Osama J. Aldraihem

Smart beams with extension and thickness-shear piezoelectric actuators

Analytical models and exact solutions for beams with thickness-shear and extension piezoelectric actuators are formulated and developed. The models are based on the first-order beam theory (FOBT) and higher-order beam theory (HOBT). The beam bending problem is solved by using the state-space approach along with the Jordan canonical form. Numerical examples of beams incorporating piezoelectric actuators with various boundary conditions are presented. In these examples, the validity of the proposed models and the feasibility of using shear-mode actuators in smart beams are investigated. For the extension-mode actuators there is slight difference between the deflections of the FOBT and that of the HOBT. For the shear-mode actuators there is pronounced difference between the deflections of the FOBT and that of the HOBT. The results of the FOBT are very sensitive to the value of the shear correction factor. The results of the present work are compared with the previously reported results in the literature, where available.

Energy Harvester with a Dynamic Magnifier

Conventional energy harvester typically consists of a piezoelectric element, which is sandwiched between a proof mass and a base subjected to sinusoidal excitation. The resulting relative motion between the proof mass and the base produces a mechanical strain in the piezoelectric element, which is converted into electrical power by virtue of the direct piezoelectric effect. In this study, harvester is provided with a dynamic magnifier consisting of a spring-mass system which is placed between the piezoelectric element and the moving base. The main function of the dynamic magnifier, as the name implies, is to magnify the strain experienced by the piezo-element in order to amplify the electrical power output of the harvester. With proper selection of the design parameters of the magnifier, the harvested power can be dramatically enhanced and the effective bandwidth of the harvester can be improved. The theory governing the operation of this class of energy harvesters with dynamic magnifier (EHDM) is developed using the Lagrangian dynamics approach. Numerical examples are presented to illustrate the performance characteristics of the EHDM in comparison with the conventional energy harvesters. The obtained results demonstrate the feasibility of the EHDM as a simple and effective means for enhancing the magnitude and spectral characteristics of conventional harvesters.

Energy harvesting from a standing wave thermoacoustic-piezoelectric resonator

In this paper, a one-dimensional thermoacoustic-piezoelectric (TAP) resonator is developed to convert thermal energy, such as solar or waste heat energy, directly into electrical energy. The thermal energy is utilized to generate a steep temperature gradient along a porous stack which is optimally sized and placed near one end of the resonator. At a specific threshold of the temperature gradient, self-sustained acoustic waves are generated inside the resonator. The resulting pressure fluctuations excite a piezoelectric diaphragm, placed at the opposite end of the resonator, which converts the acoustic energy directly into electrical energy without the need for any moving components. The theoretical performance characteristics of this class of thermoacoustic-piezoelectric resonators are predicted using the Design Environment for Low-amplitude ThermoacousticEnergy Conversion Software. These characteristics are validated experimentally on a small prototype of the system. Particular emphasis is placed on monitoring the temperature field using infrared camera, the flow field using particle image velocimetry, the acoustic field using an array of microphones, and the energy conversion efficiency. Comparisons between the theoretical predictions and the experimental results are also presented. The developed theoretical and experimental techniques can be invaluable tools in the design of TAP resonators for harvesting thermal energy in areas far from the power grid such as nomadic communities and desert regions for light, agricultural, air conditioning, and communication applications.

Deflection analysis of beams with extension and shear piezoelectric patches using discontinuity functions

The actuation performance of smart beams with extension and shear mode segments is investigated. The beam models are based on the first-order and higher-order shear deformation beam theories. The piezoelectric stress resultants are expressed in terms of Heaviside discontinuity functions. The state-space approach along with the Jordan canonical form is used to obtain an analytical solution for the static deflection of smart beams with arbitrary boundary conditions. Through demonstrative examples, a comparative study of a beam with extension mode actuators and the corresponding beam with a shear mode actuator is attained. The effects of actuator length and location on the deflected shape of the beam are studied. Results show that shear patches create the largest deflection if they are placed near the support, whereas extension patches create the largest deflection if they are placed at the beam center. For clamped-hinged and clamped-clamped beams, the actuation performance of the shear patches is superior to that of the extension patches.

Optimal Size and Location of Piezoelectric Actuator/Sensors: Practical Considerations

The problem of obtaining the optimal size and location of piezoelectric actuator/sensors is addressed. An optimization problem is formulated for a general beam that has arbitrary boundary conditions and may have as many piezoelectric actuators as desired. The proposed optimization criterion is based on a beam modal cost and controllability index. If the size of the actuator is unbounded, it frequently is optimal if it covers most, if not all, of the length of the beam. This is not realistic because there are cost, weight, and space factors to be considered. By adding a penalty term to the criterion, the size of the actuator/sensor can be reduced to a practical and reasonable size. Thus, thereis no need to preselect thesize of the actuator/sensor. Theoptimal sizeand location forbeams with various boundary conditionsare determined fora singlepair and fortwo pairs ofactuators. Theresultsare in very good agreement with those reported by other investigators. A comparison is also made between the performance of two pairs of actuators and the performance of a single pair for control of the same number of modes. The improvement in performance with two pairs is quantie ed.

Distributed Control of Laminated Beams: Timoshenko Theory vs. Euler-Bernoulli Theory

In this paper, the governing equations and boundary conditions of laminated beamlike components of smart structures are reviewed. Sensor and actuator layers are included in the beam so as to facilitate vibration suppression. Two mathematical models, namely the shear-deformable (Timoshenko) model and the shear-indeformable (Euler-Bernoulli) model, are presented. The differential equations of the continuous system are approximated by utilizing finite element techniques for both models. A cantilever laminated beam with and without a tip mass is investigated to assess the validity and the accuracy of the two models when used for vibration suppression. Comparison between the two models is presented to show the advantages and the limitations of each of the models. Since the Timoshenko beam theory is higher order than the Euler Bernoulli theory, it is known to be superior in predicting the transient response of the beam. The superiority of the Timoshenko model is more pronounced for beams with a low aspect ratio. It is shown that use of an Euler-Bernoulli based controller to suppress beam vibration can lead to instability caused by the inadvertent excitation of unmodelled modes.

Exact deflection solutions of beams with shear piezoelectric actuators

Exact deflection models of beams with n actuators of shear piezoelectric are developed analytically. To formulate the models, the first-order and higher-order beam theories are used. The exact solutions are obtained with the aid of the state-space approach and Jordan canonical form. A case study is presented to evaluate the performance of the authors previously reported models. Through a demonstrative example, a comparative study of the first-order and higher-order beams with two shear piezoelectric actuators is attained. It is shown that the first-order beam cannot predict the beam behavior when compared with the results of the higher-order beam. Further applications of the solutions are presented by investigating the effects of actuators lengths and locations on the deflected shapes of beams with two piezoelectric actuators. Some interesting deflection curves are presented. For example, the deflection curve of a H–H beam resembles saw teeth that rotate clockwise about the central location with the increase of actuators lengths. The presented exact solutions can be used in the design process to obtain detailed deformation information of beams with various boundary conditions. Moreover, the presented analysis can be readily used to perform precise shape control of beams with n actuators of shear piezoelectric. 2002 Elsevier Science Ltd. All rights reserved.

Vibration Characteristics of Metamaterial Beams With Periodic Local Resonances

Vibration characteristics of metamaterial beams manufactured of assemblies of periodic cells with built-in local resonances are presented. Each cell consists of a base structure provided with cavities filled by a viscoelastic membrane that supports a small mass to form a source of local resonance. This class of metamaterial structures exhibits unique band gap behavior extending to very low-frequency ranges. A finite element model (FEM) is developed to predict the modal, frequency response, and band gap characteristics of different configurations of the metamaterial beams. The model is exercised to demonstrate the band gap and mechanical filtering capabilities of this class of metamaterial beams. The predictions of the FEM are validated experimentally when the beams are subjected to excitations ranging between 10 and 5000 Hz. It is observed that there is excellent agreement between the theoretical predictions and the experimental results for plain beams, beams with cavities, and beams with cavities provided with local resonant sources. The obtained results emphasize the potential of the metamaterial beams for providing significant vibration attenuation and exhibiting band gaps extending to low frequencies. Such characteristics indicate that metamaterial beams are more effective in attenuating and filtering low-frequency structural vibrations than plain periodic beams of similar size and weight.

Experimental implementation of a cantilevered piezoelectric energy harvester with a dynamic magnifier

Conventional energy harvester consists of a cantilevered composite piezoelectric beam which has a proof mass at its free end while its fixed end is mounted on a vibrating base structure. The resulting relative motion between the proof mass and the base structure produces a mechanical strain in the piezoelectric elements which is converted into electrical power by virtue of the direct piezoelectric effect. In this paper, the harvester is provided with a dynamic magnifier consisting of a spring-mass system which is placed between the fixed end of the piezoelectric beam and the vibrating base structure. The main function of the dynamic magnifier, as the name implies, is to magnify the strain experienced by the piezoelectric elements in order to amplify the electrical power output of the harvester. With proper selection of the design parameters of the magnifier, the harvested power can be significantly enhanced and the effective bandwidth of the harvester can be improved. The theoretical performance of this class of Cantilevered Piezoelectric Energy Harvesters with Dynamic Magnifier (CPEHDM) is developed using ANSYS finite element analysis. The predictions of the model are validated experimentally and comparisons are presented to illustrate the merits of the CPEHDM in comparison with the conventional piezoelectric energy harvesters (CPEH). The obtained results demonstrate the feasibility of the CPEHDM as a simple and effective means for enhancing the magnitude and spectral characteristics of CPEH.

Mechanics and control of coupled bending and twisting vibration of laminated beams

A shear-deformable beam theory is proposed to model the coupled bending and twisting vibration in laminated beams. Two types of coupling are considered: mass coupling and stiffness coupling. The control of the coupled vibration is accomplished by smart layers incorporated in the host structure. The capability of two different types of piezoelectric layers in detecting and supplying bending and twisting motion is addressed in this article. Traditional lead zirconate titanate (PZT) piezoelectric layers can detect and supply a twisting motion only indirectly, while a PZT/epoxy piezoelectric composite (PZT/Ep) has been shown to sense and actuate both bending and twisting motion. A modal cost and controllability analysis is discussed to compare the performance of the actuation configurations. In a series of examples, the PZT/Ep actuator has provided the best bending-twisting actuation for vibration damping.