Nonstationary axisymmetric problem of electroelasticity for a piezoceramic cylinder with circular polarization

This paper considers the problem of the propagation of forced electroelastic axisymmetric torsional waves in a hollow piezoceramic cylinder of finite dimensions, whose curvilinear electroded surfaces are subjected to shear stresses or an electrical potential. A new closed solution is constructed by expansion in vector eigenfunctions using the structural algorithm of finite integral transforms, which makes it possible to determine vibration eigenfrequencies, the stress-strain state of the element, and the potential and intensity of the induced electrical field. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 12–21, January–February, 2009.     

Radial electroelastic nonstationary vibration of a hollow piezoceramic cylinder subject to electric excitation

The paper studies the radial nonstationary vibration of a piezoceramic cylinder polarized throughout the thickness and subjected to a dynamic electric load. A numerical algorithm for solving an initial–boundary-value problem using mesh-based approximations and difference schemes is developed. The dynamic electroelastic state of the cylinder subjected to a constant potential difference applied instantaneously is analyzed Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 30–35, February 2009.     

Thermoelectroelastic state of a piezoceramic body with a spheroidal cavity in a uniform heat flow

An exact solution is obtained to the three-dimensional problem of thermoelectroelasticity for a piezoceramic body with a spheroidal cavity. The solutions of static thermoelectroelastic problems are represented in terms of harmonic functions. Far from the cavity, the body is in a uniform heat flow perpendicular to the axis of symmetry of the cavity __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 57–66, November 2005.     

Thermostressed state of a piezoelectric bodywith a plane crack under symmetric thermal load

The paper addresses a thermoelectroelastic problem for a piezoelectric body with an arbitrarily shaped plane crack in a plane perpendicular to the polarization axis under a symmetric thermal load. A relationship between the intensity factors for stress (SIF) and electric displacement (EDIF) in an infinite piezoceramic body with a crack under a thermal load and the SIF for a purely elastic body with a crack of the same shape under a mechanical load is established. This makes it possible to find the SIF and EDIF for an electroelastic material from the elastic solution without the need to solve specific problems of thermoelasticity. The SIF and EDIF for a piezoceramic body with an elliptic crack and linear distribution of temperature over the crack surface are found as an example __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 96–108, March 2008.     

Singularities of physical fields at the apex of a piezoceramic wedge (plane strain)

A uniform piezoceramic wedge is studied. Singularities of coupled physical fields at the apex of the wedge are investigated with homogeneous boundary conditions on its faces. The problem is solved by using complex representations of the components of the electroelastic field for two basic types of mechanical and electrical boundary conditions. The results of computations are presented. Sumy State University, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 89–92, March, 1999.     

Solving the equilibrium equations for a transversely isotropic piezoceramic plate

The system of equilibrium equations for nonthin transversely isotropic piezoceramic plates subject to antisymmetric (about the mid-plane) deformation is set up by expanding the unknown functions into Fourier-Legendre series in the thickness coordinate. To find the general solution of the system of equations, a method is proposed, which is then used to solve the stress problem for a plate with a circular hole under mechanical loading __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 96–106, October 2006.     

Electroelastic State of a Prolate Piezoceramic Spheroid with Two Electrodes

The electroelastic problem for a transversely isotropic prolate ceramic spheroid is solved explicitly. The spheroid surface is free from external forces. The case is considered where the piezoceramic body is subjected to a given potential difference between electrodes partially covering the surface at the vertices. The normal component of electric-flux density is equal to zero on the noneletroded portion of the surface. Plots of normal stresses in the symmetry plane of the piezoceramic body are given __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 58–67, July 2005.     

On the stress state of a piezoceramic body with a flat crack under symmetric loads

A static-equilibrium problem is solved for an electroelastic transversely isotropic medium with a flat crack of arbitrary shape located in the plane of isotropy. The medium is subjected to symmetric mechanical and electric loads. A relationship is established between the stress intensity factor (SIF) and electric-displacement intensity factor (EDIF) for an infinite piezoceramic body and the SIF for a purely elastic material with a crack of the same shape. This allows us to find the SIF and EDIF for an electroelastic material directly from the corresponding elastic problem, not solving electroelastic problems. As an example, the SIF and EDIF are determined for an elliptical crack in a piezoceramic body assuming linear behavior of the stresses and the normal electric displacement on the crack surface __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 67–77, November 2005.     

The electroelasticity problem for piezoceramic media with bilateral hyperbolic tunnel cavities

An explicit solution of the static problem of electroelasticity is obtained for a transversally isotropic medium that contains bilateral hyperbolic tunnel cavities. It is assumed that the plane of isotropy of the medium coincides with the plane of symmetry of the medium, and also that the surfaces of the cavities are free of mechanical forces and that the normal component of the electric induction vector is equal to zero on the cavities. A uniform tensile force and difference in the electric potentials are specified at a sufficient distance from the cavities in a direction perpendicular to the plane of isotropy of the medium. A solution of the corresponding problem for a piezoceramic medium containing external bilateral rectilinear cracks is obtained as a special case. S. P. Timoshenko Institute of Mechanics. National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 8, pp. 54–60, August, 1999.     

Electrically permeable crack with contact zones between two piezoelectric materials

The paper addresses a plane problem for an infinite plane consisting of two different piezoceramic half-planes with an interfacial crack with smooth contact zones and subjected to the uniformly distributed electromechanical loading applied at infinity. Methods of complex-variable theory are used to reduce the problem to a Dirichlet-Riemann mixed homogeneous boundary-value problem. Its solution is found in closed form. A system with one crack that has one or two contact zones is calculated. Expressions for stresses, electric-flux density, and displacement discontinuities at the interface are written. Equations for the determination of the length of the contact zones and expressions for the stress intensity factors at the crack tips are derived __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 66–74, March 2008.     

On the stress state of a piezoceramic medium with a tunneled elliptical recess

An explicit solution of the static problem of electroelasticity for a transversally isotropic piezoceramic medium containing a tunneled elliptical recess, one axis of which coincides with the axis of the medium's anisotropy, is constructed in this study. It is assumed that the surface of the recess is free of mechanical forces, and the normal component of the induction vector on this surface is equal to zero. Tensile forces act at a sufficient distance from the recess along its axis. The solution of the corresponding problem for a medium containing an internal crack is obtained as a special case. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 7, pp. 77–84, July, 1999.     

Nonstationary radial electroelastic vibrations of a piezoceramic cylinder under mechanical loading

The radial nonstationary vibrations of a piezoceramic cylinder polarized across the thickness and subjected to mechanical dynamic loading are studied. To solve the initial–boundary-value problem, mesh approximations and difference schemes are used. The electromechanical state of the cylinder under an instantaneously applied constant force is analyzed in detail     

Stress distribution in a transversally isotropic piezoceramic body with an elliptic crack in a uniform heat flow

An explicit solution is constructed for the static problem of thermoelectroelasticity for an infinite transversally isotropic body with a heat-insulated elliptic crack located in the isotropy plane. It is assumed that at a large distance from the crack the body is affected by a uniform heat flow perpendicular to the crack plane. Formulas are derived for the stress intensity factors at the crack end, which depend on the value of the heat flow, crack geometry, and the thermoelectroelastic properties of the piezoceramic body. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 72–82, February, 2000.     

Flexural Vibrations and Heating of a Circular Bimorph Piezoplate under Electric Excitation Applied to Nonuniformly Electroded Surfaces

The flexural vibrations and dissipative heating of a circular bimorph piezoceramic plate are studied. The plate is excited by a harmonic electric field applied to nonuniformly electroded surfaces. The viscoelastic behavior of piezoceramics is described in terms of temperature-dependent complex moduli. The nonlinear coupled problem of thermoviscoelasticity is solved by step-by-step integration in time, using the discrete-orthogonalization method to solve the mechanics equations and the finite-differences method to solve the heat-conduction equations. A numerical analysis is conducted for TsTStBS-2 piezoceramics to study the influence of the nonuniform electroding on the resonant frequency, amplitude, and modes of flexural vibrations and the amplitude- and temperature-frequency characteristics of the plate __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 94–100, September 2005.     

Nonsteady-state problem of the emission of acoustic waves by a cylindrical piezoelectric transducer near a planar boundary

We study processes developing when a cylindrical piezoceramic shell with split electrodes located near a planar boundary is excited by nonsteady-state electrical signals. We solve the problem using the Laplace integral transform with respect to time. The boundary conditions are satisfied in the space of the originals. Under these conditions, the unknowns are found from a system of Volterra integral equations. We present the calculation results and their analysis. Translated from Prikladnaya Mekhanika, Vol. 33. No. 12, pp. 60–67, December, 1997.     

Quasi-static thermoviscoelasticity of partially depolarized piezoceramic cylinder under a harmonic load

The oscillation and dissipative heating of an infinitely long piezoceramic cylinder polarized along the radius is considered in the case of partial heat depolarization, with harmonic quasi-static loading of the cylinder by a potential difference. The inner surface of the cylinder is thermally insulated; there is heat transfer at the outer surface. An analytical solution is obtained, and numerical calculations are performed for a TsTStBS-2 piezoceramic. The conditions in which the depolarized zone appears are examined, along with the stress-strain state of the cylinder. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 42–48, March, 1999.     

Averaging of an orthotropic elastic plate weakened by periodic hinges of finite stiffness

A formal asymptote of a solution of the title problem is constructed using the averaging method of N. S. Bakhvalov. The averaged equation is of an elliptic type; for small stiffness of the hinge, it is singularly perturbed, and for zero stiffness of the hinge, it is of a composite type. For the first boundary-value problem, a solution of the original problem is proved to converge to that of the limiting problem. A situation where natural boundary conditions are specified for the composite equation is treated. It is shown that the solution space of the homogeneous problem is infinite-dimensional. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 168–174, May–June, 1999.     

Solution of initial–boundary-value problems of electroelasticity revisited

The Hamilton–Ostrogradsky principle is used to substantiate the statement of initial–boundary-value problems of electroelasticity. The free vibrations of a piezoceramic layer are used as an example to illustrate some features of solving nonstationary problems of electroelasticity Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 62–69, December 2008.     

On the representation of the solutions of the equilibrium equations of a piezoelectric transversally-isotropic spherical shell

A method is proposed for constructing equilibrium equations for thickness-polarized transversally isotropic piezoceramic shells. The method is based on Fourier expanding the required functions in Legendre polynomials. The appropriate system of differential equations is formed for the expansion coefficients as functions of two independent variables. The equilibrium equations are given in particular for transversally isotropic spherical shells. A method is given for constructing the general solution in the first approximation. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 7, pp. 59–68, July, 1999.     

Stress state of an inhomogeneous piezoceramic cylinder subject to bending

The electroelastic state of a bent inhomogeneous piezoceramic cylinder with sliding restraints at the ends is examined. The boundary-value problem is reduced to a system of 12k (k = 1, 2,...) integro-differential equations. Expressions for stresses characterizing the stress state of the cylinder are derived. Relative hoop stresses are calculated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 107–114, August 2006.