Solid freeform fabrication of piezoelectric sensors and actuators

The last two decades have witnessed the proliferation piezoelectric composite transducers for an array of sensor and actuator applications. In this article, a concise summary of the major methods used in composite making, with special emphasis on Solid Freeform Fabrication (SFF), is provided. Fused Deposition of Ceramics (FDC) and Sanders Prototyping (SP) are two SFF techniques that have been utilized to make a variety of novel piezocomposites with connectivity patterns including (1-3), (3-2), (3-1), (2-2) and (3-3). The FDC technique has also been used to prototype a number of actuators such as tube arrays, spiral, oval, telescoping, and monomorph multi-material bending actuators. It has been demonstrated that SFF technology is a viable option for fabricating piezocomposite sensors and actuators with intricate geometry, unorthodox internal architecture, and complex symmetry. The salient aspects of processing of such composite sensors and actuators are summarized, and structure-processing-property relations are elaborated on.     

Genetic algorithm based optimal design for vibration control of composite shell structures using piezoelectric sensors and actuators

The present article deals with the design of optimal vibration control of smart fiber reinforced polymer (FRP) composite shell structures using genetic algorithm (GA) based linear quadratic regulator (LQR) and layered shell coupled electro-mechanical finite element analysis. Open loop procedure has been used for optimal placement of actuators considering the control spillover of the higher modes to prevent closed loop instability. An improved real coded GA based LQR control scheme has been developed for designing an optimal controller in order to maximize the closed loop damping ratio while keeping actuators voltages within limit. Results show that increased closed loop-damping has been achieved with a large reduction of control effort considering control spillover.     

Three-dimensional piezoelasticity solution for dynamics of cross-ply cylindrical shells integrated with piezoelectric fiber reinforced composite actuators and sensors

A benchmark three-dimensional (3D) exact piezoelasticity solution is presented for free vibration and steady state forced response of simply supported smart cross-ply circular cylindrical shells of revolutions and panels integrated with surface-bonded or embedded monolithic piezoelectric or piezoelectric fiber reinforced composite (PFRC) layers. The effective properties of PFRC laminas for the 3D case are obtained based on a fully coupled iso-field model. The governing partial differential equations are reduced to ordinary differential equations in the thickness coordinate by expanding all entities for each layer in double Fourier series in span coordinates, which identically satisfy the boundary conditions at the simply-supported ends. These equations with variable coefficients are solved using the modified Frobenius method, wherein the solution is constructed as a product of an exponential function and a power series. The unknown constants of the general solution are finally obtained by employing the transfer matrix method across the layers. Results for natural frequencies and the forced response are presented for single layer piezoelectric and multilayered hybrid composite and sandwich shells of revolution and shell panels integrated with monolithic piezoelectric and PFRC actuator/sensor layers. The present benchmark solution would help assess 2D shell theories for dynamic response of hybrid cylindrical shells.     

Torsional oscillations of a finite inhomogeneous piezoelectric cylindrical shell

Torsional wave motion of a finite right circular cylindrical shell of inhomogeneous piezoelectric material of (622) crystal class under time dependent electric potential on the boundary is investigated. The inhomogeneity is restricted to the variations of density and other physical constants of the medium as expf((r)) where f is a suitable function of the radial distance. Two related problems, investigated by the author, in the papers [1, 2] are shown to be particular cases of the present problem.     

Vibration characteristics of a corrugated cylindrical shell piezoelectric transducer

We study coupled extensional and flexural cylindrical vibrations of a corrugated cylindrical shell piezoelectric transducer consisting of multiple pieces of circular cylindrical surfaces smoothly connected along their generatrices. Using the classical shell theory, a theoretical solution is obtained. Based on the solution, basic vibration characteristics of resonant frequencies, mode shapes, and internal forces are calculated and examined for the corrugated transducers, consisting of a few circular pieces each about 50 μm thick, with radius of 5 mm and span angle of 120°. For these transducers the first resonance is of the order of 10-100 Hz.     

Feedback control of vibrating plates using piezoelectric patch sensors and actuators

An analysis of the solutions for various feedback control laws applied to vibrating simply supported plates is evaluated. The control is carried out via a piezoelectric patch sensor and patch actuator. By considering an integral equation formulation, which is equivalent to the differential equation formulation, the analytical results are investigated. The conversion is accomplished by introducing an explicit Green’s function. The feedback controls implemented include displacement, velocity, and a combination of these. A numerical comparison of eigenvalues is presented to illustrate the efficacy of the method and to contrast the effects of the controls. The results presented in the study can be used for benchmarking solutions based in numerical or approximation approaches.     

Torsional wave motion of a finite inhomogeneous piezoelectric cylindrical shell

Torsional oscillations of a finite right circular eylindrical shell of inhomogeneous piezoelectric material of (622) crystal class under a time dependent electric potential on the boundary is investigated. The inhomogeneity is restricted to the variations of density and other physical constants of the medium as a certain power of the radial distance. Under certain conditions, the amplitudes of torsional oscillations are found to be high for small values of the inner radius of the shell.     

Development of semianalytical axisymmetric shell models with embedded sensors and actuators

This paper presents the development of two semianalytical axisymmetric shell finite element models, which have the possibility of having embedded and/or surface-bonded piezoelectric ring actuators and/or sensors. A mixed finite element approach is used, which combines the equivalent single-layer higher-order shear deformation theory, to represent the mechanical behavior with a layerwise discretization in the thickness direction to represent the distribution of the electrical potential of each piezoelectric layer of the frusta conical finite element. The electrical potential function is represented through a layerwise discretization in the thickness direction and can be assumed linear or quadratic with two or six electrical potential ring nodes per piezoelectric layer. The displacement field and the electrical potential are expanded by Fourier series in the circumferential direction, considering symmetric and anti-symmetric terms. Several examples are presented and discussed to illustrate the accuracy and capabilities of both models.     

Geometrically non-linear analysis of composite structures with integrated piezoelectric sensors and actuators

This paper deals with the geometrically non-linear analysis of thin plate/shell laminated structures with embedded integrated piezoelectric actuators or sensors layers and/or patches. The motivation for the present developments is the lack of studies in the behavior of adaptive structures using geometrically non-linear models, where only very few published works were found in the open literature.

The model is based on the Kirchhoff classical laminated theory and can be applied to plate and shell adaptive structures with arbitrary shape, general mechanical and electrical loadings.

The finite element model is a non-conforming single layer triangular plate/shell element with 18 degrees of freedom for the generalized displacements and one electrical potential degree of freedom for each piezoelectric layer or patch.

An updated Lagrangian formulation associated to Newton–Raphson technique is used to solve incrementally and iteratively the equilibrium equations.

The model is applied in the solution of four illustrative cases, and the results are compared and discussed with alternative solutions when available.     

充液压电阻尼圆柱壳的有限元建模

基于Mindlin板理论、压电理论、粘弹性理论和理想流体方程，对充液圆柱壳主动约束阻尼结构在流固耦合条件下的建模进行了研究。利用拉格朗日方法得到结构的动力学方程，利用GHM方法描述粘弹性阻尼的本构关系，结合流体方程建立主动约束阻尼结构在流固耦合条件下的动力学方程。建立从压电材料的电压到流固耦合边界下的圆柱壳结构振动的频响函数，利用实验结果对理论计算加以验证，结果表明该建模方法是可行的。     

On the dynamic behavior of piezoelectric sensors and actuators embedded in elastic media

Summary Embedded piezoelectric sensors can be used to monitor the mechanical behaviour of structures for damage detection. This paper provides an analytical study of the dynamic behaviour of piezoelectric sensors embedded in elastic media under high frequency electromechanical loads induced by piezoelectric actuators. A generalized sensor/actuator model taking account of the deformation in both transverse and longitudinal directions of the piezoelectric sensor/actuator is developed. The dynamic load transfer between the sensors/actuators and the host medium is studied using Fourier transform method and solving the resulting integral equations in terms of the interfacial normal and shear stresses. Detailed numerical simulation is conducted to study the relation between the deformation of the sensor and that of the host medium under different loading conditions. The results show the significant effect of the geometry, the material combination and the loading frequency upon the behaviour of the sensor.     

Vibration control of a simply supported cylindrical shell using a laminated piezoelectric actuator

Summary This paper develops a novel laminated piezoelectric actuator (LPA) to control the vibration of a cylindrical shell structure, which is fabricated through bonding multiple piezoelectric layers of the same property together. The electromechanically coupled equations of the system are derived based on the classic shell theory. A parametric study is then conducted to evaluate the effects of geometric and physical properties of the actuator on actuating forces. The results show that as the number of layers increases, the actuating forces per voltage produced by LPA in the axial, circumferential and radial directions of the shell all increase noticeably. The active vibration control of a simply supported cylindrical shell using LPA of different layer numbers is simulated as well under a velocity feedback scheme. It is indicated that with the same control voltage the LPA can obtain a better control performance than the conventional single layer piezoelectric actuator as expected and the targeted radial modal vibration of the shell is attenuated significantly.     

A circular cylindrical, radially polarized ceramic shell piezoelectric transformer

We propose a circular cylindrical shell piezoelectric transformer of radially polarized ceramics operating in thickness-stretch modes. Two theoretical analyses involving different approximations are performed on the proposed transformer using the 3-D equations of linear piezoelectricity. The transforming ratio, input admittance, and efficiency of the transformer are calculated and compared with those of a previously analyzed circular cylindrical shell transformer of axially polarized ceramics operating in shear modes.     

Three dimensional analysis of piezoelectric circular cylindrical shell of finite length

Summary An exact elasticity solution for a simply supported piezoelectric circular cylindrical shell of finite length is presented. Different boundary conditions are considered, which correspond to the respective situations when it is acted as sensor or actuator. The stresses, displacements and electric potential distributions are shown. Our results show that the distributions depend strongly on the boundary conditions and can not be justified by purely elastic structures. The presented results can be used not only to assess various approximate theories but also to enhance the understanding of the response behavior of piezoelectric structures.     

Integrated optimization of structure and control for piezoelectric intelligent trusses with uncertain placement of actuators and sensors

The finite element modeling of truss structures with piezoelectric members is presented. Based on the approach of independent modal space control, the controllability and observability indices of the system related to the positions of actuators/sensors are demonstrated. Consequently, the effective damping response time is evaluated. The object of the optimization model is to minimize a specified performance index of the intelligent truss subjected to constraints on the natural frequency and the amplitude of displacement response as well as the applied voltages under a given disturbance. Structural sizing variables, control parameters and actuator/sensor placements are treated as the independent design variables. Coding, the calculation of fitness and the optimization procedure of Genetic Algorithms are discussed so as to solve the integrated optimization with two different types of design variable space: discrete and continuous. Numerical examples are presented to show the effectiveness and usefulness of integrated optimization of structure and control for piezoelectric intelligent trusses.The authors would like to thank for the support by Natural Science Foundation of China under grant 10072050 and the Doctorate Creation Foundation of Northwestern Polytechnical University under grant 200236.     

Interfacial fracture analysis of a piezoelectric–polythene composite cylindrical shell patch under axial shear

The present work studies the interfacial fracture in a piezoelectric cylindrical shell patch. The problem is solved by the methods of infinite trigonometric series and Cauchy singular integral equation, and the numerical results of the stress intensity factor (SIF) are obtained. The effects of the interfacial radius and crack’s location on the SIF are explained through the effects of the free surface, interfacial curvature, crack length, and interface end, respectively. An optimal stiffness matching relationship between the piezoelectric layer and dielectric substrate is suggested. The effects of the piezoelectric and dielectric coefficients are explained through the mechanism of piezoelectric stiffening.     

Thermo-elastic analysis of a functionally graded piezoelectric rotating hollow cylindrical shell subjected to dynamic loads

In this study, dynamo-thermo-elastic analysis of a rotating piezoelectric hollow cylinder made of functionally material is presented. Coupled differential quadrature and finite difference methods are used to solve boundary/initial value equations of the problem. Material properties are assumed to be graded in radial direction and temperature independent. Numerical results obtained and convergence are studied, and then verified with reported results in literature. Effect of variations of the grading parameter, angular velocity, thermal gradient and ratio of the outer to inner radii on the stresses, radial displacement and electrical potential are presented.     

Finite element piezothermoelasticity analysis and the active control of FGM plates with integrated piezoelectric sensors and actuators

 An efficient finite element model is presented for the static and dynamic piezothermoelastic analysis and control of FGM plates under temperature gradient environments using integrated piezoelectric sensor/actuator layers. The properties of an FGM plate are functionally graded in the thickness direction according to a volume fraction power law distribution. A constant displacement-cum-velocity feedback control algorithm that couples the direct and inverse piezoelectric effects is applied to provide active feedback control of the integrated FGM plate in a closed loop system. Numerical results for the static and dynamic control are presented for the FGM plate, which consists of zirconia and aluminum. The effects of the constituent volume fractions and the influence of feedback control gain on the static and dynamic responses of the FGM plates are examined. Received: 13 March 2002 / Accepted: 5 March 2003 The work described in this paper was supported by a grant awarded by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 1024/01E).