Stress state of a transversely isotropic piezoceramic body with a spheroidal cavity

The exact solution is found to the three-dimensional electroelastic problem for a transversely isotropic piezoceramic body with a spheroidal cavity. The solutions of static electroelastic problems are represented in terms of harmonic functions. The case of stretching the piezoceramic medium at a right angle to the spheroid axis of symmetry is analyzed numerically. The dependence of the stress concentration factor on the geometry of the spheroid and the electromechanical characteristics of the material is studied.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 92–105, November 2004.This revised version was published online in April 2005 with a corrected cover date.     

The Stress State of a Transversally Isotropic Piezoceramic Body with a Parabolic Crack in a Uniform Heat Flow

The explicit solution is constructed for a static thermoelastic problem for an infinite transversally isotropic piezoceramic body containing a heat-insulated parabolic crack in the isotropy plane. The crack surface is assumed free of forces. The body is under a uniform heat flow, which is perpendicular to the crack surface and is far from the crack itself. The problem is solved for two cases of electric conditions on the crack surface. In the first case, an electric potential is absent on the crack surface and, in the second case, the normal component of the electric-displacement vector is equal to zero. The intensity factors, which depend on the heat flow, crack geometry, and the thermoelectroelastic properties of the piezoceramic body, are determined for the force field and electric displacement near the crack tip     

Flexural Stress Concentration Near a Hyperboloidal Neck in a Transversely Isotropic Piezoceramic Cylinder

The general solution of the electroelastic problem for a transversely isotropic hyperboloid of revolution is used to find the stress concentration near a hyperboloidal neck in a piezoceramic body subjected to bending. The solution is a sum of four partial solutions for the case where the forces and the normal component of the induction vector on the neck surface are equal to zero. Numerical examples are given for specific external loads and properties of the body. The stress components and normal component of the induction vector near the neck vertex are plotted as a function of the external load and neck curvature     

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.     

Electromechanical vibrations of a piezoceramic hollow spheroid with a polar notch

A refined experimental technique for the measurement of the resonant frequencies and admittance under capacitive loading is outlined. The results of applying the technique to study the vibrations of a piezoceramic spheroid of complicated shape are discussed. It is shown that the deformation of the spheroid at all strong resonances is spatially asymmetric     

The Thermoelectroelastic State of a Transversally Isotropic Piezoceramic Body with a Spheroidal Cavity in a Uniform Heat Flow

A static thermoelectroelastic problem for an infinite transversally isotropic body containing a spheroidal cavity is explicitly solved. The symmetry axis of the spheroid coincides with the anisotropy axis of the body. It is assumed that at a rather large distance from the cavity the body is in a uniform heat flow directed along the anisotropy axis. Formulas are derived for the stress components and the projections of the electric displacement vector near the cavity, which depend on the heat-flow value, cavity geometry, and the thermoelectroelastic properties of the material. The solution of the problem for a body with a disk-like crack is obtained as a partial case from the solution of the problem for a piezoceramic body with a spheroidal cavity. The stress intensity factors for the force and electric fields are determined near the crack     

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.     

Surface effect on Bleustein-Gulyaev wave in a piezoelectric half-space

Surface effect, which is attributed to the different environment surrounding the surface or near-surface atoms from that embracing the bulk atoms, may become significant when the surface-to-volume ratio of a body is large. This paper considers the effect of a plane boundary of a piezoelectric body modeled as a thin layer with specified material properties, for which a transfer relation between the state vectors at the top and bottom surfaces is derived based on the state-space formulations. The equations of surface piezoelectricity for different orders without any bias field are then presented by making use of the power series expression of the transfer matrix. The surface effect is demonstrated by considering the Bleustein-Gulyaev wave existing in a horizontally polarized piezoceramic half-space.     

Self-induced jumping of a rigid body of revolution on a smooth horizontal surface

The article is devoted to the study of the motion of a rigid body of revolution on a rigid and perfectly smooth horizontal surface under the influence of the uniform gravitational field. Basic equations are listed and their solutions are given. The unilateral contact between the body and the plane at non-steady motion is investigated and the procedure of calculation of threshold values of the body energy above which the contact is broken is given. In contrast to Shimomura et al. [Dynamics of an axisymmetric body spinning on a horizontal surface. II. Self-induced jumping. Proc. R. Soc. A 461 (2005) 1775-1809], who assumed sliding friction in their analysis, it is found that the self-induced jumping can also occur in the absence of friction at the very beginning of the motion. The free motion after the contact is lost and impact of the body when it again makes contact with the plane is discussed. The motion of a spheroid and a disk which illustrate the results of the general theory are discussed in some detail.     

Exact Analytical Solutions of Static Electroelastic and Thermoelectroelastic Problems for a Transversely Isotropic Body in Curvilinear Coordinate Systems

An approach to the solution of three-dimensional static problems for a transversely isotropic (rectilinear anisotropy) body is expounded and the solutions for piezoceramic canonical bodies are systematized. The result of the study is explicit analytical solutions of three-dimensional problems. Bodies are examined whose boundary surface is the coordinate surfaces in coordinate systems that permit the separation of the variables in the three-dimensional Laplace equation. The stress concentration in bodies near necks, cavities, inclusions, and cracks is investigated. The stress intensity factors of the force field and electric induction near elliptic and parabolic cracks are determined. The contact interaction of a piezoceramic half-space with elliptic and parabolic dies is studied. The bodies are under various mechanical, thermal, and electric loads     

A numerical simulation of hydrodynamic forces of ground-effect problem using Lagrange's equation of motion

On the basis of the potential flow theory, Lagrange's equation of motion is used to study the unsteady ground-effect problem. The forces and moments acting on the moving body are solved in terms of the derivatives of added masses in which the generalized Taylor's formulae are applied. The singular integral equations used to solve the surface source intensities and their derivatives are regularized by the Gauss flux theorem and are therefore amenable to the direct use of the Gaussian quadrature formula. In illustration, the condition of a prolate spheroid moving in the fore-and-aft direction at constant speed past a flat ground with a protrusion is considered. The hydrodynamic forces and moments acting on the moving spheroid are investigated systematically by varying the size of the protrusion and the cruising height of the spheroid. © 1998 John Wiley & Sons, Ltd.     

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.     

Slow motion of a slip spheroid along its axis of revolution

A combined analytical and numerical study of the Stokes flow caused by a rigid spheroidal particle translating along its axis of revolution in a viscous fluid is presented. The fluid is allowed to slip at the surface of the particle. The general solution for the stream function in prolate and oblate spheroidal coordinates can be expressed in an infinite-series form of semi-separation of variables. The slip boundary condition incorporating the shear stress at the particle surface is applied to this general solution to determine its unknown coefficients of the leading orders. The solution of these coefficients can be either numerical results obtained from a boundary-collocation method or explicit formulas derived analytically. The drag force exerted on the spheroidal particle by the fluid is evaluated with good convergence behavior for various values of the slip parameter and aspect ratio of the particle. The agreement between our hydrodynamic drag results and the relevant numerical solutions obtained previously using a singularity method is excellent. Although the drag force acting on the translating spheroid normalized by that on a corresponding sphere with equal equatorial radius increases monotonically with an increase in the axial-to-radial aspect ratio for a no-slip spheroid, it decreases monotonically as this aspect ratio increases for a perfect-slip spheroid. The normalized drag force exerted on a spheroid with a given surface slip coefficient in between the no-slip and perfect-slip limits is not a monotonic function of its aspect ratio. For a spheroid with a fixed aspect ratio, its drag force is a monotonically decreasing function of the slip coefficient of the particle.     

Resonant Electromechanical Vibrations of Piezoelectric Plates

The scientific results on the resonant electromechanical vibrations of piezoceramic plates in the form of disks, rings, and polygons obtained over the last 30 years are analyzed, systematized, and generalized. Emphasis is on experimental methods. It is shown that all piezoceramic plates have vibration modes at which deformations are in-phase over the entire volume of the body __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 3–46, July 2005.     

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.     

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.     

The equilibrium of a piezoceramic cylindrical body with a parabolic crack

A conjugate electroelastic field in a piezoceramic cylinder with a parabolic crack under static loading is investigated. Uniformly tensile stresses and an electric potential are applied to the end faces of the cylinder. The following two types of electric conditions are considered at the crack boundary: the electric potential is continuous across the crack and the normal component of the electric-displacement vector on the crack surface is equal to zero. For each of these cases, expressions for some quantities characterizing the disturbed field in the crack plane and formulas to calculate the stress intensity factors are presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 72–80, March, 2000.     

Propagation of two-dimensional nonstationary vibrations in an electrically excited piezoceramic prismatic body

The paper outlines a numerical method to solve a plane problem for a piezoceramic prismatic body having rectangular cross-section and undergoing mechanically excited nonstationary vibrations. The features of the onset and propagation of vibrations are studied. The dynamic state of bodies with different widths is analyzed. The thickness and transverse displacements versus time are plotted Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 71–78, November 2008.     

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.     

Stress state of a piezoelectric ceramic body with a plane crack under antisymmetric loads

The static equilibrium of an electroelastic transversely isotropic space with a plane crack under antisymmetric mechanical loads is studied. The crack is located in the plane of isotropy. Relationships are established between the stress intensity factors (SIFs) for an infinite piezoceramic body and the SIFs for a purely elastic body with a crack of the same form under the same loads. This makes it possible to find the SIFs for an electroelastic body without the need to solve specific electroelasitc problems. As an example, the SIFs are determined for a piezoelastic body with penny-shaped and elliptic cracks under shear __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 32–42, February 2006.