Study of the effect of in-plane and interlaminar stresses on damping in fluid-filled laminated composite cylinders

The modal strain energy method is used in conjunction with a three-dimensional finite element analysis in the characterization of the effects of in-plane and interlaminar stresses in fluid-filled composite laminate cylindrical shells. A semi-analytical, 8-noded isoparametric finite element, which includes both the symmetric and antisymmetric modes in the circumferential direction, is used in the analysis. The effects of fiber angle, contained fluid height, size parameter of the shell, and stacking sequence on the contribution of in-plane and interlaminar stresses to the overall system damping in fluid-filled, composite laminate cylindrical shells are studied.     

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.     

Control of mechanical deformation of a laminate by electrical load to piezoelectric actuator considering the effects of damping and transverse shear

In this paper, we treat the control of dynamic deformation of a laminate by applying electrical load to piezoelectric actuators. Dynamic behavior of the laminate is analyzed considering the effect of damping due to interlaminar shear and the effect of transverse shear. The analytical model is a rectangular laminate composed of fiber-reinforced laminae and piezoelectric layers. The model is assumed to be a symmetric cross-ply laminate with all edges simply supported and to be subjected to unavoidable mechanical load and to electrical loads to piezoelectric actuators. Behavior of the laminate is analyzed based on the first-order shear deformation theory. The effect of damping due to interlaminar shear is incorporated into our analysis by introducing the interlaminar shear stresses which satisfy the Newton’s law of viscosity. The following quantities are obtained: (1) natural frequencies of the laminate, (2) weight functions for the deflection and rotations and (3) transient deflection due to loads varying arbitrarily with time. Moreover, the methods to control the deflection due to mechanical load by applying electrical voltage to the piezoelectric actuator are shown.     

Active control of forced vibrations in adaptive structures using a higher order model

This paper deals with a finite element formulation for active control of forced vibrations, including resonance, of thin plate/shell laminated structures with integrated piezoelectric layers, acting as sensors and actuators, based on third-order shear deformation theory. The finite element model is a single layer triangular nonconforming plate/shell element with 24 degrees of freedom for the generalized displacements, and one electrical potential degree of freedom for each piezoelectric element layer, which are surface bonded or embedded in the laminate.

The Newmark method is considered to calculate the dynamic response of the laminated structures, forced to vibrate in the first natural frequency. To achieve a mechanism of active control of the structure dynamic response, a feedback control algorithm is used, coupling the sensor and active piezoelectric layers. The model is applied in the solution of illustrative cases, and the results are presented and discussed.     

An adhesively laminated plate element for PZT smart plates

An adhesively laminated element taking into consideration peel stress is developed for a piezoelectric smart plate. In this novel finite element analysis formulation, a four node piezoelectric element is firstly derived, and an adhesive element of finite thickness with both shear and peel stiffness is sandwiched between two collocated four node plate elements to form an adhesively laminated element for a piezoelectric smart plate. In this framework of finite element analysis, because the displacement filed in this adhesively laminated element is continuous and a plate element is derived based on the Reissner–Mindlin plate theory, and thus it can be accurately applied to a thin or moderately thick host plate with bonded or debonded piezoelectric actuators and sensors. The formulation is performed for an isotropic host plate and a fiber reinforced laminate plate. Numerical results are presented to compare with those of the exact solutions for smart beams, and validate with the experimental results of the isotropic and composite host plates available in the literature. Using the present finite element analysis formulation, energy transfer stresses in the adhesive and equivalent forces induced in the host plate are investigated. The present formulation is demonstrated to allow debondings of piezoelectric patches and the debonding detection.The authors are grateful to the support of the Australian Research Council via a Discovery Projects grant (grant No: DP0346419).     

含压电作动器和传感器的复合材料层板静变形有限元分析和形状控制研究

本文研究了含压电作动器和传感器层的复合材料层板理论，建立了位移和电自由度的四节点有限元素，利用总势能最小原理推导了静力平衡方程，实现和验证了含压电作动器／传感器复合材料层板静态分析有限元程序。并对该类复合材料层板进行了形状控制研究。     

Optimal solid shell element for large deformable composite structures with piezoelectric layers and active vibration control

In this paper, we present an optimal low‐order accurate piezoelectric solid‐shell element formulation to model active composite shell structures that can undergo large deformation and large overall motion. This element has only displacement and electric degrees of freedom (dofs), with no rotational dofs, and an optimal number of enhancing assumed strain (EAS) parameters to pass the patch tests (both membrane and out‐of‐plane bending). The combination of the present optimal piezoelectric solid‐shell element and the optimal solid‐shell element previously developed allows for efficient and accurate analyses of large deformable composite multilayer shell structures with piezoelectric layers. To make the 3‐D analysis of active composite shells containing discrete piezoelectric sensors and actuators even more efficient, the composite solid‐shell element is further developed here. Based on the mixed Fraeijs de Veubeke–Hu–Washizu (FHW) variational principle, the in‐plane and out‐of‐plane bending behaviours are improved via a new and efficient enhancement of the strain tensor. Shear‐locking and curvature thickness locking are resolved effectively by using the assumed natural strain (ANS) method. We also present an optimal‐control design for vibration suppression of a large deformable structure based on the general finite element approach. The linear‐quadratic regulator control scheme with output feedback is used as a control law on the basis of the state space model of the system. Numerical examples involving static analyses and dynamic analyses of active shell structures having a large range of element aspect ratios are presented. Active vibration control of a composite multilayer shell with distributed piezoelectric sensors and actuators is performed to test the present element and the control design procedure. Copyright © 2005 John Wiley & Sons, Ltd.     

Analysis of adaptive shell structures using a refined laminated model

This work presents the development of a shell conical panel finite element model, which has the possibility of having embedded piezoelectric actuators and/or sensors patches. A mixed laminated theory is used, which combines an equivalent single layer higher order shear deformation approach for the mechanical behavior with a layerwise representation in the thickness direction to describe the distribution of the electric potential in each of the piezoelectric layers of the finite element. The electrical potential function is represented through a linear variation across the thickness with two electric potential nodes for each piezoelectric layer. Based in this model an active damping scheme applied to laminated shell structures is presented and discussed.     

Influence of damaged area on lamb wave propagation in composite plate

The influence of a specified damage on transient propagation of Lamb wave in a composite laminated plate is studied by finite element analysis. The finite element formulation is developed for the laminated plate with embedded or surface-bonded piezoelectric layers. A higher order laminate model is used to describe the displacement field of both composite laminate and piezoelectric layer. The damaged area is modeled by a localized loss of stiffness and quantified by a degradation coefficient . Piezoelectric materials act as both actuators and sensors for generating and receiving Lamb waves. Numerical results show that the waveform, wave peaks and the arrival time of the transmitted Lamb wave are distinctly correlated with quantified degradation coefficient of the damaged area, which are helpful to damage detection for a composite laminated plate in a new way.Tel (Res).: 86-29-88242204, Tel (Off).: 86-29-88213623-8026     

含压电作动器和传感器的复合材料层板静变形有限元分析和形状控制研究

本文研究了含压电作动器和传感器层的复合材料层板理论,建立了位移和电自由度的四节点有限元素,利用总势能最小原理推导了静力平衡方程,实现和验证了含压电作动器/传感器复合材料层板静态分析有限元程序。并对该类复合材料层板进行了形状控制研究。      

Active damping of laminated thin cylindrical composite panels using vertically/obliquely reinforced 1–3 piezoelectric composites

This paper deals with the analysis of active constrained layer damping (ACLD) of laminated thin composite panels using vertically and obliquely reinforced 1–3 piezoelectric composite materials as the material of the constraining layer of the ACLD treatment. A finite element model has been developed for analyzing the ACLD of laminated antisymmetric cross-ply and antisymmetric angle-ply thin composite panels integrated with the patches of such ACLD treatment. Both in-plane and out-of-plane actuations of the constraining layer of the ACLD treatment have been utilized for deriving the finite element model. The analysis revealed that the vertical actuation dominates over the in-plane actuation. Particular emphasis has been placed on investigating the performance of the patches when the orientation angle of the piezoelectric fibers of the constraining layer is varied in the two mutually orthogonal vertical planes. The analysis revealed that the vertically reinforced 1–3 piezoelectric composites which are in general being used for the distributed sensors can be potentially used for the distributed actuators of high performance light-weight smart thin composite panels.     

Hybrid‐stabilized solid‐shell model of laminated composite piezoelectric structures under non‐linear distribution of electric potential through thickness

Eighteen‐node solid‐shell finite element models have been developed for the analysis of laminated composite plate/shell structures embedded with piezoelectric actuators and sensors. The explicit hybrid stabilization method is employed to formulate stabilization vectors for the uniformly reduced integrated 18‐node three‐dimensional composite solid element. Unlike conventional piezoelectric elements, the concept of the electric nodes introduced in this paper can effectively eliminate the burden of constraining the equality of the electric potential for the nodes lying on the same electrode. Furthermore, the non‐linear distribution of electric potential in the piezoelectric layer is expressed by introducing internal electric potential, which not only can simplify modelling but also obtains the same as the exact solution. Copyright © 2003 John Wiley & Sons, Ltd.     

含压电片复合材料层合板的高阶计算模型

给出了一种分析含任意内埋压电片复合材料层合板的高阶耦合模型, 板的位移场采用三阶剪切理论, 并提出了压电片中电势场在厚度方向的三次分布模式, 可以更精确地描述力、电耦合作用下电场的非均匀分布。在平面应力的假设下给出了简化的压电材料本构方程, 推导了基于该模型的压电层合板有限元计算公式, 并对双压电片梁的弯曲和层合板的变形控制进行了计算, 压电梁的弯曲计算结果与解析结果吻合良好, 表明本文的模型和公式是精确有效的。     

Active control of FGM shells subjected to a temperature gradient via piezoelectric sensor/actuator patches

A generic static and dynamic finite element formulation is derived for the modelling and control of piezoelectric shell laminates under coupled displacement, temperature and electric potential fields. The base shell is of functionally graded material (FGM) type, which consists of combined ceramic–metal materials with different mixing ratios of the ceramic and metal constituents. A multi‐input–multi‐output (MIMO) system is applied to provide active feedback control of the laminated shell using self‐monitoring sensors and self‐controlling actuators through a close loop. Numerical studies clearly show the influence of the positional configurations of sensor/actuator pairs on the effectiveness of static and dynamic control for the shell laminates. The effects of the constituent volume fractions on the static and dynamic responses of the shell laminate are also elucidated. Copyright © 2002 John Wiley & Sons, Ltd.     

Coupled mechanics and finite element for non‐linear laminated piezoelectric shallow shells undergoing large displacements and rotations

A theoretical framework is presented for analysing the coupled non‐linear response of shallow doubly curved adaptive laminated piezoelectric shells undergoing large displacements and rotations. The formulated mechanics incorporate coupling between in‐plane and flexural stiffness terms due to geometric curvature, coupling between mechanical and electric fields, and encompass geometric non‐linearity effects due to large displacements and rotations. The governing equations are formulated explicitly in orthogonal curvilinear co‐ordinates and are combined with the kinematic assumptions of a mixed‐field shear‐layerwise shell laminate theory. Based on the above formulation, a finite element methodology together with an incremental‐iterative technique, based on Newton–Raphson method is formulated. An eight‐node coupled non‐linear shell element is also developed. Various evaluation cases on laminated curved beams and cylindrical panels illustrate the capability of the shell finite element to predict the complex non‐linear behaviour of active shell structures including buckling, which is not captured by linear shell models. The numerical results also show the inherent capability of piezoelectric shell structures to actively induce large displacements through piezoelectric actuators, by jumping between multiple equilibrium states. Copyright © 2005 John Wiley & Sons, Ltd.     

Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach

Sensor and actuator based on laminated piezocomposite shells have shown increasing demand in the field of smart structures. The distribution of piezoelectric material within material layers affects the performance of these structures; therefore, its amount, shape, size, placement, and polarization should be simultaneously considered in an optimization problem. In addition, previous works suggest the concept of laminated piezocomposite structure that includes fiber‐reinforced composite layer can increase the performance of these piezoelectric transducers; however, the design optimization of these devices has not been fully explored yet. Thus, this work aims the development of a methodology using topology optimization techniques for static design of laminated piezocomposite shell structures by considering the optimization of piezoelectric material and polarization distributions together with the optimization of the fiber angle of the composite orthotropic layers, which is free to assume different values along the same composite layer. The finite element model is based on the laminated piezoelectric shell theory, using the degenerate three‐dimensional solid approach and first‐order shell theory kinematics that accounts for the transverse shear deformation and rotary inertia effects. The topology optimization formulation is implemented by combining the piezoelectric material with penalization and polarization model and the discrete material optimization, where the design variables describe the amount of piezoelectric material and polarization sign at each finite element, with the fiber angles, respectively. Three different objective functions are formulated for the design of actuators, sensors, and energy harvesters. Results of laminated piezocomposite shell transducers are presented to illustrate the method. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal design in vibration control of adaptive structures using a simulated annealing algorithm

Advanced reinforced composite structures incorporating piezoelectric sensors and actuators are increasingly becoming important due to the development of smart structures. These structures offer potential benefits in a wide range of engineering applications such as vibration and noise suppression, shape control and precision positioning. This paper presents a finite element formulation based on the classical laminated plate theory for laminated structures with integrated piezoelectric layers or patches, acting as sensors and actuators. The finite element model is a single layer triangular nonconforming plate/shell element with 18 degrees of freedom for the generalized displacements, and one additional electrical potential degree of freedom for each surface bonded piezoelectric element layer or patch. The control is initialized through a previous optimization of the core of the laminated structure, in order to minimize the vibration amplitude and maximize the first natural frequency. Also the optimization of the patches position is performed to maximize the piezoelectric actuators efficiency. The simulated annealing algorithm is used for these purposes. To achieve a mechanism of active control of the structure dynamic response, a feedback control algorithm is used, coupling the sensor and active piezoelectric layers or patches, and to calculate the dynamic response of the laminated structures the Newmark method is considered. The model is applied in the optimization of an illustrative adaptive laminated plate case. The influence of the position and number of piezoelectric patches, as well as the control gain, are investigated and the results are presented and discussed.     

Some aspects of numerical simulation for Lamb wave propagation in composite laminates

Some aspects of numerical simulation of Lamb wave propagation in composite laminates using the finite element models with explicit dynamic analysis are addressed in this study. To correctly and efficiently describe the guided-wave excited/received by piezoelectric actuators/sensors, effective models of surface-bounded flat PZT disks based on effective force, moment and displacement are developed. Different finite element models for Lamb wave excitation, collection and propagation in isotropic plate and quasi-isotropic laminated composite are evaluated using continuum elements (3-D solid element) and structural elements (3-D shell element), to elaborate the validity and versatility of the proposed actuator/sensor models.     

Imperfection sensitivity of fiber-reinforced, composite, thin cylinders

The imperfection sensitivity of thin cylindrical shells, made out of fiber-reinforced composite material and subjected to uniform axial compression, and the effects upon it of certain parameters, are investigated. The methodology is based on linear constitutive relations, nonlinear kinematic shell equations (Donnell-type) and the usual lamination theory. The laminate consists of orthotropic laminae, stacked in a general manner (asymmetric laminate). The uniform axial compression is applied eccentrically, and the geometrically imperfect cylindrical shell can be supported in various ways at the boundaries. In this investigation a number of parametric studies are performed. The scope of these studies is to establish the effect of (a) in-plane and transverse boundary conditions and (b) load eccentricity, on the imperfection sensitivity of typical boron/epoxy laminated cylindrical shells with various stacking sequences of laminate. The sensitivity is established by calculating critical loads for various imperfection amplitudes and shapes.     

The effects of three-dimensional states of stress on damping of laminated composites

A three-dimensional finite element method is developed for the characterization of the effects of three-dimensional states of stress on the damping of laminated composites. The calculation of laminate damping is performed by the use of a strain energy method and the damping properties of the individual laminae. Particular attention is paid to the effects of interlaminar stresses on laminate damping. These effects are studied by varying the fiber orientation and the laminate width-to-thickness ratio. The predicted damping and natural frequency data from the finite element analysis are compared with experimental results obtained from an impulse-frequency response technique. This study shows that the three-dimensional finite element method is a powerful technique for the determination of damping of laminated composites, and that it provides considerable potential for full three-dimensional characterization in more complex structures and loading situations.