the shear deformation or not.     

Semi-analytical solution for three-dimensional vibration of thick continuous grading fiber reinforced (CGFR) annular plates on Pasternak elastic foundations with arbitrary boundary conditions on their circular edges

In this paper free vibration of continuous grading fiber reinforced (CGFR) annular plates on an elastic foundation, based on the three-dimensional theory of elasticity, for different boundary conditions at the circular edges is investigated. The foundation is described by the Pasternak or two-parameter model. The CGFR annular plates have an arbitrary variation of fiber volume fraction in the thickness direction. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its very high accuracy and versatility. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. Besides, results for CGFR plate with arbitrary variation of fiber volume fraction in the thickness direction of the plate are compared with discrete laminated composite plate. The main contribution of this work is to present useful results for continuous grading of fiber reinforcement in the thickness direction of a plate on an elastic foundation and comparison with similar discrete laminated composite plate. The interesting and new results show that non-dimensional natural frequency parameters of a functionally graded fiber volume fraction is larger than that of a discrete laminated and close to that of a 2-layer. The new results can be taken as the benchmark solutions for those from numerical methods and future researches.