Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators

This paper investigates the non-linear bending behaviour of functionally graded plates that are bonded with piezoelectric actuator layers and subjected to transverse loads and a temperature gradient based on Reddy's higher-order shear deformation plate theory. The von Karman-type geometric non-linearity, piezoelectric and thermal effects are included in mathematical formulations. The temperature change is due to a steady-state heat conduction through the plate thickness. The material properties are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The plate is clamped at two opposite edges, while the remaining edges can be free, simply supported or clamped. Differential quadrature approximation in the X-axis is employed to convert the partial differential governing equations and the associated boundary conditions into a set of ordinary differential equations. By choosing the appropriate functions as the displacement and stress functions on each nodal line and then applying the Galerkin procedure, a system of non-linear algebraic equations is obtained, from which the non-linear bending response of the plate is determined through a Picard iteration scheme. Numerical results for zirconia/aluminium rectangular plates are given in dimensionless graphical form. The effects of the applied actuator voltage, the volume fraction exponent, the temperature gradient, as well as the characteristics of the boundary conditions are also studied in detail. Copyright (C) 2004 John Wiley Sons, Ltd.

Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders

This paper presents an analysis of the thermomechanical behavior of hollow circular cylinders of functionally graded material (FGM). The solutions are obtained by a novel limiting process that employs the solutions of homogeneous hollow circular cylinders, with no recourse to the basic theory or the equations of non-homogeneous thermoclasticity. Several numerical cases are studied, and conclusions are drawn regarding the general properties of thermal stresses in the FGM cylinder. We conclude that thermal stresses necessarily occur in the FGM cylinder, except in the trivial case of zero temperature. While heat resistance may be improved by sagaciously designing the material composition, careful attention must be paid to the fact that thermal stresses in the FGM cylinder are governed by more factors than are its homogeneous counterparts. The results that are presented here will serve as benchmarks for future related work. (C) 2003 Elsevier Science Ltd. All rights reserved.

Modelling the input-output behaviour of piezoelectric structural health monitoring systems for composite plates

This paper investigates the input-output characteristics of structural health monitoring systems for composite plates based on permanently attached piezoelectric transmitter and sensor elements. Using dynamic piezoelectricity theory and a multiple integral transform method to describe the propagating and scattered flexural waves an electro-mechanical model for simulating the voltage input-output transfer function for circular piezoelectric transmitters and sensors adhesively attached to an orthotropic composite plate is developed. The method enables the characterization of all three physical processes, i.e. wave generation, wave propagation and wave reception. The influence of transducer, plate and attached electrical circuit characteristics on the voltage output behaviour of the system is examined through numerical calculations, both in frequency and the time domain. The results show that the input-output behaviour of the system is not properly predicted by the transducers' properties alone. Coupling effects between the transducers and the tested structure have to be taken into account, and adding backing materials to the piezoelectric elements can significantly improve the sensitivity of the system. It is shown that in order to achieve maximum sensitivity, particular piezoelectric transmitters and sensors need to be designed according to the structure to be monitored and the specific frequency regime of interest.

Optimally distributed actuator placement and control for a slewing single-link flexible manipulator

A method is proposed for determining the optimal placement and controller design for multiple distributed actuators to reduce the vibrations of flexible structures. In particular, application of piezoceramic patches to a horizontally-slewing single-link flexible manipulator modeled using the assumed modes method is investigated. The optimization method uses simulated annealing and allows placement of any number of distributed actuators of unequal length, although piezoceramics of fixed equal lengths are used in the example. It also designs an linear-quadratic-regulator controller as part of the optimization procedure. The measures of performance used in the investigation to determine optimality are the total mass of the system and the time integral of the absolute value of the hub and tip position error. This study also varies the relative weightings for each of these performance measures to observe the effects on the controller designs and piezoceramic patch positions in the optimized solutions.

Transient bending of a piezoelectric circular plate

Thin, piezoelectric circular plates are frequently used as active components in transducer and smart materials applications. This paper reports on the exact, explicit solution for the transient motion of a piezoelectric circular plate, built-in or simply supported on the edge and electrically grounded over the entire surface. Expressed by elementary Bessel functions and obtained via exact inverse Laplace transforms, the solution enables the efficient calculation of accurate system parameters. (C) 2004 Elsevier Ltd. All rights reserved.

Modal characteristics of a flexible beam with multiple distributed actuators

A flexible structure with surface-bonded piezoceramic patches is modelled using Timoshenko beam theory. Exact mode shapes and natural frequencies associated with the flexural motion are computed for various piezoceramic distributed actuator arrangements. The effects of patch placement and of shear on the modal characteristics are demonstrated using a cantilevered beam as an example. Perfect bonding of the piezoceramic to the beam substructure is assumed, and for the purposes of this paper only passive piezoceramic properties are considered. The modelling technique and results obtained in a closed form are intended to assist investigations into the modelling and control of active structures with surface-bonded piezoceramic actuators. (C) 2003 Elsevier Science Ltd. All rights reserved.

Random vibration of the functionally graded laminates in thermal environments

This work deals with the random free vibration of functionally graded laminates with general boundary conditions and subjected to a temperature change, taking into account the randomness in a number of independent input variables such as Young's modulus, Poisson's ratio and thermal expansion coefficient of each constituent material. Based on third-order shear deformation theory, the mixed-type formulation and a semi-analytical approach are employed to derive the standard eigenvalue problem in terms of deflection, mid-plane rotations and stress function. A mean-centered first-order perturbation technique is adopted to obtain the second-order statistics of vibration frequencies. A detailed parametric study is conducted, and extensive numerical results are presented in both tabular and graphical forms for laminated plates that contain functionally graded material which is made of aluminum and zirconia, showing the effects of scattering in thermo-clastic material constants, temperature change, edge support condition, side-to-thickness ratio, and plate aspect ratio on the stochastic characteristics of natural frequencies. (c) 2005 Elsevier B.V. All rights reserved.