Linear and quadratic solid–shell finite elements SHB8PSE and SHB20E for the modeling of piezoelectric sandwich structures

In this article, hexahedral piezoelectric solid–shell finite element formulations with linear and quadratic interpolation, denoted by SHB8PSE and SHB20E, respectively, are proposed for the modeling of piezoelectric sandwich structures. Compared to conventional solid and shell elements, the solid–shell concept reveals to be very attractive, due to a number of well-established advantages and computational capabilities. More specifically, the present study is devoted to the modeling and analysis of multilayer structures that incorporate piezoelectric materials in the form of layers or patches. The interest in this solid–shell approach is shown through a set of selective and representative benchmark problems. These include numerical tests applied to various configurations of beam, plate and shell structures, both in static and vibration analysis. The results yielded by the proposed formulations are compared with those given by state-of-the-art piezoelectric elements available in ABAQUS, in particular, the C3D20E quadratic hexahedral finite element with piezoelectric degrees of freedom.     

A sub-laminates FEM approach for the analysis of sandwich beams with multilayered composite faces

A finite element approach based on the Hermitian ZigZag theory and on the sub-laminates concept is proposed for the static analysis of sandwich structures. The accuracy of the model is evaluated through a set of numerical results about the static response of sandwich beams with composite multilayered faces subjected to different boundary conditions and external loads; a comparison with three-dimensional exact elasticity solutions (when available) and high-fidelity FE models is also performed. An experimental tests campaign is also carried out to further assess the HZZ model accuracy. It is shown that the proposed approach is valid in determining global and local responses of sandwich beams.     

Active vibration damping of composite structures using a nonlinear fuzzy controller

The present paper presents a comprehensive methodology for the structural active vibration damping using a fuzzy logic control. The proposed application setup consists of a cantilever beam equipped with two pairs of collocated piezoceramic (PZT) actuators and sensors. The investigated carbon composite beam is modeled using a shell 2D-model on Abaqus commercial finite element code. The PZT patches are modeled as additional layers with a coupled electromechanical effect. Experimental data corresponding to the controlled and to the uncontrolled systems are also presented considering fixed frequency and pulse force excitation.     

Theoretical analysis and experimental measurement for resonant vibration of piezoceramic circular plates

Based on the electroelastic theory for piezoelectric plates, the vibration characteristics of piezoceramic disks with free-boundary conditions are investigated in this work by theoretical analysis, numerical simulation, and experimental measurement. The resonance of thin piezoceramic disks is classified into three types of vibration modes: transverse, tangential, and radial extensional modes. All of these modes are investigated in detail. Two optical techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), are used to validate the theoretical analysis. Because the clear fringe patterns are shown only at resonant frequencies, both the resonant frequencies and the corresponding mode shapes are obtained experimentally at the same time by the proposed AF-ESPI method. Good quality of the interferometric fringe patterns for both the transverse and extensional vibration mode shapes are demonstrated. The resonant frequencies of the piezoceramic disk also are measured by the conventional impedance analysis. Both theoretical and experimental results indicate that the transverse and tangential vibration modes cannot be measured by the impedance analysis, and only the resonant frequencies of extensional vibration modes can be obtained. Numerical calculations based on the finite element method also are performed, and the results are compared with the theoretical analysis and experimental measurements. It is shown that the finite element method (FEM) calculations and the experimental results agree fairly well for the resonant frequencies and mode shapes. The resonant frequencies and mode shapes predicted by theoretical analysis and calculated by finite element method are in good agreement, and the difference of resonant frequencies for both results with the thickness-to-diameter (h/D) ratios, ranging from 0.01 to 0.1, are presented.     

On the analysis of a mixed mode bending sandwich specimen for debond fracture characterization

The mixed mode bending specimen originally developed for mixed mode delamination fracture characterization of unidirectional composites has been extended to the study of debond propagation in foam cored sandwich specimens. The compliance and strain energy release rate expressions for the mixed mode bending sandwich specimen are derived based on a superposition analysis of solutions for the double cantilever beam and cracked sandwich beam specimens by applying a proper kinematic relationship for the specimen deformation combined with the loading provided by the test rig. This analysis provides also expressions for the global mode mixities. An extensive parametric analysis to improve the understanding of the influence of loading conditions, specimen geometry and mechanical properties of the face and core materials has been performed using the derived expressions and finite element analysis. The mixed mode bending compliance and energy release rate predictions were in good agreement with finite element results. Furthermore, the numerical crack surface displacement extrapolation method implemented in finite element analysis was applied to determine the local mode mixity at the tip of the debond.     

缝线对缝合增强三明治结构(陶瓷-气凝胶-陶瓷)热防护结构静力特性的影响

为研究缝线对热防护结构拉伸特性的影响,提出一个缝线缝合增强三明治结构（陶瓷-气凝胶-陶瓷）模型。借助有限元软件程序设计语言建模,用多阶次逐步精确分析法确定缝合增强三明治结构内部应力-应变场。首先对支架和不带缝线的试件整体进行有限元分析;然后考虑缝线等详细结构;最后截取子结构进行详细分析。将三明治结构有限元模型应力变化趋势与试验结果分析对比,验证了有限元模型有效性,并且给出有限元解的变化规律。将缝合增强三明治结构与未缝合三明治结构得到的应力-应变曲线进行对比。结果表明,结构底板受单向拉伸且缝线有预应力时,缝合增强三明治结构沿长度方向（x方向）的应力峰值可有效减小（路径1上的最大应力均减小4.6%左右）;沿z方向的整体应力大幅度减小（路径3应力平均减小30%左右）。      

Large bending actuator made with SMA contractile wires: theory,numerical simulation and experiments

In this paper, the modeling, numerical simulation and experimental validation of the deformation of a composite cantilever beam actuated by shape memory alloy (SMA) wires are presented and discussed. The structural model incorporates a number of non-classical features such as laminated construction and anisotropy of constituent material layers, transverse shear deformability, distortion of the normals, and fulfillment of interfacial shear traction continuity requirement. Suitable for use in standard finite element codes, a numerical procedure is developed for solving the geometric non-linearity of the host structure and the hysteretic non-linearity of SMA wires, which is based upon the updated Lagrangian formulation. The application concerns an elastomeric beam with embedded and pre-stressed SMA wires at an offset from the neutral axis, which act as large bending actuators resulting from the thermally induced reversible transformation strains. The experiments and numerical simulation demonstrate the good predictive capability of the model proposed and the powerful role played by SMAs as large bending actuators.     

Identification of the elastic and damping properties in sandwich structures with a low core-to-skin stiffness ratio

A mixed numerical–experimental identification procedure for estimating the storage and loss properties in sandwich structures with a soft core is developed. The proposed method uses at the experimental level a precise measurement setup with an electro-dynamic shaker and a scanning laser interferometer, and at the computational level an original structurally damped shell finite element model derived from the higher-order shear deformation theory with piecewise linear functions for the through-the-thickness displacement. The parameter estimation is derived from adequate objective functions measuring the discrepancy between the experimental and numerical modal data. Through a sensitivity analysis it is shown that for sandwich structures with a soft core only one specimen is required for characterizing the dominant properties of both the core and the skins. The procedure is then applied to two test cases for which all the influent elastic properties and the major damping parameters could be estimated with a fairly good precision.     

磁流变夹层简支梁的有限元分析

智能材料——磁流变液(MRF)的流变特性如粘性、剪切弹性模量等随外加磁场可迅速、可逆变化,MRF可用于复合智能夹层梁板结构。建立了MRF简支夹层梁有限元模型,分别形成每层的单元矩阵,推导了MRF夹层梁的动力学方程,研究了上下面板为铝板条的MRF夹层梁的振动特性,进行了实验验证,计算与实验结果吻合较好:随着外加磁场强度的增加,梁的固有频率和损耗因子均增大,说明磁流变液在外加磁场作用下对夹层梁有显著的抑振作用。     

基于剪切耗能假设的黏弹性夹芯梁的振动和阻尼特性

基于一阶剪切变形理论和哈密顿原理建立了三层粘弹性夹芯梁结构的有限元模型并对其振动和阻尼特性进行了研究。建模时认为粘弹材料层不可压缩,振动能量是依靠粘弹性层的剪切变形来耗散的。为验证本模型的正确性,将其与解析解作了对比。同时,为了证明本方法的优越性,将其与常用的“实特征模态”、“近似复特征模态”、“钻石法”和“近似法”四种数值方法做了比较。结果表明本方法的精度在这几种数值方法中是最好的。最后,讨论了粘弹性夹芯梁结构参数变化对系统固有频率和损耗因子的影响,得到了一些有工程实际意义的结论。     

Torsion of carbon fiber composite pyramidal core sandwich plates

A combined theoretical, experimental and numerical investigation of carbon fiber composite pyramidal core sandwich plates subjected to torsion loading is conducted. Pyramidal core sandwich plates are made from carbon fiber composite material by a hot compression molding method. Based on the Classical Laminate Plate Theory and Shear Deformation Theory, the equivalent mechanical properties of laminated face-sheet are obtained; based on a homogenization concept combined with a mechanical of materials approach, the equivalent in-plane and out-of-plane shear moduli of pyramidal core are obtained. A torsion solution is derived with Prandtl stress function and can be used in the sandwich plate with orthotropic face-sheets and orthotropic core. The influences of material properties and geometrical parameters on the equivalent torsional stiffness are explored. In order to verify the accuracy of the analytical torsion solution, experimental tests of sandwich plate samples with different face-sheet thicknesses are conducted and two types of finite element models are developed. Good agreements among analytical predictions, finite element simulations and experimental evaluations are achieved, which prove the validity of the present derivation and simulation. The proposed method could also be applied in design applications and optimization of the pyramidal core sandwich structures.     

A methodology for identification of damage in beams

In this work, a parameter based on correlation of signals using mathematical morphology and other two parameters based on energy of a vibration signal using wavelet transform and bispectrum theory are used for approximate location of damage in a steel clamped-free beam. The experimental data are obtained through accelerometers placed along the sample. The system is excited using impact hammer. A preliminary location of the damage is found using the position of the accelerometer that has a higher energy change when it is compared to the signal of the system with and without damage. The mathematical models are obtained using 2D elasticity theory and the finite element method. The numerical and experimental data are approximated using the particle swarm optimization method, and this way, it is possible to adjust the location and severity of the damage. The procedure is also applied to a free–free steel beam with two damages and a sandwich beam.     

Finite element modelling of hybrid active–passive vibration damping of multilayer piezoelectric sandwich beams—part II: System analysis

An electromechanically coupled finite element model has been presented in Part 1 of this paper in order to handle active–passive damped multilayer sandwich beams, consisting of a viscoelastic core sandwiched between layered piezoelectric faces. Its validation is achieved, in the present part, through modal analysis comparisons with numerical and experimental results found in the literature. After its validation, the new finite element is applied to the constrained optimal control of a sandwich cantilever beam with viscoelastic core through a pair of attached piezoelectric actuators. The hybrid damping performance of this five‐layer configuration is studied under viscoelastic layer thickness and actuator length variations. It is shown that hybrid active–passive damping allows to increase damping of some selected modes while preventing instability of uncontrolled ones and that modal damping distribution can be optimized by proper choice of the viscoelastic material thickness. Copyright © 2001 John Wiley & Sons, Ltd.     

Identification of structural parameters including crack using one dimensional PZT patch model

This article presents a new concept of using the one-dimensional piezo-electric patch on beam model for structural identification (SI). A hybrid element constituted of one-dimensional beam element and a PZT sensor is used with reduced material properties. Accuracy of this element is first verified against a corresponding 3D finite element model. Then SI is carried out as an inverse problem whereby parameters are identified by minimizing the deviation between the predicted and measured voltage response of the patch, when subjected to impulse excitation. A non-classical optimization algorithm Particle Swarm Optimization is used to minimize this objective function. Identified parameters involve stiffness, damping as well as the depth and location of crack in a beam. The validity of the proposed approach is proved by numerical studies on a beam, nine member frame and crack depth and location identification using various patch lengths. The signals are polluted with 5% Gaussian noise to simulate experimental noise. The results show there is a significant improvement in identification accuracy compared to other methods. The proposed method is also successfully verified experimentally.     

夹芯梁结构有效性能的多尺度变分渐近模型

为有效分析夹芯梁结构性能,基于变分渐近法建立多尺度变分渐近模型。首先基于旋转张量分解概念建立三维夹芯梁几何非线性的能量方程;利用梁结构细长和非均质较小的特征,将三维夹芯梁结构各向异性、非均质问题严格分解为宏观层面的梁轴线的一维非线性分析和细观层面的单胞本构分析。基于最小势能原理,通过对单胞应变能泛函变分主导项最小化得到有效属性和波动函数解,代入梁的一维模型进行全局非线性响应分析。利用得到的全局响应、波动函数解重构局部场。由于变分特性,构建多尺度模型可以很容易通过有限元数值实现。通过三类夹芯梁结构算例表明:构建模型得到的全局位移和局部应力场与三维有限元具有很好的一致性,但计算成本和建模工作量明显减少,为结构设计人员在初始设计阶段对夹芯梁结构性能评估提供了一种简洁的途径。      

Multi-scale nonlinear modelling of sandwich structures using the Arlequin method

The paper presents a combination of the Arlequin Method (AM) and the Asymptotic Numerical Method (ANM) for studying nonlinear problems related to the mechanical behavior of sandwich composite structures. The Arlequin Method is a multi-scale method in which different models are crossed and glued to each other. The ANM is an alternative method which falls into the category of numerical perturbation techniques. By introducing the power series expansions into the equilibrium equation, the nonlinear problem is transformed into a sequence of linear problems and solved by the standard finite element method. Compared to other classical solvers (Newton–Raphson Method, Modified Newton–Raphson Method), ANM offers a considerable interest in the computation time and reliability. To validate this method, the AM is combined with the ANM to simulate the local damage of 2D–2D and 2D–2D-coupled sandwich beams. The simulation results are compared to a reference solution calculated from a 2D beam without any coupling. In case of the 2D–2D-coupled sandwich beam, the simulation shows a good agreement with the reference solution for both the local damage and the deformation at the loaded point. However, in case of 2D–1D-coupled sandwich beam, the simulation deviate from the reference solution due to the constant thickness of the 1D zig-zag element used to model the 1D zone of the sandwich beam.     

带有1-5型压电芯子的自适应夹层梁的分析

利用１－５型压电材料作为芯子的夹层梁是一种新型压电自适应结构，本文对此进行了有限元法分析和实验分析。利用正交各向异性材料的本构方程和压电材料的压电方程，推导出了这种压电自适应夹层梁的控制方程，压电材料的驱动效应被等效为力学载荷，从而简化了计算过程。算例１的分析结果与实验符合，算例２的分析结果也与文献［６］非常吻合。     

Investigation of Functionally Graded and Viscoelastic Layers Effects on the Dynamic Behavior of Functionally Graded Electro-Rheological Sandwich Beams

Vibration characteristics of functionally graded electro-rheological (FGER) sandwich beams are investigated. While a vast majority of studies have been reported about functionally graded material (FGM) or electrorheological fluids (ERF) composite beams, few, if any, works are conducted about FGER models. In order to validate the present finite element formulation of the FGER beam model, the results of the developed finite element (FE) model are compared with the results of an experimental test on a fabricated ERF composite beam. The effects of FGM volume fraction index, electric field, and thickness of the viscoelastic core are studied on the natural frequencies and modal loss factors of the FGER beam.     

Suppression of nonlinear composite panel flutter with active/passive hybrid piezoelectric networks using finite element method

For the suppression of nonlinear panel flutter, a new optimal active/passive hybrid control design with piezoceramic actuators is proposed using finite element methods. This approach has the advantages of both active (high performance, feedback action) and passive (stable, low power requirement) systems. Piezoceramic actuators are connected in series with an external voltage source and a passive resonant shunt circuit which consists of an inductor and resistor. The shunt circuit should be tuned correctly to suppress the flutter effectively with less control effort as compared to purely active control. To obtain the best effectiveness, active control gains are simultaneously optimized together with the value of the resistor and inductor through a sequential quadratic programming method. The governing equations of the electromechanically coupled composite panel flutter are derived through an extended Hamilton’s principle, and a finite element discretization is carried out. The adopted aerodynamic theory is based on the quasi-steady first-order piston theory, and the von Kármán nonlinear strain–displacement relation is used. Nonlinear modal equations are obtained through a modal reduction technique. Optimal control design is based on linear modal equations of motion, and numerical simulations are based on nonlinear-coupled modal equations. Using the Newmark integration method, suppression results of a hybrid control and a purely active control are presented in the time domain.