各向异性复合材料对称角铺设层合板非线性弯曲强迫振动

笔者曾经研究讨论了各向异性复合材料反对称角铺设层合板的非线性弯曲强迫振动问题[1]。本文是这一研究领域的继续和扩展。在这里,笔者详细研究了各向异性复合材料对称角铺设层合板在简谐激振力作用下的非线性弯曲强迫振动问题,做了包括算例的全解析过程分析,得到了各向异性对称角铺设层合板在各种量级载荷作用下的幅一频关系,分析了对称角铺设层合板结构的铺设方向角对非线性弯曲强迫振动的幅一频关系影响,所求得的解析形式结果保证了结果的可靠性。本文无疑是对复合材料层合板非线性强迫振动问题研究的一个有意义的深入扩展,它们对于探讨其它复合材料结构的非线性动力问题具有一定的意义。      

复合材料层合板故障诊断的一种新方法

本文计算了无损板在给定模态下各单元的能量,求得每个单元对该阶模态下全板能量的贡献,并通过模态实验得到损伤前后各阶固频的变化.分析发现两者之间存在着内在联系,从而得到一种分析小损伤位置和范围的新方法.     

Transient analysis of FGM and laminated composite structures using a refined 8-node ANS shell element

In this paper, we investigate the vibration analysis of functionally graded material (FGM) and laminated composite structures, using a refined 8-node shell element that allows for the effects of transverse shear deformation and rotary inertia. The properties of FGM vary continuously through the thickness direction according to the volume fraction of constituents defined by sigmoid function, but in this method, their Poisson’s ratios of the FGM plates and shells are assumed to be constant. The finite element, based on a first-order shear deformation theory, is further improved by the combined use of assumed natural strains and different sets of collocation points for interpolation the different strain components. We analyze the influence of the shell element with the various location and number of enhanced membrane and shear interpolation. Using the assumed natural strain method with proper interpolation functions the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. The natural frequencies of plates and shells are presented, and the forced vibration analysis of FGM and laminated composite plates and shells subjected to arbitrary loading is carried out. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To validate and compare the finite element numerical solutions, the reference solutions of plates based on the Navier’s method, the series solutions of sigmoid FGM (S-FGM) plates are obtained. Results of the present theory show good agreement with the reference solutions. In addition the effect of damping is investigated on the forced vibration analysis of FGM plates and shells.     

各向异性反对称角铺设层合板的非线性弯曲强迫振动分析

笔者以具有代表性的各向异性复合材料反对称角铺设层合板为例,对其在简谐激振力作用下的非线性弯曲强迫振动问题做了包括算例在内的全解析过程分析.得到各向异性反对称角铺设层合板在各种级别荷载作用下的幅-频关系,以及层合板结构铺设层数的变化对非线性弯曲强迫振动幅-频关系的影响,所求得的解析形式的结果保证了结果的可靠性以及由此所推得的结论的代表性.本文工作无疑是复合材料层合板非线性动力问题的一个有意义的尝试,它们对于以后探讨各向异性层合板其它方面的非线性动力问题具有一定的意义.      

层合阻尼结构各向异性设计之阻尼特性分析

将各向异性设计引入层合阻尼结构中,从理论上分析了各向异性层合阻尼结构的阻尼特性及其控制机理,从而验证了建立约束阻尼层合结构各向异性优化设计新体系的可行性。文中衡量结构阻尼减振效果的重要指标是结构系统的损耗因子,采用半无限简支板为例,对各种铺层形式作了大量的计算;并以最大损耗因子为目标函数,以铺层角度、频率、厚度等为约束条件进行结构优化设计。分析研究表明,该结构内部柔性层对阻尼的影响要比应力耦合对其影响大得多;在高于基本模式的固有频率下,能显著地提高损耗因子。     

Effects of local damage on vibration characteristics of composite pyramidal truss core sandwich structure

The effects of local damage on the natural frequencies and the corresponding vibration modes of composite pyramidal truss core sandwich structures are studied in the present paper. Hot press molding method is used to fabricate intact and damaged pyramidal truss core sandwich structures, and modal testing is carried out to obtain their natural frequencies. A FEM model is also constructed to investigate their vibration characteristics numerically. It is found that the calculated natural frequencies are in relatively good agreement with the measured results. By using the experimentally validated FEM model, a series of numerical analyses are conducted to further explore the effects of damage extent, damage location, damage form on the vibration characteristics of composite pyramidal truss core sandwich structures as well as the influence of boundary conditions. The conclusion derived from this study is expected to be useful for analyzing practical problems related to structural health monitoring of composite lattice sandwich structures.     

基于灵敏度分析的复合材料层合板优化设计

工程结构中的复合材料层合板的几何参数往往具有随机性质.如何研究随机参数层合板的灵敏度,并对参数进行优化分析,这对正确估计结构设计的可靠性有着非常重要的意义.根据层合板的一阶剪切理论,采用样条有限元法,推导并建立了层合板的振动方程,刚度矩阵,质量矩阵,比例阻尼矩阵以及求解反对称层合板响应灵敏度的计算公式,在基于灵敏度分析的基础上,进行了复合材料层合板的基频分析和优化设计,并用网格法计算最佳铺层角.数值算例验证了算法的有效性.     

Transient dynamic and damping analysis of laminated anisotropic plates using a refined plate theory

A refined model is presented for the linear transient dynamic and damping analysis of laminated anisotropic composite plates. Experimental measurements of specific damping capacity of unidirectional composite beams are used to predict the specific damping capacity of laminated composite plates in various modes of vibration. A finite element idealization is adopted, and the quadratic Lagrangian element is used together with selective/reduced integration. A viscous damping approximation is then employed to calculate the damped transient response of laminated plates. The effects of transverse shear deformation, symmetry condition, boundary conditions, anisotropy, aspect ratio, fibre orientation and the lamination scheme on specific damping capacity and damped transient response are investigated. Realistic examples illustrate the importance of these parameters. The present results agree very closely with experimental results available in the literature and can serve as a benchmark for future comparison by other investigators.     

Vibration analysis of symmetric laminated composite plates with attached mass

In this study, vibration of symmetrically laminated composite plates with attached mass is studied. The Ritz method with algebraic polynomial displacement field is used. The plates with at least two adjacent free edges are considered in the formulations. The effect of various parameters (number of layers, ratio of attached mass to the plate mass, position of attached mass, fiber orientation) upon the frequencies and mode shapes is investigated. It is found that attachment of a mass has important effects on the vibration characteristics of composite laminated plates.     

Free and forced vibration analysis of laminated composite plates and shells using a 9-node assumed strain shell element

The natural frequencies of isotropic and composite laminates are presented. The forced vibration analysis of laminated composite plates and shells subjected to arbitrary loading is investigated. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To develop a laminated shell element for free and forced vibration analysis, the equivalent constitutive equation that makes the computation of composite structures efficient was applied. The Mindlin-Reissner theory which allows the shear deformation and rotary inertia effect to be considered is adopted for development of nine-node assumed strain shell element. The present shell element offers significant advantages since it consistently uses the natural co-ordinate system. Results of the present theory show good agreement with the 3-D elasticity and analytical solutions. In addition the effect of damping is investigated on the forced vibration analysis of laminated composite plates and shells.     

Three-dimensional free and transient vibration analysis of composite laminated and sandwich rectangular parallelepipeds: Beams,plates and solids

This paper presents an efficient method for predicting the free and transient vibrations of multilayered composite structures with parallelepiped shapes including beams, plates and solids. The exact three-dimensional elasticity theory combined with a multilevel partitioning hierarchy, viz., multilayered parallelepiped, individual layer and layer segment, is employed in the analysis. The continuity constraints on common interfaces of adjacent layer segments are imposed by a modified variational principle, and the displacement components of each layer segment are assumed in the form of orthogonal polynomials and/or trigonometric functions. Numerical studies are given for free vibrations of composite laminated and sandwich beams, plates, and solids. Some in-plane shear vibration modes missed in previous elasticity solutions for multilayered plates are examined. The natural frequencies derived from Reddy’s high-order shear deformation theory and layerwise theory for soft-core sandwich plates show significant deviation from elasticity solutions. Transient displacement and stress responses for angle-ply laminated and sandwich plates under four types of impulsive loads (including rectangular, triangular, half-sine and exponential pulses) are obtained by the Newmark integration procedure. The present solutions may serve as benchmark data for assessing the accuracy of advanced structural theories and new developments in numerical methods.     

基于遗传算法和复合二次径向基函数的复合材料层合板自由振动分析

为了提高复合材料层合板自由振动分析的精度,采用无网格径向基配点法分析复合材料材料层合板的自由振动问题,径向基函数的形状参数对计算精度有很大影响。利用遗传算法对复合二次径向基函数的形状参数进行优化,用优化后的形状参数的复合二次径向基函数计算复合材料层合板的固有频率,计算结果与文献中的结果具有较好的一致性。遗传算法在形状参数优化方面具有很大的潜力,所提出的方法具有较高的计算精度。     

Estimation of composite damage model parameters using spectral finite element and neural network

A multi-layer perceptron (MLP) network using error back propagation algorithm is employed in this paper to estimate the damage parameters from broad-band spectral data as diagnostic signal. Various existing models of damage in laminated composite and the resulting stiffness degradation are discussed from comparative view-point. Degradation of ply properties can be considered to be one of the damage model parameters while monitoring transverse matrix cracks in cross-ply, splitting in longitudinal ply, and evolution of consecutive stages of damage, such as delaminations and fiber fracture. The stiffness degradation factor, the location and size of the damaged zone in laminated composite beam are considered as damage model parameters in the present paper. Fourier spectral data, which is typical to most of the diagnostic wave measurements, are used as input to the neural network. Since, training the neural network in such case involves many data sets and all of these data are difficult to generate using experiments, a spectral finite element model (SFEM) with embedded degraded zone in laminated composite beam is developed. Numerical simulation using this element is carried out, which shows the nature of temporal signal that are likely to be measured. Analytical studies on the performance of the neural network are presented based on numerically simulated data. Effect of measurement noise on the network performance is also reported.     

Assessing the Scaling Subtraction Method for Impact Damage Detection in Composite Plates

The scaling subtraction method (SSM) is a non-destructive measurement approach used to extract nonlinear features from the elastic response of a structure. As such it can be used for damage detection purposes by identifying nonlinearities that may result from the presence of micro cracks or inclusions in granular and metallic materials. The effectiveness of such a technique to detect the presence of damage modes typical of laminated composite materials has not been yet assessed. With the purpose of filling this gap, in this paper the SSM is applied to inspect two laminated composite plates with different sizes, impact positions and sensor arrangement. Intact and damaged specimens are tested under harmonic excitations of different amplitude and frequency (the latter selected among the ultrasonic natural frequencies of the two plates). For each excitation case the recorded vibration signals are subtracted from the linearly rescaled reference signals and the SSM nonlinear indicators are calculated. The sensitivity of the method to the presence of damage is assessed in different sensor-receiver scenarios as well as for different excitation frequency and amplitude levels. Finite element numerical investigations are also performed to make comparisons with the experimental results.     

Analysis of stiffness loss in cross-ply composite laminates

The behaviour of laminated composite plates beyond first-ply failure has been the subject of much research work. It is well known that generally, the load-bearing capability of laminated composite plates can remain significant despite the presence of some damage in the plies. Traditionally, the ply-discount method has been used among analysts and designers, although the approach is generally regarded as too conservative. It is therefore desirable to develop models for the prediction of the mechanical properties of damaged composite laminates at various applied loads, and to be able to correlate the changes in properties with the amount of damage and cracking within each constituent ply. Generally, if the models are to be useful as predictive tools, they must be capable of not only sufficiently describing the damage state but also the nature of the damage evolution with loading. This ‘evolution law’ is often obtained through fracture analysis, although it should be noted that the diffused nature of cracks and the multiplicity of failure modes in composites in general greatly complicates the analysis. The problem of transverse matrix cracking in cross-ply laminates under uniaxial tension is considerably simpler because it is essentially dominated by mode I fracture. Thus it is necessarily the first step for any model aiming to predict stiffness losses in composite laminates. In this paper, a constitutive model of the damage state for composite laminates, first proposed by Allen et al., is used with a damage evolution criterion based on strain energy to predict the stiffness loss due to matrix cracking in cross-ply laminated composite plates. Although the constitutive model does not require the determination of many constants, the state of damage is described by a vector of internal state variables (ISV), which contains information on the crack geometry and fracture modes. A series of parametric finite element analyses was performed to determine the effects of relative ply thicknesses, crack density and crack opening profile on the vector of ISVs. A computer algorithm was written for the analysis of cross-ply laminates based on the damage evolution criterion proposed in this work. The results of the analysis compare favourably with experimental measurements of progressive stiffness loss in damaged cross-ply graphite-epoxy laminates obtained from other researchers.     

Vibration characteristics of laminated composite plates with embedded shape memory alloys

Shape memory alloy (SMA) is commercially available for a variety of actuator and damping materials. Recently, SMA wires have also become commercially available for the design of smart composite structures because SMA wires with a small diameter can be easily produced. In this work, two types of SMA-based composites are presented for investigating the vibration characteristics. First, laminated composite plates containing unidirectional fine SMA wires are fabricated. By measuring the vibration mode of a clamped cantilever, the influence of both SMA arrangement and temperature on the vibration characteristics is made clear. Next, laminated composite plates with embedded woven SMA layer are fabricated. The stiffness tuning capability is evaluated by impact vibration tests with different temperatures. It is found that the stiffness tuning capability may be improved by increasing the volume fraction of SMAs and by controlling accurately the internal stress according to the phase transformation temperature of SMAs from martensite to austenite. The theoretical prediction on the natural frequency considering the SMAs behavior and laminated structures is proposed and their results agree reasonably with experimental ones.     

A meshless local radial point collocation method for free vibration analysis of laminated composite plates

In this paper, a meshless local radial point collocation method based on multiquadric radial basis function is proposed to analyze the free vibration of laminated composite plates. This method approximates the governing equations based on first-order shear deformation theory using the nodes in the support domain of any data center. Natural frequencies of the laminated composite plates with various boundary conditions, side-to-thickness ratios, and material properties are computed by present method. The choice of shape parameter, effect of dimensionless sizes of the support domain on accuracy, convergence characteristics are studied by several numerical examples. The results are compared with available published results which demonstrate the accuracy and efficiency of present method.     

Thermal postbuckling analysis of fiber–metal laminated plates including interfacial damage

Considering the effects of interfacial damage, geometric nonlinearity and transverse shear deformation, thermal postbuckling of fiber–metal laminated plates including interfacial damage is analyzed in detail. Firstly, the Heaviside step function and higher order shear deformation functions are introduced into displacement field so that the damage degree can be characterized. Then, the shape functions can be determined by using the stress continuity conditions between interfaces and the stress boundaries on surfaces. By using the generalized variational principle, the thermal postbuckling equilibrium equations of fiber–metal laminated plates including interfacial damage are established. Finally, the thermal postbuckling problem is solved by adopting finite difference method and iteration method. In numerical examples, the effects of interfacial damage, width-to-thickness ratio and thermal load on the thermal postbuckling of fiber–metal laminated plates including interfacial damage are investigated.     

Analysis for buckling and vibrations of composite stiffened shells and plates

This paper deals with development of triangular finite element for buckling and vibration analysis of laminated composite stiffened shells. For the laminated shell, an equivalent layer shell theory is employed. The first-order shear deformation theory including extension of the normal line is used. In order to take into account a non-homogeneous distribution of the transverse shear stresses a correction of transverse shear stiffness is employed. Based on the equivalent layer theory with six degrees of freedom (three displacements and three rotations), a finite element that ensures C⁰ continuity of the displacement and rotation fields across inter-element boundaries has been developed. Numerical examples are presented to show the accuracy and convergence characteristics of the element. Results of vibration and buckling analysis of stiffened plates and shells are discussed.