Averaging of electrical properties of anisotropic fiber-metal composites

The electrical properties of fiber-metal composites with anisotropic components were averaged within the framework of a regular structure model. The corresponding current problem was reduced to a system of two integral equations with elliptical kernels. The effective electrical conductivity tensor of such materials was defined as several functionals based on integral equation solutions for the boundary problem. The calculation results are given.Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 263–268, March–April, 1997.     

The shear wave diffraction on tunnel cavities in an elastic layer and a half-layer

Summary  The antiplane steady dynamic problem of the theory of elasticity for an isotropic layer and a half-layer weakened by tunnel cavities of arbitrary cross section is investigated. A radiating monochromatic shear wave (SH-wave) is considered as loading. Using the constructed Green's functions for a layer and a half- layer, the corresponding boundary problems are reduced to the Fredholm's integral equations of the second kind. The obtained algorithm is realized numerically by the quadrature method. Results specifying the influence of the openings configuration, their number and relative position, types of edge conditions and inertia effects on tangential stress concentration are given. Received 13 July 1999; accepted for publication 20 July 2000     

Concentration of electroelastic fields in a composite piezoceramic plate with a hole intersecting the interface of materials

A plane problem of electroelasticity is considered for an infinite compound plate with a hole located in both constituents of the plate. The corresponding boundary value problems is reduced to a system of singular integral equations of second kind, which is solved in numerical quadratures. Calculation results are presented that describe the concentration of electroelastic fields near the hole upon action at infinity of the vectors of mechanical stresses and electric field strength.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 359–366, May–June, 1999.     

Boundary Control of Physical Fields in a Piezoceramic Layer Having a Tunnel Hole with a System of Electrodes

An approach to the optimal (from the viewpoint of minimum energy consumption) control of the characteristics of coupled fields is illustrated with the example of an antiplane dynamic problem of electroelasticity for a piezoceramic layer with a tunnel hole. The vibrations in the layer are excited by time-dependent harmonic loads of two types: by the difference of electric potentials applied to a pair of infinitely long electrodes located on the surface of the hole and by shear forces or electric charges continuously distributed on the given sections of the layer base, which are assumed as control actions. The inverse problem is solved by using the solution of the corresponding direct mixed antiplane problem of electroelasticity, with the help of which the optimization problem is reduced to the -problem of moments. The functions of optimal control allowing one, for example, to disconnect the external circuit of the generator of electric voltage are given.     

On the non-classical problem of thermal conduction on anisotropic layers in R3

We propose a solution methodology for boundary problems of parabolic and hyperbolic thermal conduction on anisotropic layers in R³. We study the wave nature of heat transfer with pulse thermal effects in bounded bodies with cavity. We compare the solutions of the parabolic and hyperbolic equations of thermal conduction and we show that the assumption on the wave nature of energy transfer is justified under the conditions for high-speed processes.     

Tension of a compound piezoceramic plate with a hole intersecting the phase interface

We study the two-dimensional electroelastic problem for an unbounded compound plate with an arbitrary hole located in both components of the plate. The corresponding boundary-value problem is reduced to a system of singular integral equations of second kind, which for the case of an elliptic hole can be solved numerically by the method of quadratures. We give the data of computations that characterize the concentration of the electroelastic fields near the hole subject to action at infinity by fields of mechanical stresses and electric tension. It is noted that in the case of the inverse piezoelectric effect the influence of inhomogeneities of the plate on the stress concentrations is sharply expressed. Six figures. Bibliography: 7 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 67–75.     

The excitation of symmetric and antisymmetric lamb waves in a piezoelectric strip by surface electrodes

Solutions of the problems of the excitation by surface electrodes of symmetric and antisymmetric Lamb waves in a strip of piezoelectric material are obtained. The solutions of the problems are reduced to systems of singular integral equations in auxiliary functions, proportional to the jump in charge density at the electrodes. Approximate solutions of the systems of singular integral equations are obtained by the Bubnov-Galerkin method using Chebyshev polynomials of the first kind. The results of numerical calculations of the electro-elastic fields for a strip of cadmium sulphide are given.     

Asymptotic Method of Homogenization in Problems of Heating Composite Plates of Periodic Structure in a High-Frequency Electromagnetic Field

In this paper, we examine the influence of electromagnetic and thermal fields on an inhomogeneous medium of periodic structure and heating of a laminated composite of periodic structure in a high-frequency electromagnetic field.     

Antiplane Problem of Electroelasticity for a Hollow Piezoceramic Cylinder Excited by a System of Surface Electrodes

An antiplane mixed boundary-value problem of electroelasticity is considered for a hollow piezoceramic cylinder with an arbitrary system of active surface electrodes generating its harmonic vibrations. The problem is solved using a method elaborated earlier for investigating vibrations of a solid piezoceramic cylinder with a system of active surface electrodes. The scheme of numerical solution of the obtained singular integro-differential equations of the boundary-value problem is based on the quadrature method. Calculation results are presented that describe the amplitude-frequency characteristics of a hollow cylinder and the behavior of some mechanical and electric quantities both within the cylinder and on its boundary.     

The plane frictionless contact of two elastic bodies — the inclusion problem

Summary The mixed boundary value problem of the contact of two plane elastic bodies of arbitrary shape is solved for zero friction in their contact zone. It is reduced to a system of four singular integral equations referred to the contact zone and the remaining parts of the boundaries of the two bodies. The system is complemented by two more equations derived from the single-valuedness of the displacements along the contact boundaries. The solution of these equations yields the distribution of the contact stresses and the contact length. The method is applied to the symmetric case of an infinite elastic plate containing an oversized elastic inclusion, with and without axial forces applied to the plate at infinity. The evolution of contact relaxation and the progress of the gap between the inclusion and the plate is also given.

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Der ebene reibungslose Kontakt von zwei elastischen Körpern — Das Problem der Einlagerung

Übersicht Das gemischte Randwertproblem der Berührung zweier ebener elastischer Körper von beliebiger Form wird im Falle verschwindender Reibung in der Kontaktzone gelöst. Das Problem wird reduziert auf ein System von vier singulären Integralgleichungen, welche sich auf die Kontaktzone und die übrigen Ränder der zwei Körper beziehen. Das System wird mit zwei weiteren Gleichungen vervollständigt, welche von der Eindeutigkeit der Verschiebungen längs der berührenden Ränder hergeleitet werden. Die Lösung dieser Gleichungen gibt die Verteilung der Kontaktspannungen und die Kontaktlänge. Die Methode wird auf den symmetrischen Fall einer unendlichen elastischen Platte (mit und ohne axiale Kräfte auf den unendlich fernen Rändern), welche eine elastische Einlagerung mit Übermaß enthält, angewandt. Die Entwicklung der Kontaktauflösung und der Vorschrift der Lücke zwischen Einlagerung und Platte werden mit Hilfe der Lösung obiger Gleichungen angegeben.