Search Results (9)

Piezoelectric composites have found a wide range of applications in smart structures and devices and effective numerical methods should be developed to simulate not only the macroscopic coupled piezoelectric performances, but also the details of the local distributions of the stress and electric field. In this paper, we proposed a multi-scale asymptotic algorithm based on the Second-Order Two-Scale (SOTS) analysis method for the piezoelectric eigenvalue problem in perforated domain with periodic micro-configurations. The eigenfunctions and eigenvalues are expanded to the second-order terms and the homogenized eigensolutions; the expressions of the first- and second-order correctors are derived successively. The first- and second-order correctors of the eigenvalues are determined according to the integration forms of the correctors of the corresponding eigenfunctions. Explicit expressions of the homogenized material coefficients are derived for the laminated structures and the finite element procedures are proposed to compute the homogenized solutions and the correctors numerically. The error estimations for the approximations of eigenvalues are proved under some regularity assumptions and a typical numerical experiment is carried out for the two-dimensional perforated domain. The computed results show that the SOTS analysis method is efficient in identifying the piezoelectric eigenvalues accurately and reproducing the original eigenfunctions effectively. This approach also provides an efficient computational tool for piezoelectric eigenvalue analysis and can extend to other multi-physics problems with complex microstructures. Full article

Due to the uncertainty of material properties of plate-like structures, many traditional methods are unable to locate the impact source on their surface in real time. It is important to study the impact source-localization problem for plate structures. In this paper, a data-driven machine learning method is proposed to detect impact sources in plate-like structures and its effectiveness is tested on three plate-like structures with different material properties. In order to collect data on the localization of the impact source, four piezoelectric transducers and an oscilloscope were utilized to construct an experimental platform for impulse response testing. Meanwhile, the position of the impact source on the surface of the test plate is generated by manually releasing the steel ball. The eigenvalue of arrival time in the time domain signal is extracted to build data sets for machine learning. This paper uses the Back Propagation (BP) neural network to learn the difference in the arrival time of each sensor and predict the location of the impact source. The results demonstrate that the machine learning method proposed in this paper can predict the location of the impact source in the plate-like structure without relying on the material properties, with high test accuracy and robustness. The research work in this paper can provide experimental methods and testing techniques for locating impact damage in composite material structures. Full article

Piezoelectric semiconductors, being materials with both piezoelectric and semiconducting properties, are of particular interest for use in multi-functional devices and naturally result in multi-physics analysis. This study provides analytical solutions for thick piezoelectric semiconductor plates with periodic boundary conditions and includes an investigation of electromechanical coupling effects. Using the linearization of the drift-diffusion equations for both electrons and holes for small carrier concentration perturbations, the governing equations are solved by the extended Stroh formalism, which is a method for solving the eigenvalues and eigenvectors of a problem. The solution, obtained in the form of a series expansion with an unknown coefficient, is solved by matching Fourier series expansions of the boundary conditions. The distributions of electromechanical fields and the concentrations of electrons and holes under four-point bending and three-point bending loads are calculated theoretically. The effects of changing the period length and steady-state carrier concentrations are covered in the discussion, which also reflects the extent of coupling in multi-physics interactions. The results provide a theoretical method for understanding and designing with piezoelectric semiconductor materials. Full article

This study investigates the effects of magnetic constraints on a piezoelectric energy harvesting absorber while simultaneously controlling a primary structure and harnessing energy. An accurate forcing representation of the magnetic force is investigated and developed. A reduced-order model is derived using the Euler–Lagrange principle, and the impact of the magnetic force is evaluated on the absorber’s static position and coupled natural frequency of the energy harvesting absorber and the coupled primary absorber system. The results show that attractive magnet configurations cannot improve the system substantially before pull-in occurs. A rigorous eigenvalue problem analysis is performed on the absorber’s substrate thickness and tip mass to effectively design an energy harvesting absorber for multiple initial gap sizes for the repulsive configurations. Then, the effects of the forcing amplitude on the primary structure absorber are studied and characterized by determining an effective design of the system for a simultaneous reduction in the primary structure’s motion and improvement in the harvester’s efficiency. Full article

In this study, a Monte Carlo simulation (MCs)-based isogeometric stochastic Finite Element Method (FEM) is proposed for uncertainty quantification in the vibration analysis of piezoelectric materials. In this method, deterministic solutions (natural frequencies) of the coupled eigenvalue problem are obtained via isogeometric analysis (IGA). Moreover, MCs is employed to solve various uncertainty parameters, including separate elastic and piezoelectric constants and their combined cases. Full article

This paper presents a dynamic study of sandwich functionally graded beam with piezoelectric layers that are used as sensors and actuators. This study is exploited later in the formulation of the active control laws, while using the optimal control Linear Quadratic Gaussian (LQG), accompanied by the Kalman filter. The mathematical formulation is based on Timoshenko’s assumptions and the finite element method, which is applied to a flexible beam divided into a finite number of elements. By applying the Hamilton principle, the equations of motion are obtained. The vibration frequencies are found by solving the eigenvalue problem. The structure is analytically then numerically modeled and the results of the simulations are presented in order to visualize the states of their dynamics without and with active control. Full article

Non-propagating waves have great potential for crack evaluation, but it is difficult to obtain the complex solutions of the transcendental dispersion equation corresponding to the non-propagating wave. This paper presents an analytical approach based on the orthogonal function technique to investigate non-propagating Lamb-like waves in a functionally graded piezoelectric spherical curved plate. The presented approach can transform the set of partial differential equations for the acoustic waves into an eigenvalue problem that can give the generally complex wave numbers and the field profiles. A comparison of the obtained results with the well-known ones in plates is provided. The obtained solutions of the dispersion equation are shown graphically in three dimensional frequency-complex wave number space, which aids in understanding the properties of non-propagating waves better. The properties of the guided wave, including real, purely imaginary, and complex branches in various functionally graded piezoelectric spherical curved plates, are studied. The effects of material piezoelectricity, graded fields, and mechanical and electrical boundary conditions on the dispersion characteristics, are illustrated. The amplitude distributions of displacement and electric potential are also discussed, to analyze the specificities of non-propagating waves. Full article

Mathematical analysis of the well known model of a piezoelectric energy harvester is presented. The harvester is designed as a cantilever Timoshenko beam with piezoelectric layers attached to its top and bottom faces. Thin, perfectly conductive electrodes are covering the top and bottom faces of the piezoelectric layers. These electrodes are connected to a resistive load. The model is governed by a system of three partial differential equations. The first two of them are the equations of the Timoshenko beam model and the third one represents Kirchhoff’s law for the electric circuit. All equations are coupled due to the piezoelectric effect. We represent the system as a single operator evolution equation in the Hilbert state space of the system. The dynamics generator of this evolution equation is a non-selfadjoint matrix differential operator with compact resolvent. The paper has two main results. Both results are explicit asymptotic formulas for eigenvalues of this operator, i.e., the modal analysis for the electrically loaded system is performed. The first set of the asymptotic formulas has remainder terms of the order $O\left(\frac{1}{n}\right)$ , where n is the number of an eigenvalue. These formulas are derived for the model with variable physical parameters. The second set of the asymptotic formulas has remainder terms of the order $O\left(\frac{1}{n^2}\right)$ , and is derived for a less general model with constant parameters. This second set of formulas contains extra term depending on the electromechanical parameters of the model. It is shown that the spectrum asymptotically splits into two disjoint subsets, which we call the $\alpha$ -branch eigenvalues and the $\theta$ -branch eigenvalues. These eigenvalues being multiplied by “i” produce the set of the vibrational modes of the system. The $\alpha$ -branch vibrational modes are asymptotically located on certain vertical line in the left half of the complex plane and the $\theta$ -branch is asymptotically close to the imaginary axis. By having such spectral and asymptotic results, one can derive the asymptotic representation for the mode shapes and for voltage output. Asymptotics of vibrational modes and mode shapes is instrumental in the analysis of control problems for the harvester. Full article

In this paper, a feedback control mechanism and its optimization for rotating disk vibration/flutter via changes of air-coupled pressure generated using piezoelectric patch actuators are studied. A thin disk rotates in an enclosure, which is equipped with a feedback control loop consisting of a micro-sensor, a signal processor, a power amplifier, and several piezoelectric (PZT) actuator patches distributed on the cover of the enclosure. The actuator patches are mounted on the inner or the outer surfaces of the enclosure to produce necessary control force required through the airflow around the disk. The control mechanism for rotating disk flutter using enclosure surfaces bonded with sensors and piezoelectric actuators is thoroughly studied through analytical simulations. The sensor output is used to determine the amount of input to the actuator for controlling the response of the disk in a closed loop configuration. The dynamic stability of the disk-enclosure system, together with the feedback control loop, is analyzed as a complex eigenvalue problem, which is solved using Galerkin’s discretization procedure. The results show that the disk flutter can be reduced effectively with proper configurations of the control gain and the phase shift through the actuations of PZT patches. The effectiveness of different feedback control methods in altering system characteristics and system response has been investigated. The control capability, in terms of control gain, phase shift, and especially the physical configuration of actuator patches, are also evaluated by calculating the complex eigenvalues and the maximum displacement produced by the actuators. To achieve a optimal control performance, sizes, positions and shapes of PZT patches used need to be optimized and such optimization has been achieved through numerical simulations. Full article