International Journal of Applied Electromagnetics and Mechanics

This paper intends to conform the mathematical correspondence between electric and mechanical variables to the physical correspondence in electroelastic problem when a piezoelectric material is subjected to stress field \sigma_{ij} and electric field E_i or displacement {\bf u} and electric displacement D_i . E_i is expressed with an antisymmetric electric field tensor V_{ij} , and D_i is expressed with an antisymmetric electric displacement tensor P_{ij} which can be expressed with ‘induction potential’ \psi_i . Then stress equilibrium and electric field equations can be described by a second order canonical differential equation system of u_i and \psi_i . As an example, the coupled electroelastic fields in an inclusion or inhomogeneity embedded in an infinite matrix are obtained in a manner directly analogous to Eshelby’s classical elastic solution. The electroelastic fields inside the ellipsoidal inclusion or inhomogeneity and just outside the ellipsoidal inclusion or inhomogeneity are also given. In addition, we analyze the energies of the inclusion. The results in this paper are the backbone in the development of the electric damage theory and ferroelectric constitutive theory.

An electrical field model governing copper electrodeposition process on printed circuit board (PCB) aided by the presence an ultrasonic field is presented in this paper. The problems associated with plating of copper and the current distribution into through-holes and advantages gained by ultrasonic intensification of the electrodeposition process are well known and are the subject of many investigations. Our experiments indicate that a copper layer in a through-hole grows faster than on their flat surface of PCB in this process.

On the basis of measurements, a numerical (FEM) model has been proposed. The inverse problem has been formulated for coupled (a boundary conditions) fields making it possible to control the current density and the layer thickness. An artificial neural network is applied to solve this problem.

The coupled electromagnetic, thermal and mechanical simulation is described for new technological processes of induction heating of large steel disks. Non-uniform temperature distribution of induction heated disks may cause plastic deformations and buckling. The goal of this investigation is to determine the mechanical behaviour of induction heated disks by means of coupled finite element computation in different formulations. The paper contains the detailed description of an applied numerical technique and of obtained results including elastic-plastic stress distribution, plastically deformed state and the most likely modes of the disk buckling.

A gradient-based optimization method is used to solve a frequency domain inverse problem for a multi-layered dielectric structure for which the permittivity, the position and the thickness of each layer are unknown. To overcome the problem of local minima, the inverse problem is solved in two steps. An optimization algorithm based on an ODE solver for a continuous profile is used in the first step to obtain a rough estimate of the multi-layered profile, with the help of a discontinuity marker. This estimated piecewise homogeneous profile is then used in the next step as the initial guess in an optimization algorithm based on a multi-layered propagation matrix.

Zero-dimensional equations for motions of a rectangular piezoelectric parallelepiped are derived from the three-dimensional equations of linear piezoelectricity by triple power series expansion in the length, width and thickness directions. The resulting equations are ordinary differential equations with time as the only independent variable. The lowest order equations can describe motions with homogeneous shearing and stretching deformations as well as uniform electric fields. It is a generalization of the zero-dimensional theory of elastic bodies in the sense that electric coupling is included. The equations obtained are employed in the analysis of a ceramic plate thickness–shear piezoelectric gyroscope. Results useful to the understanding and design of the gyroscope are obtained.

Using mathematical transforms, we present an improved method to compute magnetic fields from current coils with cylindrical symmetry. For some typical model systems, the closed-forms are given for the convenience of use in engineering design. The method we present can generally be used to calculate magnetic field distributions for practical engineering designs with greater efficiency than conventional methods. This method can potentially be applied to other physical problems, such as deriving gravitational potential.