Boundary-value problem of heat conduction for a layer with foreign cylindrical inclusion

Using generalized functions, we obtain a heat-conduction equation with discontinuous and singular coefficients for an isotropic layer with heat-generating foreign cylindrical inclusion. Using a piecewise-linear approximation of temperature on the surfaces of the inclusion and the Hankel integral transformation, we construct an analytic solution of the boundary-value problem of heat conduction with heat emission. A numerical analysis of the considered system is carried out.     

Dynamic problem of thermoelasticity for a hollow cylinder

We consider a dynamic problem of thermoelasticity for a hollow cylinder in which we assume the heat propagation speed to be finite.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.21, No. 1, pp. 145–151, July, 1971.     

A plane dynamic axisymmetric problem for a hollow cylinder

A dynamic problem for an elastic hollow cylinder whose surfaces are subjected to the action of arbitrary forces is solved by a new method based on the use of finite differences only with respect to time [12]. The numerical analyses of the time dependences of stress concentration are carried out for hollow cylinders of different thickness under impact loading. The proposed method is tested by solving a problem of circular hole in an infinite body subjected to the action of impact loads over the entire surface. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 1, pp. 7–13, January–February, 2008.     

Axisymmetric problem of thermoelasticity for a hollow cylinder of finite length

The axisymmetric problem of heat conduction is examined for a hollow cylinder of finite length with mixed boundary conditions; a solution is given for the corresponding quasi-static problem of thermoelasticity.     

Plane contact thermoelasticity problem for a two-layer circular hollow cylinder with heat generation

We consider a contact thermoelasticity problem for a two-layer hollow cylinder. One of the layers rotates with respect to the other with a constant angular velocity. Constant stresses on the interface of cylindrical layers are caused by (a) compressive radial stresses or displacements on the side surfaces of the body and (b) a positive difference between ambient temperatures inside and outside the two-layer cylinder. Heat is generated as a result of friction on the contacting surfaces of the layers. We study the effects of the intensity of heat generation and physicomechanical properties of the cylinders on the distributions of stresses, displacements, and temperatures in the body.Franko L'viv State University, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 6, pp. 24–30, November – December, 1994.     

Homogeneous solutions of the electroelasticity equations for piezoceramic layers in R 3

We present a procedure for the derivation of homogeneous solutions for piezoceramic layers within the framework of electroelasticity. The proposed approach simplifies considerably the Lurié (J Appl Math Mech 6:151–169, 1942) method. Two cases of mechanical boundary-conditions for piezoceramic layers are examined, namely, when the bases are (a) built in, and (b) free from the influence of forces. In both cases, the bases of the layer are assumed to be covered by grounded electrodes. It is shown that in the case of boundary conditions of the first type and for the symmetric, with respect to the mid-surface of the layer, electro-elastic state, the homogeneous solutions do not contain any biharmonic terms. We also calculate the distribution of the characteristic values of the corresponding spectrum problems for every given type of boundary conditions. The derived homogeneous solutions can be used for solving boundary-value problems for piezoceramic cylinders and layers within the framework of electroelasticity. We illustrate our approach through a practical example considering an oblique-symmetric boundary-value problem for layers which weaken due to a side to side elliptic cavity.     

Axisymmetric crack problem for a hollow cylinder imbedded in a dissimilar medium

The analytical solution for the linear elastic problem of flat annular crack in a transversely isotropic hollow cylinder imbedded in a transversely isotropic medium is considered. The hollow cylinder is assumed to be perfectly bonded to the surrounding medium. This structure, which can represent a cylindrical coating-substrate system, is subjected to uniform crack surface pressure. Because of the geometry and the loading, the problem is axisymmetric. The z = 0 plane on which the crack lies, is also a plane of symmetry. The composite media consisting of the hollow cylinder and the surrounding medium extends to infinity in z and r directions. The mixed boundary value problem is formulated in terms of the unknown derivative of the crack surface displacement by using Fourier and Hankel transforms. By extending the crack to the inner surface and to the interface, the cases of surface crack and crack terminating at the interface are obtained. Asymptotic analyses are performed to derive the generalized Cauchy kernel and associated stress singularities. The resulting singular integral equation is solved numerically. Stress intensity factors for various crack configurations, crack opening displacements and stresses along the interface and on z = 0 plane are presented for sample material combinations and geometric parameters.     

On the dynamical thermoelasticity problem for a hollow funtionally graded cylinder

A thermoelasticity problem of a pressurized infinite cylinder made of functionally graded material is solved analytically where material properties vary with radial position. Time dependent thermal and mechanical boundary conditions are assumed to act on the inner and outer surfaces of the cylinder. For thermal boundary conditions, temperature is prescribed on both surfaces, whereas for mechanical boundary conditions, tractions are prescribed on the boundaries. Obtaining distribution of temperature throughout the cylinder, the dynamical structural problem is solved and closed form relations are extracted for distributions of stress components.     

Ultrasonic piezoceramic transducers with a magnetoacoustic layer

We describe the design and present the results of calculations of the properties of an ultrasonic transducer based on a piezoceramic plate in mechanical contact with a layer of a magnetoacoustic material. The transducer is characterized by strong dependence of the velocities of both transverse and longitudinal waves on the magnetic field. This allows the resonance frequency and the bandwidth to be effectively controlled even in the case of low-Q piezoelectric ceramics and makes it possible to create a tunable frequency standard based on a high-Q piezoelectric material.     

A conjugate problem of thermal explosion of a hollow cylinder

A conjugated problem of heat conduction for two hollow cylinders that are in close contact, with one consisting of a reagent, has been solved analytically. The problem has been solved by the backward method under boundary conditions of the first kind. The critical conditions of thermal explosion were investigated as functions of the parameters of a reagent and of an inert body. An engineering method for determining the critical conditions of a thermal explosion is suggested. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 4, pp. 110–113, July–August, 2006.     

Investigation of the direct and inverse piezoeffect in the dynamic problem of electroelasticity for an unbounded medium with a tunnel opening

Summary An effective approach to the investigation of antiplane electroacoustic wave fields in an unbounded piezoelectric medium weakened by a tunnel opening with the given system of surface electrodes is suggested. The approach is based on the method of boundary integral equations. It is assumed that the medium excitation occurs due to the effect of the given electrodes electric potential differences (inverse piezoeffect). The solution of the boundary-value problem of electroelasticity is also considered in the case of the direct piezoeffect when as a result of diffraction on the opening of monochromatic shear waves the generation of electric potential difference takes place on electrode coverings. An approximate scheme of numerical realization of the solvable system of singular integro-differential equations of the second kind with discontinuous kernels is given. There are presented some examples.     

Transient thermal contact problem for axial crack in a hollow circular cylinder

The transient behavior of an axial-cracked hollow circular cylinder subjected to a sudden heating is investigated. It is shown that surface heating may induce compressive thermal stress near the inner surface of the cylinder which in turn may force the cracked surfaces to close together. Assuming that the existence of the crack does not alter the temperature distribution, this problem can be divided into two parts and solved by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without a crack are obtained by finite element/implicit time integration method. The calculated temperature and thermal stress distributions are in good agreement with the values predicted by the analytical method. Secondly, the opposite senses of the stress distributions along the cracked surfaces, which are obtained previously, are treated as the traction boundary conditions, and the contact length and contact pressure of the real cracked cylinder are obtained by a modified elimination finite element scheme. In this scheme, the concepts of contact-node-pairs' penetration, contact-double-forces and compliance matrix are introduced. The calculated results indicate that the contact length ratio becomes smaller when the crack length ratio increases, and becomes larger as the radius ratio increases. Finally, the normalized stress intensity factor for the crack tip of the cylinder is obtained. It is shown that the larger the crack length ratio the higher the stress intensity factor.     

A periodic problem of heat conduction in a hollow infinite cylinder

The problem of radial distribution of temperature in an infinite hollow cylinder is solved in the presence of heat exchange with the surrounding medium in the case in which the heat exchange coefficients are periodic functions of time.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 17, No. 5, pp. 880–891, November, 1969.     

Radial vibration of a thick-shell hollow piezoceramic sphere

Summary A thick-shell hollow piezoceramic sphere electroded completely on both inside and outside surfaces and radially polarized can be used as a source and receiver of underwater sound. Restricting the analysis to moderately thick shells the electromechanical equations of displacement are solved to generate the frequency equation for the pure radial modes. The frequency equation is specialized to reflect the behavior of a barium-titanate shell and numerical values are tabulated for the first three frequencies for a broad range of shell thicknesses.

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Zusammenfassung Eine dickwandige Hohlkugel aus piezokeramischem Material, als Unterwasser-Schallsender und-empfänger verwendbar, trägt beidseitig einen Elektrodenbelag und ist radial polarisiert. Unter Beschränkung auf mäßige Wandstärke werden die elektromechanischen Verschiebungsgleichungen gelöst, um die Frequenzgleichung für die Radialschwingung zu erhalten. Dieser Frequenzgleichung wird für eine Bariumtitanat-Hohlkugel spezialisiert und es werden numerische Werte für die ersten drei Eigenfrequenzen innerhalb eines weiten Wandstärkebereiches angegeben.

     

A boundary layer theory for the end problem of a circular cylinder

Summary This paper discusses the nature of an approximate solution for the hollow circular cylinder whose fixed ends are given a uniform relative axial displacement and whose cylindrical surfaces are free from traction. We shall take the solution of this problem to be given by a super-position of the following two problems: problem I considers a finite length cylinder whose ends are given a relative axial displacement, but are no longer fixed; problem II removes the radial displacement at the end of the cylinder obtained in problem I.Nomenclature a mid-surface radius of cylinder - c half-height of cylinder - E, in-plane elastic moduli - E_t, _t, G_t transverse elastic moduli - _z, , _r axial, circumferential, and normal strain - _rz transverse shear strain - h cylinder thickness - _z, , _r axial, circumferential, and normal stress - _rz transverse shear stress - z, r axial and radial coordinates - u_z, u_r axial and normal displacements     

Generalized thermoelastic diffusion problem for an infinitely long hollow cylinder for short times

In this work, we consider the problem of a thermoelastic infinitely long hollow cylinder in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The outer surface of the cylinder is taken traction free and subjected to a thermal shock, while the inner surface is taken to be in contact with a rigid surface and is thermally insulated. Laplace transform techniques are used. The solution is obtained in the Laplace transform domain by using a direct approach. The solution of the problem in the physical domain is obtained numerically using a numerical method for the inversion of the Laplace transform based on Fourier expansion techniques. The temperature, displacement, stress and concentration as well as the chemical potential are obtained. Numerical computations are carried out and represented graphically.