Active damping of rotating composite thin-walled beams using MFC actuators and PVDF sensors

The object of this research is to enhance the damping performance for vibration suppression of rotating composite thin-walled beams using MFC actuators and PVDF sensors. The formulation is based on single cell composite beam including a warping function, centrifugal force, Coriolis acceleration and piezoelectric effect. Adaptive capability of the beam is acquired through the use of a negative velocity feedback control algorithm. Numerical analysis is performed using finite element method and Newmark time integration method is used to calculate the time response of the model. It is observed that the feedback control gain has an effect on damping performance. The paper continues with an investigation into influences of parameters such as the rotating speed and the fiber orientation in host structures. Also, it is confirmed that effective damping performance is achievable through the suitable arrangement and distributed size of sensor and actuator pair using case study.     

A modified couple stress model for bending analysis of composite laminated beams with first order shear deformation

Based on a modified couple stress theory, a model for composite laminated beam with first order shear deformation is developed. The characteristics of the theory are the use of rotation–displacement as dependent variable and the use of only one constant to describe the material’s micro-structural characteristics. The present model of beam can be viewed as a simplified couple stress theory in engineering mechanics. An example as a cross-ply simply supported beam subjected to cylindrical bending loads of f_w = q₀ sin (πx/L) is adopted and explicit expression of analysis solution is obtained. Numerical results show that the present beam model can capture the scale effects of microstructure, and the deflections and stresses of the present model of couple stress beam are smaller than that by the classical beam mode. Additionally, the present model can be reduced to the classical composite laminated Timoshenko beam model, Isotropic Timoshenko beam model of couple stress theory, classical isotropic Timoshenko beam, composite laminated Bernoulli–Euler beam model of couple stress theory and isotropic Bernoulli–Euler beam of couple stress theory.     

Stress analysis and material tailoring in isotropic linear thermoelastic incompressible functionally graded rotating disks of variable thickness

We analyze axisymmetric deformations of a rotating disk with its thickness, mass density, thermal expansion coefficient and shear modulus varying in the radial direction. The disk is made of a rubberlike material that is modeled as isotropic, linear thermoelastic and incompressible. We note that the hydrostatic pressure in the constitutive relation of the material is to be determined as a part of the solution of the problem since it cannot be determined from the strain field. The problem is analyzed by using an Airy stress function φ. The non-homogeneous ordinary differential equation with variable coefficients for φ is solved either analytically or numerically by the differential quadrature method. We have also analyzed the challenging problem of tailoring the variation of either the shear modulus or the thermal expansion coefficient in the radial direction so that a linear combination of the hoop stress and the radial stress is constant in the disk. For a rotating annular disk we present the explicit expression of the thermal expansion coefficient for the hoop stress to be uniform within the disk. For a rotating solid disk we give the exact expressions for the shear modulus and the thermal expansion coefficient as functions of the radial coordinate so as to achieve constant hoop stress. Numerical results for a few typical problems are presented to illuminate effects of material inhomogeneities on deformations of a hollow and a solid rotating disk.     

湿热环境对旋转复合材料梁摆振特性的影响

首先,基于复合材料在湿热环境下的本构关系推导了旋转复合材料梁轴力和弯矩的表达式,分析了温度和湿度对轴力和弯矩的影响,然后,基于d’Alembert原理建立了旋转复合材料梁摆振控制方程,并应用Galerkin法进行求解,分析了温度和湿度对旋转复合材料梁刚度的影响,最后,通过数值模拟讨论了湿热环境对旋转复合材料梁摆振动力学特性的影响。结果表明:湿热环境对旋转复合材料梁的摆振频率和模态影响显著,摆振频率随湿热环境加剧而降低,热膨胀效应对摆振频率的影响大于材料性能变化对其的影响,湿热环境与旋转的联合作用使模态的节点位置发生明显偏移。     

Vibration analysis of shape-optimized rotating cantilever beams

The shape optimization of rotating beams is carried out in order to minimize the vibrations. The objective is the maximization of the fundamental frequency with constraints on the beam mass and static tip deflections. The finite-element method (FEM) is used to model the rotating beam and sequential quadratic programming (SQP) is used for the optimization. The effects of beam frequency maximi-zation and hub–beam frequency maximization on the optimized shapes and the dynamic characteristics of these shapes are studied. The beam shapes are optimized for different speeds. The natural frequencies and time responses of these optimized shapes are studied using numerical simulation. Based on the numerical study, suggestions for formulating an appropriate optimization problem in a given context are made.     

复合材料封闭变截面薄壁梁自由振动分析

摘要：基于拉格朗日方程建立了复合材料封闭变截面薄壁梁的自由振动微分方程,给出了两种刚度配置下的变矩形截面悬臂直梁的自由振动方程简化形式及其相应的迦辽金法求解的固有频率。基于大型通用有限元软件ANSYS,计算了薄壁变截面悬臂梁的固有频率,并且与迦辽金法的求解结果进行了对比。分析了复合材料的弹性耦合,铺层角度和截面变化对薄壁梁的自由振动的影响。     

Three-dimensional analysis of multi-layer composite plates of arbitrary shape and boundary conditions with shear slip interfaces

An accurate semi-analytical method for three-dimensional static analysis of composite plates consisting of several anisotropic layers with shear slip imperfection is presented. The geometry and boundary conditions of the composite plate are arbitrary. At given interfaces, the imperfections are modeled via linear springs. The in-plane displacements are represented by appropriate expressions such that their discontinuity across the interfaces is incorporated accordingly. Also, the out-of-plane displacement normal to the interface must be continuous while the out-of-plane normal strain is discontinuous across the interface. In this approach, the essential boundary conditions are satisfied exactly, and the continuity of the inter-layer traction is captured with high accuracy.     

Finite element analysis and parametric study of steel-concrete composite beams

A finite element model is presented to predict the stresses and deformations in steel-concrete composite beams. The model takes into account the effect of cracking and tension-stiffening in the tensed concrete, and of longitudinal slip between the steel beam and the concrete slab due to the ‘partial interaction’ of theconnectors. Some comparisons with experimental data available in literature are reported to validate the efficiency of the proposed model. Finally, a parametric study was done to investigate the effects of the geometric and mechanical variables as boundary conditions and the slip modulus of the connectors.     

Analytical solution for the singular stress distribution due to V-notch in an orthotropic plate material

On the basis of general solutions of two-dimensional linear elasticity, displacement and singular stress fields near the singular point in orthotropic materials are derived in closed form expressions. According to the presented expressions, analysis formulas of displacement and singular stress fields near the tip of a V-notch under the symmetric and the anti-symmetric modes are obtained subsequently. The open literatures devoted to developing stress singularity near the tip of the V-notch in anisotropic or orthotropic materials. In this study, however, not only direct eigenequations were derived, but also the explicit solutions of displacement and singular stress fields were obtained. At the end, the correctness of the formulas of the singular stress field near the tip of the V-notch has been verified by FEM analysis.     

Prediction of material coupling effect on structural damping of composite beams and blades

The present paper investigates the effect of material coupling on static and modal characteristics of composite structures. Incorporation of stiffness and damping coupling terms into a beam formulation yields equivalent section stiffness and damping properties. Building upon the damping mechanics, an extended beam finite element is developed capable of providing the stiffness and damping matrices of the structure. Validation cases on beams and blades demonstrate the importance of all stiffness and damping terms. Numerical results validate the predicted effect of material coupling on static characteristics of composite box-section beams. The effect of the full coupling damping matrices on modal frequencies and structural modal damping of composite beams is investigated. Box-section beams and small blade models with various ply angle laminations at the girder segments are considered. Finally, the developed finite element is applied to the prediction of the modal characteristics of a 19 m realistic wind-turbine model blade.     

The stress analysis method for three-dimensional composite materials

This study proposes a stress analysis method for three-dimensionally fiber reinforced composite materials. In this method, the rule-of mixture for composites is successfully applied to 3-D space in which material properties would change 3-dimensionally. The fundamental formulas for Young's modulus, shear modulus, and Poisson's ratio are derived. Also, we discuss a strength estimation and an optimum material design technique for 3-D composite materials. The analysis is executed for a triaxial orthogonally woven fabric, and their results are compared to the experimental data in order to verify the accuracy of this method. The present methodology can be easily understood with basic material mechanics and elementary mathematics, so it enables us to write a computer program of this theory without difficulty. Furthermore, this method can be applied to various types of 3-D composites because of its general-purpose characteristics.     

旋转压电复合圆柱的弹性分析

针对由各向同性弹性核和压电层组成的两层复合圆柱的旋转问题,给出了弹性力学解。先从压电层的静电平衡方程出发,得到含一个待定常数的电位移形式解,并由此分别给出弹性核和压电层的位移通解,然后利用力学和电学边界条件以及界面处的连续条件确定出所有各层中引入的待定常数,最终得到原问题的解。数值结果表明：当压电层的内外表面均接地时,压电层中的径向应力幅值随弹性核材料的杨氏模量增大而增大,而环向应力则正好相反。弹性核材料的泊松比及外加在压电层内外表面上的电势对旋转两层复合圆柱内的应力响应均有显著的影响。     

Large amplitude vibration analysis of composite beams: Simple closed-form solutions

Large amplitude vibration analysis of laminated composite beam with axially immovable ends is investigated with symmetric and asymmetric layup orientations by using the Rayleigh–Ritz (R–R) method. The displacement fields used in the analytical formulation are coupled by using the homogeneous governing static axial equilibrium equation of the beam. Geometric nonlinearity of von-Karman type is considered which accounts for the membrane stretching action of the beam. The simple closed-form solutions are presented for the nonlinear harmonic radian frequency as function of central amplitude of the beam using the R–R method. The nonlinear harmonic radian frequency results obtained from the closed-form solutions of the R–R method in general show good agreement with the results obtained from simple iterative finite element formulation. Furthermore, the closed-form expressions are corrected for the harmonic motion assumption from the available literature results on the existence of quadratic and cubic nonlinearity. It is interesting to note that the composite beams can result in asymmetric frequency vs. amplitude curves depending upon the nature of direction of displacement in contrast to isotropic beams which exhibit cubic nonlinearity only and leads to symmetric frequency vs. amplitude curves with respect to sign of the amplitude.     

Applications of thermoelastic stress analysis to composite materials

A number of applied thermoelastic stress analysis (TSA) studies on composite components and assemblies are described, for the purpose of illustrating the potential of the technique for use with composite materials.     

旋转柱面产生动态散斑的统计特性分析

高斯光束照射到以角速度ω 旋转的圆柱体表面时,反射空间将出现的动态散斑随着被测表面的运动连续变化,这是一个随机过程。研究了当旋转圆柱体表面满足弱散射体条件时,在菲涅尔衍射场形成的动态散斑的统计特性;给出了几种特定情况下描述动态散斑时间-空间相关性质的参数——动态散斑的空间相关长度,动态散斑的相关时间,动态散斑的平移距离和相关距离。这些参数表明动态散斑的统计特性与圆柱体曲率半径、入射光束、表面微观形貌、物体旋转角速度、光学几何结构因素有关;依据参数分析了动态散斑运动形式,动态散斑纯沸腾运动取决于观察面到散射屏出射平面的距离,投射到散射屏出射平面上的照明光波波面的曲率半径和散射体的曲率半径。     

螺栓夹持填充孔复合材料层压板层间应力分析

为了研究含螺栓复合材料层压板连接接头的层间应力分布规律,提出了采用填充孔形式和虚拟界面层方法求解层间应力,并建立了三维有限元模型对受面内压缩载荷的螺栓夹持填充孔层压板进行分析。结果表明:层压板层间应力集中不仅发生在孔边,还会在螺栓头边缘附近出现,且夹持力越大螺栓头边缘附近的层间应力集中越严重;合理的螺栓夹持力能改善孔边应力状态,提高孔边抵抗分层的能力,但无法改善螺栓头边缘附近的层间剪切应力集中状态。因此,在进行含螺栓夹持的层压板机械连接结构孔边层间强度设计时,也要考虑螺栓头边缘的层间剪切应力集中问题,以提高复合材料结构的安全性。     

Three-dimensional vibration analysis of multilayered piezoelectric composite plates

We investigate the free vibration of multilayered piezoelectric composite plates. A brief review of the theoretical developments in piezoelasticity that are relevant to smart composite structures is presented. An analysis is performed using the differential quadrature (DQ) technique to solve three-dimensional equations of piezoelasticity, and technical issues are thoroughly discussed. Solutions for piezoelastic laminated plates are made possible with the development and implementation of the DQ layerwise modeling technique, which allows different boundary conditions to be imposed at the edges of the plates. The numerical results of different plate problems are presented, and the effects of the piezoelasticity of these problems are investigated. The DQ model predictions are validated against existing results, with good agreement found.     

Coupled deflection analysis of thin-walled Timoshenko laminated composite beams

For the deflection analyses of thin-walled Timoshenko laminated composite beams with the mono- symmetric I-, channel-, and L-shaped sections, the stiffness matrices are derived based on the solutions of the simultaneous ordinary differential equations. A general thin-walled composite beam theory considering shear deformation effect is developed by introducing Vlasov’s assumptions. The shear stiffnesses of thin-walled composite beams are explicitly derived from the energy equivalence. The equilibrium equations and force-deformation relations are derived from energy principles. By introducing 14 displacement parameters, a generalized eigenvalue problem that has complex eigenvalues and multiple zero eigenvalues is formulated. Polynomial expressions are assumed as trial solutions for displacement parameters and eigenmodes containing undetermined parameters equal to the number of zero eigenvalues are determined by invoking the identity condition to the equilibrium equations. Then the displacement functions are constructed by combining eigenvectors and polynomial solutions corresponding to nonzero and zero eigenvalues, respectively. Finally, the stiffness matrices are evaluated by applying the member force-displacement relations to the displacement functions. In addition, the finite beam element formulation based on the classical Lagrangian interpolation polynomial is presented. In order to verify the validity and the accuracy of this study, the numerical solutions are presented and compared with the finite element results using the isoparametric beam elements and the detailed three-dimensional analysis results using the shell elements of ABAQUS. Particularly the effects of shear deformations on the deflection of thin-walled composite beams with the mono-symmetric I-, channel-, and L-shaped sections with various lamination schemes are investigated.     

An elastic–plastic thermal stress analysis of aluminum metal–matrix composite beams

In this study, an elastic–plastic thermal stress analysis is carried out on steel fiber-reinforced aluminum metal–matrix composite beams. Temperature is chosen to vary linearly. It is zero and T₀ at the upper and lower surfaces, respectively. The beam is fixed by two rigid planes at the ends. The solution is performed at 0°, 30°, 45°, 60° and 90° orientation angles. The plastic region is expanded at the lower side of the beam. It is found that the intensity of the residual stress component of σ_x and the equivalent plastic strain are maximum at lower surface of the beam. The residual stress is found to be greatest for the 0° orientation angle. In addition, the intensity of the equivalent plastic strain is the greatest for the same angle.     

A mixed stress model for linear elastodynamics of arbitrarily curved beams

This work presents a mixed stress finite element for linear elastodynamics of arbitrarily curved beams based on a modified Hellinger–Reissner functional. A rational approach to choose the stress approximation is proposed. In particular, the self‐equilibrated stress is augmented by some stress modes obtained from the lower‐order displacement approximation using the equilibrium equations, in such a way that the total number of stress modes is equal to the number of strain modes. The rationale is to preserve all the interactions among the stresses, proper of a curved structure without compromising the flexibility of the element. An arbitrarily curved geometry is described using a parametric Hermitian interpolation scheme tuned by minimizing the initial curvature of the arch. The effectiveness of the present approach is numerically demonstrated. Copyright © 2007 John Wiley & Sons, Ltd.