Dongchang Sun

Vibration Control of Plates Using Discretely Distributed Piezoelectric Quasi-Modal Actuators/Sensors

A novel approach is presented for vibration control of smart plates using discretely distributed piezoelectric actuators and sensors. The new method consists of techniques for designing quasi-modal sensors and quasi-modal actuators. The modal coordinates and the modal velocities are obtained approximately from the outputs of the discretely distributed piezoelectric sensor elements, whereas the modal actuators are implemented by applying proper voltages on each actuator element. The observation error of the modal sensor is analyzed, and an upper bound for the observation error is determined. The control spillover of the modal actuator is also estimated, and an upper bound of the control spillover is also found. The criteria are developed for finding the optimal locations and sizes of both piezoelectric sensor and actuator elements. In the optimality criteria the optimal locations and sizes of the sensor elements can be found by minimizing the observation error of the modal sensor, and those of the actuator elements can be obtained by minimizing both the control energy and the control spillover. The results obtained using the present optimal criteria show that they do not depend on the initial condition of vibration of the structures, nor do they depend on the control gains.

Effects of piezoelectric sensor/actuator debonding on vibration control of smart beams

Abstract In vibration control of smart structures, piezoelectric sensors/actuators are usually bonded to the surface of a host structure. Debonding may occur between the piezoelectric sensors/actuators and the host structure, and it may decrease the control efficiency of vibration suppression or even lead to an unstable closed loop control system. This paper investigates the effect of the debonding on vibration control of beams with piezoelectric sensors and actuators. Presented is a novel model, which takes into account both flexural and longitudinal displacements of the host beam and piezoelectric layers as well as the peel and shear strains of the adhesive layer. Both collocated and non-collocated control schemes are used to study the effects of sensor or actuator debonding on active vibration control of smart beams.

Modal control of smart shells by optimized discretely distributed piezoelectric transducers

Active vibration control of the shell structures with discretely distributed piezoelectric sensor and actuator patches is investigated. The quasi-modal sensor is developed to estimate the dominant mode coordinates of the shell from the outputs of the sensor patches, and a criterion for finding the optimal locations and sizes of the sensor elements is given by minimizing the observation spillover. The quasi-modal actuator is also designed to actuate the designated modes by means of modulating the voltage distribution of the piezoelectric actuator patches, and a criterion for optimal placement of the actuator patches is presented based on the energy and control spillover consideration. Furthermore, the compensators are employed to filter out the residual components with high frequencies from the estimated modal coordinates. Based on the quasi-modal sensor and quasi-modal actuator, the independent modal control is performed approximately to control the vibration of smart shells. The simulation examples show that the vibration of the shells can be controlled effectively by using the presented method.

Design optimization of piezoelectric actuator patterns for static shape control of smart plates

This paper presents an investigation into design optimization of actuator patterns for static shape control of composite plates with piezoelectric actuator patches. An energy optimization based method for finding the optimal control voltages that can actuate a structure shape close to the desired one within a given error is described. Moreover, a voltage limitation for each actuator is also imposed to keep its control voltage within a practical range. An evolutionary actuator pattern optimization scheme is presented in which trivial actuators with the smallest voltages are electrically or physically removed step by step until the given tolerable error is reached. Finally, illustrative examples are given to demonstrate the effectiveness of the present equivalent element and the design optimization scheme. Numerical results show that satisfactory static shape control can be achieved even after a number of actuators are removed.

Sensing and actuating behaviours of piezoelectric layers with debonding in smart beams

This paper presents an analytical model for investigating the effect of debonding between piezoelectric actuators/sensors and the host beam on the sensing and actuating behaviour. In this model, both flexural and longitudinal displacements of the host beam and the piezoelectric layers are considered using classical beam theory. For the adhesive layer, only through-thickness peel strain and transverse shear strain are taken into account, and they are assumed to be constant across the adhesive thickness. When a debonding occurs between the host beam and an actuator or sensor, the stresses transferred via the adhesive layer are assumed to be zero. Using this model, the effects of debonding on the sensing and actuating behaviour are examined. Numerical results reveal that debonding can have remarkable effects on the distributions of strains and internal forces as well as frequency spectrum and charge output.

Closed-loop based detection of debonding of piezoelectric actuator patches in controlled beams

Abstract A practical closed loop control based damage detection scheme is presented aiming at detecting small damage in controlled structures. In this detection method, a deliberately designed sensitive control system is used to augment small frequency shifts caused by small structural damage. Since a small frequency change can destabilize such a sensitive control system, it can be easily observed and thus the small damage can be detected. To perform active control of structures, a modal velocity observer (MVO) is designed by combining two observers, which can be used for multi-mode control. By properly choosing the parameters in the MVO, it can be made very sensitive to the frequency shift suitable for small damage detection. To demonstrate this method in detecting small debonding of piezoelectric patches on a smart beam, a detailed model of beam with partly debonded piezoelectric patches is established based on the Timoshenko’s beam theory, in which both transverse and longitudinal vibrations are modeled, and a characteristic equation is also derived to examine the effect of the debonding on the control performance. Both the model and the control law are validated by an active vibration control experiment. Finally, an example is given to illustrate application of the method in piezoelectric actuator debonding detection. The results show that even a small edge debonding in a piezoelectric actuator patch can make the sensitive control system unstable, and therefore can be detected.

Dynamic characteristics of a beam system with active piezoelectric fiber reinforced composite layers

In this paper, a one-dimensional piezoelectric mass-dashpot-spring parallel model is presented to evaluate the effective Youngs modulus, coefficient of shear viscosity for active piezoelectric fiber reinforced viscoelastic composite materials based on the well-known iso-field assumptions. An illustrative analysis is carried out to investigate the dynamic characteristics of a beam system with active piezoelectric fiber reinforced viscoelastic composite damping layers. Numerical results are presented to show the effects of major parameters of composite damping layers and electrode pattern on the dynamic characteristics of the beam system. It is noted that the damping factor for the considered case of the beam system with the interdigitated electrode or circular-link interdigitated electrode can be higher than twice of that with the laminar electrode (LE). For the sake of suppressing the axial or transverse vibration of the beam system, the required electric field and settling time for the LE case are greater than that for the IDE or CLIDE case.

Static shape control of structures using nonlinear piezoelectric actuators with energy constraints

Static shape control of composite plates with nonlinear piezoelectric actuators subject to energy constraint is investigated in this paper. The optimal control voltages are determined by using Lagrange multipliers so as to minimize a weighted generalized error function at a given energy level. An eigenspace based algebraic equation of the unknown Lagrange multiplier is derived in order to reduce the computation load of finding the multipliers. Two methods, an iteration algorithm and a shape updating algorithm, are presented for iteratively finding the optimal control voltages for the nonlinearly actuated composite plates. In the iteration algorithm, a control voltage vector is calculated after the Lagrange multipliers are solved for in each iteration, and the iteration continues until an assigned precision is satisfied. In the shape updating algorithm, the actuated shape is calculated in each iteration and then the difference between the actuated and the desired shape is used as the new desired shape in the next iteration. The control voltage vector will be updated using new desired shapes repeatedly until convergence is reached. Finally, a simulation example is given to demonstrate the effectiveness of the present methods.

Modeling and analysis of curved beams with debonded piezoelectric sensor/actuator patches

In this paper, a mathematical model for thin-walled curved beams with partially debonded piezoelectric actuator/sensor patches is presented for investigating the effect of debonding of the actuator/sensor on their open- and closed-loop behaviors. The actuator equations and the sensor equations of the curved beam in perfectly bonded and debonded regions are derived. In the perfect bonding region, the adhesive layer is modeled to carry constant peel and shear stresses; while in the debonding area, it is assumed that there is no peel and shear stress transfer between the host beam and the piezoelectric layer. Both displacement continuity and force equilibrium conditions are imposed at the interfaces between the bonded and debonded regions. Based on the model and the sensing equation of the sensor, a closed-loop vibration control for the curved beams is performed. To obtain the frequency response from the presented model, a solution scheme for solving the complex governing equations is given. Using this model and the solution scheme, the effects of the debonding of actuator and sensor patches on open- and closed-loop control are investigated through an example. The results show that edge debonding of the piezoelectric patch has a significant side effect on the closed-loop control of the curved beams.

Effect of debonding in active constrained layer damping patches on hybrid control of smart beams

Abstract A new model for a smart beam with a partially debonded active constrained layer damping (ACLD) patch is presented, and the effects of the debonding of the ACLD patch on both passive and hybrid control are investigated. In this model, both shear and compressional vibrations of the viscoelastic material (VEM) layer are considered. The moment inertia and the transverse shear effect are also taken into account based on the Timoshenko’s beam theory. The adhesive layer between the host beam and the piezoelectric sensor patch is modeled as an elastic load transferring media. The debonding of the ACLD patch is approximated by removing the VEM between the constraining layer and the host beam in the debonding region, and the continuity conditions are imposed based on displacement continuity and force balance. A modal velocity observer-based modal control scheme is also given to perform the active modal control of the beam. In order to examine the effects of part debonding of the ACLD patch, the characteristic equation of the beam treated with an ACLD patch is derived. The simulation example results show that an edge debonding of the ACLD patch can significantly affect both passive and hybrid control. It is also found that the additional mode induced by the debonding has unique effects on the modal damping ratios and frequencies of both open-loop and closed-loop system.