Surface-bonded Piezoelectric Patches Research Articles

Finite element modeling and analysis of adhesive layer effects in surface-bonded piezoelectric sensors and actuators including non-uniform thickness

A finite element model for multi-functional structures containing surface-bonded piezoelectric patches is proposed with two main objectives: to reduce the computational cost of detailed and accurate analyses; and to fully account for the adhesive layer between structure and patches, including non-uniform thickness. The proposed model is verified and used to assess the effect of adhesive layer properties on the performance of piezoelectric sensors and actuators, based on frequency responses and effective electromechanical coupling coefficient. Results indicate that increases of bonding layer thickness and thickness non-uniformity are not always detrimental to the actuation/sensing performance and could be explored as design parameters.

Distributed transfer function-based unified static solutions for piezoelectric short/open-circuit sensing and voltage/charge actuation of beam cantilevers

Closed-form unified solutions using the distributed transfer functions (DTFs) method are presented for the first time for the static short/open-circuit sensing and voltage/charge actuation of moderately thick beam cantilevers with co-localized surface-bonded piezoelectric patches. For this purpose, the smart beam is divided into three segments, of which the clamp and free sides parts are elastic, while the middle one is made of an elastic core sandwiched between two electroded piezoelectric patches. The latter can be different in material properties and thickness but should have the same length, and their widths can be different from the host elastic beam. The theoretical formulation is based on Timoshenko’s first-order shear deformation theory for the kinematics and piezoelectric constitutive equations and the principle of virtual works for the variational equations. The latter integrate explicitly the physical equipotential constraints on the patches electrodes. The balance equations and boundary conditions are derived for the three segments independently and then connected at their interfaces by the equilibrium equations and continuity conditions. The unified static solutions for the resulting four problems are derived analytically in closed form using the DTF approach. These are validated against only open literature benchmarks having tabulated results or analytical formulas in order to avoid curves induced inherent additional deviations. Very good correlations were obtained in comparison with the found reference two-dimensional (2D) plane strain/stress analytical and 2D plane strain/stress and three-dimensional finite element results.

Optimal passive shunted damping configurations for noise reduction in sandwich panels

This article addresses the issue of vibration and noise reduction in laminated sandwich plates using piezoelectric patches with passive shunted damping. A finite element implementation of a laminated sandwich plate with viscoelastic core and surface bonded piezoelectric patches is used to obtain the frequency response of the panels. The sound transmission characteristics of the panels are evaluated by computing their radiated sound power using the Rayleigh integral method. Resistor and inductor shunt damping circuits are used to add damping to the sandwich panels. The optimal location of the surface-bonded piezoelectric patches is then obtained, along with the resistor and inductor circuits resistance and inductance, using direct multisearch optimization to minimize added weight, number of patches, and noise radiation. Trade-off Pareto optimal fronts and the respective optimal patch configurations are obtained.

Attitude and vibration control of a satellite containing flexible solar arrays by using reaction wheels, and piezoelectric transducers as sensors and actuators

The primary purpose of this paper is to provide insight into control-structure interaction for satellites comprising flexible appendages and internal moving components. The physical model considered herein aiming to attend such purpose is a rigid-flexible satellite consisting of a rigid platform containing two rotating flexible solar panels. The solar panels rotation is assumed to be in a sun-synchronous configuration mode. The panels contain surface-bonded piezoelectric patches that can be used either as sensors for the elastic displacements or as actuators to counteract the vibration motion. It is assumed that in the normal mode operation the satellite platform points towards the Earth while the solar arrays rotate so as to follow the Sun. The vehicle moves in a low Earth polar orbit. The technique used to obtain the mathematical model combines the Lagrangian formulation with the Finite Elements Method used to describe the dynamics of the solar panel. The gravity-gradient torque as well as the torque due to the interaction of the Earth magnetic field and the satellite internal residual magnetic moment is included as environmental perturbations. The actuators are three reaction wheels for attitude control and piezoelectric actuators to control the flexible motion of the solar arrays. Computer simulations are performed using the MATLAB® software package. The following on-orbit satellite operating configurations are object of analysis: i) Satellite pointing towards the Earth (Earth acquisition maneuver) by considering the initial conditions in the elastic displacement equal to zero, aiming the assessment of the flexible modes excitation by the referred maneuver; ii) the satellite pointing towards the Earth with the assumption of an initial condition different from zero for the flexible motion such that the attitude alterations are checked against the elastic motion disturbance; and iii) attitude acquisition accomplished by taking into account initial conditions different from zero for both attitude and elastic vibrations. Additionally, the control efforts for the three cases are compared. Results indicate that the attitude control is able to excite the solar panels' vibration modes and vice-versa. The piezoelectric vibration control shows significant performance improvement when compared to contributions of the attitude control to the vibration damping.

Low-frequency locally resonant band gaps induced by arrays of resonant shunts withAntoniou’s circuit: experimental investigation on beams

A periodic array of resistive inductive (RL) shunted piezoelectric (PZT) patches is appliedto achieve tunable low-frequency locally resonant (LR) band gaps in a flexible isotropicbeam. Each pair of surface-bonded PZT patches is linked to an independent RL circuit. Allthe circuits are the same and are tuned synchronously. A transfer matrix methodologyis used to calculate the frequency range and attenuation properties of the LRband gap. Two main differences are found between the LR band gaps inducedby shunting circuits and traditional oscillators. Antoniou’s circuits are used toproduce large ideal inductances necessary for low eigenfrequencies. The theoreticalresults are experimentally validated by measuring the harmonic response of thebeam. Significant attenuation in the low-frequency LR band gap is observed.

Spectral Element Modelling of Wave Propagation and Impedance Based SHM Systems

In recent years many SHM approaches based on elastic waves that are generated and sensed by surface-bonded piezoelectric patches have been developed. Some of those utilize wave propagation phenomena; others use changes in the electromechanical impedance to detect structural damage. The capability of most approaches strongly depends on adequate choice of SHM system parameters like excitation signals and actuator/sensor types and positions. For this reason there is a growing interest in efficient and accurate simulation tools to shorten time and cost of the necessary tedious pretests. To detect small damage generally high frequency excitation signals have to be used. Because of this a very dense finite element mesh is required for an accurate simulation. As a consequence a conventional finite element simulation becomes computationally inefficient. A new approach that seems to be more promising is the time domain spectral element method. This contribution presents the theoretical background and some results of numerical calculations of the propagation of waves. The simulation is performed using the spectral element method (SEM), which leads to a diagonal mass matrix. Besides a significant saving of memory this leads to a crucial reduction of complexity of the time integration algorithm for the wave propagation calculation. A new approach to simulate the E/M impedance using time domain spectral elements is shown. An example demonstrates a good correlation of simulation and measurement data, so that the proposed simulation methodology seems to be a promising tool to make impedance based SHM systems more efficient, especially regarding the necessary parameter studies.

Static analysis of rubber components with piezoelectric patches using nonlinear finite element

In order to reduce vibration or to control shape of structures made of metal or composites, piezoelectric materials have been extensively used since their discovery in 1880. A recent trend is also seen to apply piezoelectric materials to flexible structures made of rubber-like materials. In this paper a non-linear finite element model using updated Lagrangian (UL) approach has been developed for static analysis of rubber-elastic material with surface-bonded piezoelectric patches. A compressible stain energy function has been used for modeling the rubber as hyperelastic material. For formulation of the nonlinear finite element model a twenty-node brick element is used. Four degrees of freedom u, v and w and electrical potential j per node are considered as the field variables. PVDF (polyvinylidene fluoride) patches are applied as sensors/actuators or sensors and actuators. The present model has been applied to bimorph PVDF cantilever beam to validate the formulation. It is then applied to study the smart rubber components under different boundary and loading conditions. The results predicted by the present formulation are compared with the analytical solutions as well as the available published results. Some results are given as new ones as no published solutions available in the literatures to the best of the authors\' knowledge.

Visco-piezo-elastic parameter estimation in laminated plate structures

A parameter estimation technique is presented in this article, for identification of elastic, piezoelectric and viscoelastic properties of active laminated composite plates with surface-bonded piezoelectric patches. The inverse method presented uses experimental data in the form of a set of measured natural frequencies of free vibration and corresponding modal loss factors. An equivalent single layer higher order numerical model is used for the free vibration analysis of active laminated plate structures and the response of the model is adjusted in order to match the experimental data, hence determining the material parameters for the best fit. The solution of the inverse problem is obtained by gradient-based optimization techniques, through constrained minimization of an error functional, which expresses the deviation of the numerical model's response with respect to the experimentally measured data. Results are presented for the estimation of elastic, piezoelectric and viscoelastic properties in laminated plates.

Damage indication in smart structures using modal effective electromechanical couplingcoefficients

This work explores the use, in structural health monitoring, of the so-called modal effectiveelectromechanical coupling coefficient (EMCC) as a damage indicator for structures withfailures such as cracks. For this purpose, a discrete layered finite element (FE) modelfor smart beams is proposed and applied to short-circuit (SC) and open-circuit(OC) modal analyses of healthy and damaged (cracked) cantilever beams withsymmetrically surface-bonded piezoelectric patches. Focus is made here on enhancing theelectrical behavior modeling by introducing a quadratic bubble function in theelectric potential through-the-thickness approximation. Therefore, the correspondinghigher-order potential (HOP) degree of freedom is condensed at the ply level,leading to a passive stiffening effect (SE) similar to the so-called higher-orderinduced potential (HIP); then the physical equipotential (EP) electrode effect, oftenneglected in the piezoelectric FE literature, is here implemented after the electrodes’FE assembly. After its validation against available analytical and experimental results,the proposed piezoelectric FE is used for parametric analyses of SC-based andOC-based EMCC change factors (ECFs) and frequency change factors (FCFs) interms of the crack depth and position ratios. It was found that the EP effectwas more influential on the ECF than the SE. However, for the FCFs, the EPeffect was influential only when it is defined from the OC frequencies. Finally, theECFs were found to be higher than the FCFs, in particular for higher modes.

Strength improvement of a smart adhesive bonded joint system by partially integrated piezoelectric patches

In order to reduce the stress concentration in the adhesive layer of an adhesively bonded joint, a smart adhesive joint system was developed by integration of piezoelectric sensors/actuators patches, bonded to the surfaces of the adherends, near the ends of the joint area. By adjusting the applied electric field on the piezoelectric layer in the developed smart joint system, one can produce additional forces and moments which would act oppositely to those developed internally, thereby alleviating the stress concentration in the joint edges. This would, in turn, improve the performance of the adhesively bonded joint. In our work, the strength enhancement of the developed smart bonded joint system was first evaluated by an experimental investigation. In addition, a theoretical analysis model was developed for predicting the effect of the applied electric field on the surface-bonded piezoelectric patches.

Robust Vibration Control of a Plate Using Self-sensing Actuators of Piezoelectric Patches

Piezoelectric actuators and sensors are increasingly being used in applications involving vibration/position/shape control devices. Based on the self-sensing actuator (SSA) concept in which the sensors and actuators are seamlessly collocated, this paper presents a study on the robust control of a clamped plate. An analytical model of a plate with surface-bonded piezoelectric patches is derived and a μ-synthesis controller is designed to suppress multi-mode vibrations of the clamped plate under perturbations. The experimental results show that the symmetrical and asymmetrical modes can be effectively suppressed with designed feedback control using two piezoelectric patches which are positioned symmetrically and asymmetrically on the plate, respectively.

An Impedance-Based System Modeling Approach for Induced Strain Actuator-Driven Structures

This paper presents the theoretical development and experimental verification of a system model of piezoelectric (PZT) patch actuators for induced strain actuation of two-dimensional active structures. The model includes the dynamic interaction between PZT actuators and their host structures. Analytical solutions of the output behavior of the PZT actuators have been developed based upon the actuator input impedance and the mechanical impedance of the host structures. The impedance-based model was then applied to thin plates and thin shells, and to beams. The case studies demonstrate the generality and utility of the impedance modeling approach. A simply-supported thin plate with surface-bonded PZT patches was built and tested so that the ability of the impedance model to accurately predict the dynamic performance of the actuator and the host structure has been verified. When compared with conventional static models, the impedance modeling method offers insight into the dynamic coupling of the integrated PZT/substrate systems.

Integration and Design of Piezoelectric Patch Actuators

The design of induced strain actuators is a comprehensive issue, involving not only the materials and geometry of the actuators, but also the behaviors of the coupled host structures. In particular, the design of the actuators is essentially related to the prediction of induced strain or stress. A high stress or strain level in the actuators is useful to excite host structures; however, degradation or fatigue damage of the actuators may take place at the same time. This paper presents a dynamic analytical approach for the design of piezoelectric (PZT) patch actuators locally coupled with host structures. Several critical design issues are addressed. These issues include the determination of actuator dynamic outputs, the prediction of energy conversion efficiency, the estimation of system power requirement, and the limitation of induced alternate peak stress. A coupled electromechanical analytical model was developed to reveal the inherent connections among these issues. The mechanical stress behavior of PZT patch actuators was investigated. The attention in parametric design was directed to the thickness and location of the actuators. A simply-supported thin plate with surface-bonded PZT patches was built and tested to directly measure the induced dynamic strain of the PZT actuator so that the prediction accuracy and ability of the design model could be validated.