低速冲击激励下嵌入黏弹性阻尼芯层的纤维金属混杂层合板动态响应预测模型

本文首次从解析角度建立了低速冲击激励下嵌入黏弹性阻尼芯层的纤维金属混杂层合板动态响应预测模型. 首先,结合经典层合板理论和冯$\cdot$卡门假设,建立了嵌入黏弹性芯层的纤维金属混杂层合板弹性损伤本构关系. 然后,将层合板受冲击时的变形分成接触和拉伸两个区域,在接触区域内,对金属层采用 Von Mises 失效准则,纤维层采用 Tsai-Hill 失效准则和对黏弹性层采用指数 Drucker-Prager 失效准则判断层合板损伤情况. 考虑不同材料层对冲击动态响应的贡献来修正两个变形区域的位移公式,进而计算结构因弹性变形产生的应变能,以及接触区域因塑性变形消耗的能量,实现每次失效事件发生后各层材料的能量、位移和冲击接触力的理论求解,并给出了结构动态响应分析的具体流程图. 最后,以嵌入 Zn33 黏弹性芯层的 TA2 钛合金混杂 T300 碳纤维/树脂层合板为研究对象,开展落锤冲击实验. 验证结果表明,理论预测与测试获得的冲击接触力、位移响应以及冲击载荷-位移曲线吻合较好,且关注的峰值点计算误差最大不超过 9%,进而验证了所提出的理论模型的有效性.      

APPROXIMATE SOLUTIONS FOR TRANSIENT RESPONSE OF CONSTRAINED DAMPING LAMINATED CANTILEVER PLATE

The series composed by beam mode function is used to approximate the displacement function of constrained damping of laminated cantilever plates, and the transverse deformation of the plate on which a concentrated force is acted is calculated using the principle of virtual work.By solving Lagrange＇s equation, the frequencies and model loss factors of free vibration of the plate are obtained, then the transient response of constrained damping of laminated cantilever plate is obtained, when the concentrated force is withdrawn suddenly.The theoretical calculations are compared with the experimental data, the results show：both the frequencies and the response time of theoretical calculation and its variational law with the parameters of the damping layer are identical with experimental results.Also, the response time of steel cantilever plate, unconstrained damping cantilever plate and constrained damping cantilever plate are brought into comparison, which shows that the constrained damping structure can effectively suppress the vibration.     

Nonlinear low-velocity impact on damped and matrix-cracked hybrid laminated beams containing carbon nanotube reinforced composite layers

This paper investigates the low-velocity impact response of a shear deformable laminated beam which contains both carbon nanotube reinforced composite (CNTRC) layers and carbon fiber reinforced composite (CFRC) layers. The effect of matrix cracks is considered, and a refined self-consistent model is selected to describe the degraded stiffness caused by the damage. The beam including damping effects rests on a two-parameter elastic foundation in thermal environments. Based on a higher-order shear deformation theory and von Kármán nonlinear strain–displacement relationships, the motion equations of the beam and impactor are established and solved by means of a two-step perturbation approach. The material properties of both CFRC layers and CNTRC layers are assumed to be temperature-dependent. To assess engineering application of this hybrid structure, two conditions for outer CNTRC layers and outer CFRC layers are compared. Besides, the effects of the crack density, volume fraction of carbon nanotube, temperature variation, the foundation stiffness and damping on the nonlinear low-velocity impact behavior of hybrid laminated beams are also discussed in detail.

     

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。     

含黏弹性夹芯FG-GRC后屈曲梁的低速冲击响应

研究了含黏弹性夹芯的功能梯度石墨烯增强复合材料(functionally graded graphene reinforced composite, FG-GRC)后屈曲梁在低速跌落冲击下的跳跃振荡行为.采用修正Halpin-Tsai细观模型预测FG-GRC的材料宏观属性.使用赫兹点接触模型确定冲击器和梁之间的接触力.提出了考虑轴向预应力的复合材料层本构关系和阻尼层的Kelvin型黏弹性本构.通过一种广义高阶剪切变形锯齿梁模型建立夹芯梁的非线性位移场. 基于Hamilton 能量变分原理, 推导了动力学控制方程组. 通过两步分析,首先获得弹性后屈曲平衡路径作为冲击问题的初始状态. 随后, 结合四阶龙格库塔法,拓展了两步摄动-伽辽金法计算接触力的时程曲线以及后屈曲梁的位移时程曲线.研究了后屈曲梁在单次和两次撞击下双稳态大幅振荡过程的动力学特征.讨论了轴向载荷、冲击速度、黏弹性阻尼特性、冲击器材料等因素对于碰撞接触力以及后屈曲梁动力响应的影响规律.结果表明, 接触力仅对冲击速度较为敏感,一定的结构碰撞参数设计可以在接触力变化不大的情况下,使得后屈曲梁由单势能阱运动转变为双阱大幅振荡.      

Dynamic analysis of composite plate with multiple delaminations based on higher-order zigzag theory

In a recent paper, Cho and Kim [Journal of Applied Mechanics] proposed a higher-order cubic zigzag theory of laminated composites with multiple delaminations. The proposed theory is not only accurate but also efficient because it work with a minimal number of degrees of freedom with the application of interface continuity conditions as well as bounding surface conditions of transverse shear stresses including delaminated interfaces. In this work, we investigate the dynamic behavior of laminated composite plates with multiple delaminations. A four-node finite element based on the efficient higher-order zigzag plate theory of laminated composite plates with multiple delaminations is developed to refine the prediction of frequencies, mode shape, and time response. Through the dynamic version of the variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. Natural frequency prediction and time response analysis of a composite plate with multiple delaminations demonstrate the accuracy and efficiency of the present finite element method. To prevent penetration violation at the delamination interfaces, unilateral contact constraints by Lagrange multiplier method are applied in the time response analysis. The present finite element is suitable for the prediction of dynamic response of thick composite plates with multiple and arbitrary shaped delaminations.     

Optimum design of laminated composite foam-filled sandwich plates subjected to strength constraint

Optimum design of laminated composite sandwich plates with both continuous (core thickness) and discrete (layer group fiber angles and thicknesses) design variables subjected to strength constraint is studied via a two-level optimization technique. The strength of a sandwich plate is determined in a failure analysis using the Tsai–Wu failure criterion and the finite element method which is formulated on the basis of the layerwise linear displacement theory. In the first level optimization of the design process, the discrete design variables are temporarily treated as continuous variables and the corresponding minimum weight of the sandwich plate is evaluated subject to the strength constraint using a constrained multi-start global optimization method. In the second level optimization, the optimal solution obtained in the first level optimization is used in the branch and bound method for solving a discrete optimization problem to determine the optimal design parameters and the final weight of the plate. Failure test of laminated composite foam-filled sandwich plates with different lamination arrangements are performed to validate the proposed optimal design method. A number of examples of the design of laminated composite foam-filled sandwich plates are given to demonstrate the feasibility and applications of the proposed method.     

Influence of rotatory inertia on dynamic stability of the viscoelastic symmetric cross-ply laminated plates

The dynamic stability problem of the symmetrically laminated cross-ply plates made of the viscoelastic Voigt–Kelvin material, compressed by time-dependent stochastic membrane forces, is investigated. The effect of rotatory inertia is included in the present formulation. It is assumed that all elastic moduli have the same retardation times. By using the direct Liapunov method, bounds of the almost sure stability of cross-ply plates as a function of viscous damping coefficient, retardation time, variances of the stochastic forces, ratio of the principal lamina stiffnesses, number of layers, plate aspect ratio, cross-ply ratio and intensity of the deterministic components of axial loading are obtained. Numerical calculations are performed for the Gaussian process with a zero mean, as well as an harmonic process with random phase.     

Active vibration control of thin constrained composite damping plates with double piezoelectric layers

Vibrations and the damping behaviour of thin constrained composite plates with double piezoelectric layers are analytically explored by using Fourier transformation and classical laminated plate theory. Electric potential equations in the double piezoelectric layers are solved with respect to closed and open circuit boundary conditions, an exterior dielectric slab and active control. The natural frequencies and loss factors of the constrained smart composite plates with passive control methods are not notably changed in comparison with those of the constrained composite plates without piezoelectric effects since vibrational energy does not efficiently convert to electrical energy. The loss factors of the composite plates with active constrained damping increase and the natural frequencies have significant variations as the proportional derivative gains increase. Transverse displacement power spectra of the piezoelectric composite plates with active control are compared with those of the piezoelectric composite plates with passive control showing that active control has the best suppression performance of vibrations for the constrained laminated plates with double piezoelectric layers. Radial power spectral density, phase angles and cylindrical-wave power spectral density are calculated. Interesting patterns of wave propagation are explained when plane wave expansion is used to obtain Bessel cylindrical waves.     

考虑面内破坏过程的含分层损伤复合材料加筋层合板的动力响应

基于复合材料层合板一阶剪切理论，推导了复合材料层合板单元的刚度阵和质量阵列式；同时采用了Adams应交能法与Rayleigh阻尼模型相结合的方法，构造了相应的阻尼阵列式；为了防止在低阶模态中分层处出现的上、下子板不合理的嵌入现象，建立了含分层损伤复合材料加筋层合板动力分析的分层分析模型和虚拟界面联接模型。在上述模型和理论基础上，采用了Tsai提出的刚度退化准则和动力响应分析的精细积分法，对含分层损伤复合材料加筋层合板结构进行了动力响应和破坏分析。通过算例，分别讨论了外载频率、分层位置，以及破坏过程的刚度退化对含损伤复合材料加筋层合板动力响应特征的影响，得到了一些具有理论和工程价值的结论。     

Effect of permanent indentation on the delamination threshold for small mass impact on plates

Small mass impacts on composite structures are common cases caused by hailstones and runway debris. Small mass impactors usually result in a wave controlled local response, which is independent of boundary conditions. This response occurs before the reflection of waves from the boundaries and cannot be modeled by large mass drop weight tests. An elasto-plastic contact law, which accounts for permanent indentation and damage effects, was used here to study small mass impact on laminated composite plates. By comparing with results from the Hertzian contact law, it was found that damage can change the dynamic response of the structure significantly with increasing impact velocity. Due to smaller contact force generated for the case of using elasto-plastic contact, the central displacement of the plate is also less than the one using Hertzian contact law. The linearized version of the contact law was then used to derive the closed-form approximations of the contact force, indentation and plate central displacement for the impact loading of composite laminates. The threshold velocity for delamination onset under small mass impact was predicted analytically based on the obtained peak contact forces by combining with an existing quasi-static delamination threshold load criterion. A good agreement was found between the predicted threshold values and published experimental results.     

泡沫结构阻尼仪板动态性能试验分析

本文对一种新型塑料加粘弹材料的复合夹芯减振仪表板的动力性能进行了分析,通过振动试验测试了系统的动力响应,分析其响应总均方根和频率特性,表明复合结构粘弹阻尼仪表板系统具有较好的动力性能,可有效地衰减振动能量。根据对不同结构的泡沫塑料复合结构粘弹阻尼仪表板的试验数据进行比较,证实增加粘弹材料,系统的动力性能可以有极大改善。     

正交铺设层合板的蠕变屈曲分析

研究了正交铺设层合板的蠕变失稳问题。为了更好地模拟实际情况，在单层板的本构关系中，材料各主方向模量的松也时间均取不同值，并在建立控制方程时考虑了横向剪切变形的影响，通过理论分析，得到了粘弹性层合板的瞬时弹性临界载荷和持久临界载荷，并在算例中首次利用时间增量方法得到了有初始度层合板在长期受地的蠕变变表，计算结果表明了持久临界载荷对于粘弹性层合板的具体含义，从而使粘弹性层合板的为屈曲问题有了较为完整的     

Transient dynamic response of debonded sandwich plates predicted with finite element analysis

Dynamic transient response of a composite sandwich plate with a penny-shaped debonded zone has been studied by using the finite element analysis within the ABAQUS/Explicit code in this paper. In order to accurately predict the response of the debonded sandwich plate to impulsive loading, contact–impact and sliding conditions along the damaged skin-to-core interface were imposed in the model through a kinematic predictor/corrector contact algorithm. The accuracy of the finite element (FE) model used was verified by comparing between numerical predictions and experimental data known in literature for the frequency spectrum of a cracked polycarbonate laminated beam containing a delamination. By analyzing nonlinear aspects of the transient dynamics of the sandwich plate, it is shown that the presence of the debond significantly alters its short-term response. In this respect, a considerable influence of contact events within the debonded region on the plate’s global dynamic response was found out. These results were presented in both time and frequency domains. The predictions performed also showed that the FE model applied would be useful for nondestructive evaluation of defects in composite sandwich plates, and for studying dynamic response of such plates to impact.     

黏弹夹芯板的有限元建模及实验研究

从有限元分析和数值模拟及实验验证的角度研究了黏弹夹芯板的频率依赖振动特性。夹芯板中间层为黏弹性材料,其刚度和阻尼的频率依赖性行为直接影响系统的模态频率和阻尼,并导致振动模式求解的复杂化。采用三阶七参数Biot模型描述黏弹性材料频率相关的黏弹性行为。开发了三层四节点28自由度的夹芯板单元,基于经典板理论和哈密顿原理建立了黏弹夹芯板的有限元动力学方程。通过引入辅助耗散坐标,将Biot模型和黏弹夹芯板的有限元动力学模型结合起来,并将其转化为常规二阶线性系统形式,极大简化了求解非线性振动特性的过程。对一边固定、另三边自由的黏弹夹芯板进行了前三阶固有频率和损耗因子的预测,并与实验结果对比。数值模拟结果和实验结果吻合良好,说明所提有限元方法是正确有效的。     

粘弹层合板的自由振动和横向应力

Based on Reddy＇s layerwise theory, the governing equations for dynamic response of viscoelastic laminated plate are derived by using the quadratic interpolation function for displacement in the direction of plate thickness. Vibration frequencies and loss factors are calculated for free vibration of simply supported viscoelastic sandwich plate, showing good agreement with the results in the literature. Harmonious transverse stresses can be obtained. The results show that the transverse shear stresses are the main factor to the delamination of viscoelastic laminated plate in lower-frequency free vibration, and the transverse normal stress is the main one in higher-frequency free vibration. Relationship between the modulus of viscoelastic materials and transverse stress is analyzed. Ratio between the transverse stress＇s maximum value and the in-plane stress＇s maximum-value is obtained. The results show that the proposed method, and the adopted equations and programs are reliable.     

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。     

INFLUENCE OF THE MIDDLE WEAK LAYER ON THE IMPACT BEHAVIOR OF LAMINATED STRUCTURES

In this paper, a calculation model based on the subsection displacement theory and the large deflection analysis is developed to describe the dynamic response of isotropic laminated circular plates impacted by a soft body. The model takes into account the interlaminar shear effect induced by the middle weak layer. It is proved by numerical examples that the difference between the model developed in this paper and that based on the classical laminated theory mainly depends on three factors, the elastic modulus of the glue, the radius of the circular plate and the impact force.     

约束阻尼层合板的稳态响应

基于Reddy分层理论推导出约束阻尼层合板的稳态振动方程,得到了约束阻尼层合板的振动频率和损耗因子;分别分析了约束阻尼层合板的粘弹性夹层厚度、模量对固有频率和损耗因子的影响;得到了稳态振动时振幅和频率曲线以及横向应力与面内应力。数值计算结果表明所采用的算法是可靠的。     

Stability of parametric vibrations of hybrid composite plates

In this paper, the dynamic stability of laminated hybrid composite plates subjected to periodic uniaxial stress and bending stress is studied. The governing equations of motion of Mathieu-type are established by using the Galerkin method with reduced eigenfunctions transforms. Based on Bolotin's method the regions of dynamic instability of laminated hybrid composite plates are determined by solving the eigenvalue problems. The effects of layer thickness ratio, layer number, core material and load parameter on the dynamic instability of laminated hybrid composite plates are investigated and discussed.