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.King Saud Universit

Dynamic stability of stepped beams under moving loads

The dynamic stability of a stepped beam subjected to a moving mass is investigated in this study. The equations of motion for transverse vibrations of the beam are developed in distributed parameter and finite element forms. The impulsive parametric excitation theory is used to predict the stability of the beam when subjected to periodic parametric excitations. The accuracy of the theory is verified by obtaining the stability boundaries of a simply supported beam and comparing the results with the results reported in the literature. Stability maps are then obtained for clamped-free uniform beams as well as clamped-free stepped beams. It is found that the stability of certain beam modes can be improved by providing the beam with appropriately spaced steps. It is shown that better stability characteristics can be obtained by using piezoelectric actuators. Stability analyses of beams with periodic piezoelectric and/or viscoelastic steps are a natural extension of the present work.King Saud Universit

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.King Saud Universit

Bending and twisting vibration control of flexible structures using piezoelectric materials

A number of thin structural elements such as plates, shells, beams, and panels experience both bending and twisting vibration in response to external loadings. To control the vibration and reject disturbances, structural excitation is produced by actuators according to a control law. Of primary importance is the ability to actuate all types of vibration observed (bending, twisting, in-plane, etc.), since observed modes that cannot be actuated can lead to instability. In this paper, possible ways to actuate both bending and twisting are discussed, including structural coupling through the use of orthotropic materials, orthotropic actuators, external masses or stores attached to the structure, and directionally attached piezoelectrics. The importance of having sensors with suitable material symmetry is reviewed. Examples are given on how to excite plate bending and twisting as well as on how to suppress vibration in a beam with structural and/or mass coupling that links bending and twisting.King Saud Universit

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.King Saud Universit

Modeling and characterization of a linear piezomotor

This article presents the modeling and characterization of a new class of piezoelectric linear motor. The motor relies in its operation on a set of piezoelectric bimorphs which are sequentially activated to linearly move a drive rod along spring loaded rollers. Emphasis in this article is placed on studying the dynamic behavior of this class of piezoelectric motors, both theoretically and experimentally, in an effort to predict the piezomotor response to various loads and excitation schemes. To this end, a numerical model has been developed to simulate the dynamics of the piezoelectric bimorphs comprising the piezomotor. Friction between the bimorph elements and the drive rod are handled using an appropriate friction model. Experimental testing of the motor is carried out to validate the predictions of the theoretical model.King Saud Universit

Realistic determination of the optimal size and location of piezoelectric actuator/sensors

In this paper, we address the problem of obtaining the optimal size and location of piezoelectric actuator/sensors. An optimization problem is formulated for a general beam which can be subject to any boundary and may have as many piezoelectric patches as needed. The proposed optimization criterion is based on the beam modal cost and modal controllability. By adding a penalty term to the criterion, the size of the actuator/sensor can be reduced to a practical and reasonable size. Thus there is no need to pre-select the size of the actuator/sensor. The optimal size and location for beams with various boundary conditions are determined for a single pair and for two pairs of piezoelectric patches. The results in this paper are 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. It has been shown that the two pair actuators can control the bending vibration more efficiently than a single pair.King Saud Universit