Piezoelectric Patch Actuators Research Articles

Chatter suppression for milling of thin-walled workpieces based on active modal control

Owing to the low stiffness of workpiece, chatter easily occurs in milling of thin-walled structures, which may cause poor surface quality and uncontrolled machining accuracy. For suppressing milling chatter of thin-walled workpieces, this paper presents an active control method with a piezoelectric patch actuator. As a flexible body, thin-walled workpieces have more than one modals participating in milling vibration, and its dynamic characteristics vary with tool position. This paper establishes dynamic model of the thin-walled workpiece with a semi-analytical method. Considering three order modals of workpiece, actuator position is optimized and active controller is designed. The varying dynamic characteristics of workpiece are overcome by designing controller with the parameters on the maximum vibration position to stabilize the whole process. Experiments verify the necessity of considering more than one modals of workpiece in active control through various chatter characteristics dominant by different modals. With the designed control method, the stable cutting depth improves from 0.2 mm to 1 mm.

Nonlinear static analysis of composite beams with piezoelectric actuator patches using the Refined Zigzag Theory

Piezoelectric actuators have been highly successful in a wide range of structural control applications. As such, there is an ongoing need for rapid and accurate structural analysis techniques, particularly for highly heterogeneous composite materials and accounting for the actuator as a patch.Here, a new model based on the Refined Zigzag Theory (RZT) formulation that includes geometric nonlinearities is proposed for buckling, postbuckling and nonlinear static response analyses of geometrically imperfect composite beams with piezoelectric actuators.Both the analytical and the finite element (FE) formulation are presented for symmetrically and non-symmetrically laminated beams. The FE approximation is further generalised to the case of beams with geometric discontinuities to model composite beams with piezoelectric actuator patches. The new RZT model is numerically verified through comparisons to Abaqus solutions for buckling and postbuckling analyses and for the geometrically nonlinear response to an applied voltage of geometrically imperfect composite beams with piezoelectric actuator patches.This work presents a new model for composite beams with piezoelectric actuators and confirms the remarkable advantages of RZT in terms of accuracy and computational efficiency also for challenging nonlinear analyses, where the RZT computational time is generally less than half the time required by the FE commercial code.

Shear actuation-based hybrid damping treatment of sandwich structures using a graphite particle-filled viscoelastic layer

In this work, the effectiveness of a shear actuation-based hybrid active-passive damping treatment is investigated by incorporating the inclusion of graphite particles within the viscoelastic damping layer. The study is performed through the flexural vibration analysis of a sandwich plate-strip where the core is made of a laminate of active layers and graphite particle-filled viscoelastic layers in two different stacking sequences. The active layers are comprised of shear mode piezoelectric actuator patches that are activated according to a shear-based velocity feedback control strategy. The analysis is performed by deriving a closed-loop finite element model of the sandwich plate-strip, and it reveals that the hybrid damping is significantly dependent on the stacking sequence of active and passive damping layers at the core. The inclusion of graphite particles not only provides augmented passive damping but also causes enhanced transfer of shear actuation force from the active layers to other layers. As a result, a significantly improved shear actuation-based hybrid active-passive damping is achieved due to the inclusion. The effectiveness of this hybrid damping in attenuation of resonant displacement-amplitude is also presented by configuring the volume fraction of graphite particles and shear actuator patches in an optimal manner.

Nonlinear vibration of conical shell with a piezoelectric sensor patch and a piezoelectric actuator patch

In this study, nonlinear vibration of a conical shell with a piezoelectric sensor patch and a piezoelectric actuator patch is evaluated. The strain displacement relation is considered to be nonlinear and based on that the equations of motion and piezoelectric sensor output signal are extracted. For the first time, nonlinear electromechanical equations of motion for the conical shell with a piezoelectric sensor layer and a piezoelectric actuator layer are extracted in detail and presented. The producer of extraction of conical shell electromechanical equations of motions is presented for further clarifications. The output signal of the piezoelectric sensor patch considering the nonlinear strain displacement equation of motion is derived. For controlling the vibration actively, a proportional controller is defined by which the applied actuator signal is determined. The nonlinear electromechanical equations of motion are expanded based on conical shell strains. By applying the Galerkin method, the nonlinear time-domain equations are extracted. The complicated attained equations are solved using the harmonic balance method. Conical shell nonlinear frequency response in uncontrolled condition and controlled condition is computed and compared with each other. The frequency response shows that the active vibration control of the conical shell increases the nonlinearity of the system and reduces the vibration amplitude. In addition, free nonlinear vibration of the proposed system is calculated and presented. The results show higher impacts of piezoelectric patches on the conical shell free vibration response and they can reduce the vibration amplitude dramatically.

Active feedforward control of flexural waves in an Acoustic Black Hole terminated beam

Acoustic Black Holes (ABHs) are structural features that are typically realised by introducing a tapering thickness profile into a structure that results in local regions of wave-speed reduction and a corresponding enhancement in the structural damping. In the ideal theoretical case, where the ABH tapers to zero thickness, the wave-speed reaches zero and the wave entering the ABH can be perfectly absorbed. In practical realisations, however, the thickness of the ABH taper and thus the wave-speed remain finite. In this case, to obtain high levels of structural damping, the ABH is typically combined with a passive damping material, such as a viscoelastic layer. This paper investigates the potential performance enhancements that can be achieved by replacing the complementary passive damping material with an active vibration control (AVC) system in a beam-based ABH, thus creating an active ABH (AABH). The proposed smart structure thus consists of a piezo-electric patch actuator, which is integrated into the ABH taper in place of the passive damping, and a wave-based, feedforward AVC strategy, which aims to minimise the broadband flexural wave reflection coefficient. To evaluate the relative performance of the proposed AABH, an identical AVC strategy is also applied to a beam with a constant thickness termination. It is demonstrated through experimental implementation, that the AABH is able to achieve equivalent broadband performance to the constant thickness beam-based AVC system, but with a lower computational requirement and a lower control effort, thus offering significant practical benefits.

Observer based sliding mode control for subsonic piezo-composite plate involving time varying measurement delay

In this study, an observer based sliding mode control (SMC) scheme is proposed for vibration suppression of subsonic piezo-composite plate in the presence of time varying measurement delay by using the piezoelectric patch (PZT) actuator. Firstly, the state space form of the subsonic piezo-composite plate model is derived by Hamilton’s principle with the assumed mode method. Then an state observer involving time varying delay is constructed and the sufficient condition of the asymptotic stability is derived by using the Lyapunov-Krasovskii function, descriptor method and linear matrix inequalities (LMIs) for the state estimation error dynamical system. Subsequently, a sliding manifold is constructed on the estimation space. Then an observer-based controller is synthesized by using the SMC theory. The proposed SMC strategy ensures the reachability of the sliding manifold in the state estimate space. Finally, the simulation results are presented to demonstrate that the proposed observer-based controller strategy is effective in active aeroelastic control of subsonic piezo-composite plate involving time varying measurement delay.

A coupled efficient layerwise finite element model for free vibration analysis of smart piezo-bonded laminated shells featuring delaminations and transducer debonding

This paper presents a computationally efficient multifield finite element (FE) model for accurate analysis of smart composite and sandwich shells equipped with piezoelectric patch actuators and sensors, featuring multiple delaminations and transducer debonding. It employs a facet shell element with four physical nodes and one electric node, based on the third order zigzag theory approximations for displacements and a piecewise quadratic through-thickness variation for the electric potential. A hybrid point-least squares method recently proposed by the authors is extended to impose the condition of continuity of the nonlinear displacement field at the delamination, debonding, and patch fronts. The methodology is generic for multiple patch transducers, delaminations, and debonding, occurring at any arbitrary interface and in-plane locations. The model shows excellent accuracy in comparison with the coupled full-field 3D FE solutions, for the natural frequencies and complex global, local and hybrid mode shapes of delaminated smart composite shells and soft-core sandwich plates, with partially debonded actuators and sensors. The developed model will be of immense use for the design of active vibration control and structural health monitoring strategies for smart laminated shell-type structures featuring such damages.

Estimation of stress intensity factor reduction for a center-cracked plate integrated with piezoelectric actuator and composite patch

Active repair of a damaged structure using piezoelectric (PZT) actuators has played a significant role during the last two decades in reducing crack damage propagation in structures due to its electro-mechanical effect. Similarly, passive repair of damaged structures using composite materials has been widely used in recent years, and it has been divided into many types. In this paper, the hybrid repair of center-cracked plate using PZT actuators at the front of a plate and a composite patch at the back of the plate is analytically and numerically investigated. First, the solution is obtained from Rose's equations for the center-cracked plate integrated with a composite patch and a passive PZT actuator under uniform uniaxial load. Second, the stress intensity factor (SIF) for a center-cracked plate due to stress produced by a PZT actuator is analytically modeled using the weight functions method. The superposition principle is then used to superimpose the aforementioned solutions in order to yield the PZT actuator and composite patch's hybrid stress intensity factor for the center-cracked plate. Finally, the proposed analytical method was verified using the finite element method. The results demonstrate low relative errors between the analytical and the FE of below 5% in all the cases studied in this paper.

Conical shell vibration control with distributed piezoelectric sensor and actuator layer

In this study, a simply supported conical shell with distributed piezoelectric sensor and actuator layers is considered and the shell’s vibration reduction is investigated. Four kinds of piezoelectric layer distribution which are upper circumferential, middle circumferential, lower circumferential, and longitudinal distribution are considered. The output voltage of each piezoelectric sensor patch which is proportional to the shell deformation is calculated. A PD controller is considered which magnifies sensor output voltage and applies it on the allocated piezoelectric actuator patch. By this method the amplitude of conical shell vibration reduced. The effect of a distributed sensor and actuator on the conical shell vibration is evaluated. Controller type, controller constant, sensor/actuator distributions effectiveness on the free vibration response, the frequency response is evaluated. The results show that derivative controllers can affect more on natural frequencies of conical shells and it can increase the damping of the structure. The circumferential distribution can change natural frequencies easily and it has more effects on the dynamic of the conical shell than longitudinal distribution, especially the lower circumferential distribution. The maximum voltage for the piezoelectric actuator patch is also calculated and better distribution with lower actuator voltage and higher vibration reduction is chosen.

Numerical analysis based on finite element method of active vibration control of a sandwich plate using piezoelectric patches

Abstract An active method of vibration control of a smart sandwich plate (SSP) using discrete piezoelectric patches is investigated. In order to actively control the SSP vibration, the plate is equipped with three piezoelectric patches that act as actuators. Based on the classical plate theory, a finite element model with the contributions of piezoelectric sensor and actuator patches on the mass and stiffness of the sandwich plate was developed to derive the state space equation. LQR control algorithm is used in order to actively control the SSP vibration. The accuracy of the present model is tested in transient and harmonic loads. The applied piezoelectric actuator provides a damping effect on the SSP vibration. The amplitudes of vibrations and the damping time were significantly reduced when the control is ON.

Observer-based sliding mode control for piezoelectric wing bending-torsion coupling flutter involving delayed output

An observer-based sliding mode control scheme is proposed for suppressing bending-torsion coupling flutter motions of a wing aeroelastic system with delayed output by using the piezoelectric patch actuators. The wing structure is modeled as a thin-walled beam, and the aerodynamics on the wing are computed by the strip theory. For the implementation of the control algorithm, the piezoelectric patch is bonded on the top surface of the beam to act as the actuator. Ignoring the effect of piezoelectric actuators on structural dynamics, only considering the bending moments induced by piezoelectric effects, the corresponding dynamic motion equation is established by using the Lagrange method with the assumed mode method. The flutter speed and frequency of the closed-loop system with time delay are obtained by solving a polynomial eigenvalue problem. An observer-based controller that does not dependent on time delay is developed for suppressing the flutter, and the corresponding gain matrices are obtained by solving linear matrix inequalities. The sufficient condition for the asymptotic stability of the closed-loop system is derived in terms of linear matrix inequalities. The simulation results demonstrate that the proposed control strategy based on the piezoelectric actuator is effective in wing bending-torsion coupling flutter system with a delayed output.

Tailoring the stability of an axially compressed circular-cylindrical shell using piezoelectric patch actuators

The ability to control equilibrium trajectory to buckling via uniform/non-uniform prebuckling stresses introduced using piezoelectric actuators creates interesting possibilities for designing smart structures. Recent innovative applications consider buckling as a favorable phenomenon in contrast to the conventional wisdom that considers the peak load carrying capacity as the sole design consideration. A circular-cylindrical shell under axial compression can be effectively used in many such applications if active tailoring of its buckling response is demonstrated. The effect of localized as well as distributed placement of piezoelectric patch actuators is analyzed in the present study based on the mechanics of deformation of a cylindrical shell under axial compression. The study establishes the possibility of active tailoring of buckling parameters such as peak load carrying capacity, initial stiffness, and first critical load. The results indicate that the principal curvatures of the cylindrical shell surface play a significant role in dictating the inter-actuator gap for the effective placement of discrete actuators.

Numerical and Experimental Investigation of the Design of a Piezoelectric De-Icing System for Small Rotorcraft Part 1/3: Development of a Flat Plate Numerical Model with Experimental Validation

The objective of this research project is divided in four parts: (1) to design a piezoelectric actuator-based de-icing system integrated to a flat plate experimental setup and develop a numerical model of the system with experimental validation, (2) use the experimental setup to investigate actuator activation with frequency sweeps and transient vibration analysis, (3) add ice layer to the numerical model and predict numerically stresses for different ice breaking with experimental validation, and (4) bring the concept to a blade structure for wind tunnel testing. This paper presents the first objective of this study. First, preliminary numerical analysis was performed to gain basic guidelines for the integration of piezoelectric actuators in a simple flat plate experimental setup for vibration-based de-icing investigation. The results of these simulations allowed to optimize the positioning of the actuators on the structure and the optimal phasing of the actuators for mode activation. A numerical model of the final setup was elaborated with the piezoelectric actuators optimally positioned on the plate and meshed with piezoelectric elements. A frequency analysis was performed to predict resonant frequencies and mode shapes, and multiple direct steady-state dynamic analyses were performed to predict displacements of the flat plate when excited with the actuators. In those steady-state dynamic analysis, electrical boundary conditions were applied to the actuators to excite the vibration of the plate. The setup was fabricated faithful to the numerical model at the laboratory with piezoelectric actuator patches bonded to a steel flat plate and large solid blocks used to mimic perfect clamped boundary condition. The experimental setup was brought at the National Research Council Canada (NRC) for testing with a laser vibrometer to validate the numerical results. The experimental results validated the model when the plate is optimally excited with an average of error of 20% and a maximal error obtained of 43%. However, when the plate was not efficiently excited for a mode, the prediction of the numerical data was less accurate. This was not a concern since the numerical model was developed to design and predict optimal excitation of structures for de-icing purpose. This study allowed to develop a numerical model of a simple flat plate and understand optimal phasing of the actuators. The experimental setup designed is used in the next phase of the project to study transient vibration and frequency sweeps. The numerical model is used in the third phase of the project by adding ice layers for investigation of vibration-based de-icing, with the final objective of developing and integrating a piezoelectric actuator de-icing system to a rotorcraft blade structure.

Estimation and measurement of effective line mobility on a non-deterministic thin plate excited by a piezoelectric patch

This paper derived the expression to estimate the effective line moment mobility of a non-deterministic thin plate under moment excitation by a piezoelectric patch actuator. The piezoelectric patch actuator is assumed to generate purely line moments at each of its edges and regarded as a finite number of point moments acting on an infinite plate, which is achieved by integration method. The theoretical model is validated using MATLAB simulation and compared with experimental measurements on a randomized thin plate. The derived effective line moment mobility managed to closely estimate high-frequency response while cutting significant computational time and resource. Results from this study can be used in many applications ranging from vibration isolation where power transmission between the isolator with an area distribution and its host structure can be determined more accurately, and to design the optimal shunt circuit of a piezoelectric shunt damper for maximum power dissipation in order to reduce vibration of a non-deterministic thin plate.

Controllability and actuator placement optimization for active damping of a thin rotating ring with piezo-patch transducers

A study on optimal actuator placement for controlling flexural vibration of a thin rotating ring is reported. Piezoelectric patch actuators and sensors may be applied with feedback control to provide active damping of structural vibration involving circumferential travelling waves. To determine the optimum patch positions, a model-based cost function is defined involving a time-weighted controllability Gramian, with balanced model realization for combined treatment of sensors and actuators in collocated pairs. Analytical and numerical results indicate that, without rotation, at least two actuator/sensor pairs are required to achieve controllability of any given set of natural vibration modes. Also, the optimal angular separation varies with rotational speed due to the combined influence of initial damping and Coriolis forces on the vibratory dynamics. To obtain a practical solution, a finite range of speeds is considered within a mini-max optimization criterion for the placement problem. Experiments have been conducted on a thin steel ring where a synthetic proof-mass-damper control law was used to suppress vibration involving the six lowest frequency vibration modes (with natural frequencies of 161, 442 and 846 Hz without rotation). The results show that, although a single actuator-sensor pair can achieve improved damping at high rotational speeds, the optimized configuration of two pairs provides effective damping over the full range of operating speeds.

Flexible-link robots with combined trajectory tracking and vibration control

This work deals with asymptotic trajectory tracking and active damping injection on a flexible-link robot by application of Multiple Positive Position Feedback. The flexible-link robot is modeled and validated by using finite element methods and experimental modal analysis, and then a reduced order model of the flexible-link robot dynamics, up to the first dominant vibration modes, is employed for experimental evaluation on a test rig. Then, a combined control scheme is synthesized in two parts: first, a Sliding-Mode Control based on a cascaded Proportional-Integral-Derivative for regulation and trajectory tracking tasks, via a direct current motor torque as the control input for the overall system dynamics, and, second, a Multiple Positive Position Feedback for active vibration control and attenuation of residual vibrations on the tip position, via the input voltage applied to a piezoelectric patch actuator attached directly on the flexible beam. The results are evaluated on an experimental platform, where the dynamic performance of the overall active vibration control scheme leads to fast and effective tracking results, with damping ratios increased up to 300%.

Nonlinear Attitude Control of a Spacecraft with Distributed Actuation of Solar Arrays

This paper presents a novel control architecture and algorithm for precision attitude control of a one-degree-of-freedom dynamic model of a spacecraft. To achieve a parametric model-based control design approach for this new spacecraft actuation and control architecture, the nonlinear dynamics of the open-loop plant are modeled as an ordinary differential equation (ODE)–partial differential equation (PDE) system. The ODE describes the spacecraft single-axis rigid-body rotation, and the PDE describes the spatially continuous flexible dynamics of the solar array including an allocation for a multi-input distributed piezoelectric actuation system bonded on the solar array. This distributed actuation system is called strain-actuated solar arrays. Based on this plant model, a nonlinear ODE–PDE feedback controller for attitude trajectory tracking and slewing is presented with detailed stability proofs. From an end-to-end point of view, the controller drives the distributed piezoelectric actuator patches with voltages that induce bending deflections in the solar arrays, causing controlled reaction torques on the bus to yield target-following motions and precision spacecraft attitude control. The proposed algorithm can be extended to any distributed actuation system with appropriate control input to actuator input mapping. The benefits and limitations of the proposed attitude control method using strain actuation are discussed later in terms of solar array inertia and structural rigidity. This paper also reports experimental results that demonstrate command-following rotations of a cylindrical bus via closed-loop control of its flexible appendages.

3D mixed finite elements for curved, flat piezoelectric structures

ABSTRACTThe Tangential-Displacement Normal-Normal-Stress (TDNNS) method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric materials. It uses tangential components of the displacement and normal components of the normal stress vector as degrees of freedom for elasticity. For the electric field, the electric potential is used. The TDNNS method has been shown to provide elements which do not suffer from shear locking. Therefore thin structures (e.g. piezoelectric patch actuators) can be modeled efficiently. Hexahedral and prismatic elements of arbitrary polynomial order are provided in the current contribution. We show that these elements can be used to discretize curved, shell-like geometries by curved elements of high aspect ratio. The order of geometry approximation can be chosen independently from the polynomial order of the shape functions. We present two examples of curved geometries, a circular patch actuator and a radially polarized piezoelectric semi-cylinder. Simulation results of the TDNNS method are compared to results gained in ABAQUS. We obtain good results for displacements and electric potential as well as for stresses, strains and electric field when using only one element in thickness direction.

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.

An active-system approach for eliminating the wolf note on a cello.

Wolf notes are generally undesirable sounds that occur in string instruments, particularly in cellos. State-of-the-art passive wolf note eliminators affect the whole cello sound and can become ineffective when environmental conditions and, therefore, the cello's structural properties change. In this paper, an approach is presented that uses smart materials to eliminate the wolf note with little effects to the cello's sound. Based on preliminary measurements, a mathematical model of the cello for generating the wolf note and for developing a wolf note elimination controller is set up. The controller consists of a wolf detection criterion that triggers a velocity feedback controller to actively induce damping into the cello's body whenever a wolf note is detected. The controller setup is experimentally validated by an implementation on a test cello. The velocity feedback to induce the active damping is implemented by means of a piezoelectric patch actuator attached to the cello's body. Both the results of the mathematical model and the results of the experimental investigation show a good performance in eliminating the wolf note on a cello.