Ya-Peng Shen

The general solution of three-dimensional problems in magnetoelectroelastic media

The general solution of three-dimensional problems in transversely isotropic magnetoelectroelastic media is obtained through five newly introduced potential functions. The displacements, electric potential, magnetic potential, stresses, electric displacements and magnetic inductions can all be expressed concisely in terms of the five potential functions, all of which are harmonic. The derived general solution is then applied to find the fundamental solution for a generalized dislocation and also to derive Greens functions for a half-space magnetoelectroelastic solid.

Semi-active control of structures incorporated with magnetorheological dampers using neural networks

Semi-active control of buildings and structures with magnetorheological (MR) dampers for earthquake hazard mitigation represents a relatively new research area. In this paper, the Bingham model of MR damper is introduced, and the formula relating the yielding shear stress and the control current of MR dampers is put forward that matches the experimental data. Then an on-line real-time control method for semi-active control of structures with MR dampers is proposed. This method considers the time-delay problem of semi-active control, which can solve distortion of the responses of structures. Finally, through a numerical example of a three-storey reinforced concrete structure, a comparison is made between controlled structure and uncontrolled structure. The calculated results show that MR dampers can reduce the seismic responses of structures effectively. Moreover, the on-line real-time control method is compared with the traditional elastoplastic time-history analysis method, and the efficacy of the on-line real-time control method is demonstrated. In addition, the Levenberg–Marquardt algorithm is used to train the on-line control neural network, and studies show that the algorithm has a very fast convergence rate.

A high order theory for functionally graded piezoelectric shells

A high order theory is presented to examine the electromechanical behavior of piezoelectric generic shells with graded material properties in the thickness direction. Different types of charge equations, depending upon whether the driving signal of piezoelectrics is free charge or electric voltage, have been derived. The obtained equations can be readily reduced to typical structures, such as beams, plates and circular cylindrical shells. The high order theory has been used to study the sensing and actuating behavior of a simply supported inhomogeneous piezoelectric circular cylindrical shell and, for comparison and validation purposes, a homogeneous shell. Comparison between the obtained numerical results to those available exact solutions for homogeneous shell shows that the developed theory is accurate. The effects of graded material properties on the piezoelectrically induced displacements, stresses, electric potential and electric displacements distributions are also quantified, clearly showing the advantage of functionally graded piezoelectrics over homogeneous ones in terms of the usages as sensors and actuators.

AN EXACT SOLUTION FOR FUNCTIONALLY GRADED PIEZOTHERMOELASTIC CYLINDRICAL SHELL AS SENSORS OR ACTUATORS

Abstract An analytical study for piezothermoelastic behavior of a functionally graded piezoelectric cylindrical shell subjected to axisymmetric thermal or mechanical loading is presented. For the case that the material properties obey an identical power law in the radial direction, exact solutions are obtained using the power series expansion method together with the Fourier series expansion method. Both direct and inverse piezoelectric effects are considered. Although this paper considers a case when the material constants are of power functions in the radial variable, the technique is applicable to other forms of material inhomogeneity. Numerical examples are given and discussed to show the significant influence of material inhomogeneity, and adopting a certain value of the inhomogeneity parameter β can optimize the mechanical–electric responses. This will be of particular importance in modern engineering design.

Inclusions of arbitrary shape in magnetoelectroelastic composite materials

Analytic solutions are obtained for the two-dimensional problem of a magnetoelectroelastic inclusion of arbitrary shape in an entire plane, or interacting with a circular magnetoelectroelastic inhomogeneity, or within one of the two bonded dissimilar magnetoelectroelastic half-planes. The eigenfield imposed on the inclusion consists of uniform anti-plane eigenstrains, uniform in-plane eigenelectric field, and uniform in-plane eigenmagnetic field. Several examples of practical practice are also presented to demonstrate the obtained solutions.

Exact solution of orthotropic cylindrical shell with piezoelectric layers under cylindrical bending

An exact elasticity solution for an orthotropic cylindrical shell with piezoelectric layers is obtained in this paper. The stress and displacement distributions are presented. The influence of the piezoelectric layers on the mechanical behavior of structures is studied. Both the direct piezoelectric effect and the converse piezoelectrical effect of the piezoelectric material are investigated. Results presented in this paper can be used to study various approximate shell theories used in the numerical simulations of piezoelectric structures.

State space approach to one-dimensional thermal shock problem for a semi-infinite piezoelectric rod

The theory of generalized thermoelasticity, based on the theory of Lord and Shulman with one relaxation time, is used to solve a boundary value problem of one-dimensional semi-infinite piezoelectric rod with its left boundary subjected to a sudden heat. The governing partial differential equations are solved in the Laplace transform domain by the state space approach of the modern control theory. Approximate small-time analytical solutions to stress, displacement and temperature are obtained by means of the Laplace transform and inverse transform. It is found that there are two discontinuous points in both stress and temperature solutions. Numerical calculation for stress, displacement and temperature is carried out and displayed graphically.

Optimal control of active structures with piezoelectric modal sensors and actuators

Independent modal space control (IMSC) is adopted in this paper for vibration control of piezoelectric active structures. Single-mode controllability and observability conditions are presented. A set of modal sensors and actuators is proposed. Although they are to some extent approximate when compared to those developed previously, their design and application are much simpler. Numerical results are shown to illustrate the feasibility of the approximate modal sensors and actuators.

Piezothermoelasticity analysis for a circular cylindrical shell under the state of axisymmetric deformation

An analytical study for the piezothermoelastic behavior of a circular cylindrical shell laminated with a piezoelectric layer is presented. The solution is obtained through the Power Series Expansion method in conjunction with axisymmetric thermal and mechanical loadings expanded as Fourier series. Both the direct and the inverse piezoelectric effects are studied in detail. Results presented are valuable for both assessing numerical results (e.g. the finite element method) obtained from approximate methods and understanding the piezothermoelastic response of piezoelectric smart shells. It is implied from the present study that the straightforward application of some assumptions adopted to develop analytical models for piezoelectric structures to piezothermoelectric shell structures must be careful.

Effects of stress and electric field on the electromechanical properties of Pb(Mg1∕3Nb2∕3)O3–0.32PbTiO3 single crystals

The effects of constant bias stress and electric field on the electromechanical behavior of ⟨001⟩-oriented Pb(Mg1∕3Nb2∕3)O3–0.32PbTiO3 (PMN–0.32PT) relaxor ferroelectric single crystals have been investigated. Both unipolar and bipolar responses are considered. Obtained results show that compressive bias stress with appropriate magnitude can significantly increase the piezoelectric constant. It is also found that bias electric field in the poling direction stabilizes the microstructure of PMN–0.32PT and reduces the hysteresis loss. The observed effects of bias stress and bias electric field on the electromechanical properties of ⟨001⟩-oriented PMN–0.32PT single crystals can be interpreted in terms of phase-transformation-induced polarization rotation through intermediate phases.