The coupled problem of thermoelastic vibrations of a cylinder with cavities

Using a method based on the machinery of analytic functions of complex variables, we construct the solution of the problem of steady planar strain of an isotropic cylinder with curvilinear cavities caused by uneven heating of the surfaces of the cylinder and the cavities. It is an exact solution of the equations and an approximate solution of the boundary conditions. The results of numerical studies are given for a hollow cylinder undergoing thermoelastic radially symmetric vibrations. Two figures. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 82–86.     

The mixed problem for a transtropic cylinder under local heating of the surfaces

By the method of homogeneous solutions we study the stressed state of a transversally isotropic cylinder under local heating of the lateral surfaces. We describe the results of numerical studies as functions of the elastic properties of the material, the geometric characteristics, and the variation of the heating zone on one of the lateral surfaces of the cylinder. Five figures, 3 tables. Bibliography: 3 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, Vol. 27, 1997, pages 3–10.     

Drag on an elliptic cylinder in a fluid particle suspension

An elliptic cylinder is performing oscillations parallel to either of the principal axes of the cross-sectional ellipse in a fluid particle suspension. The stream function governing the flow and the velocity components are determined in terms of Mathieu functions. The drag on the cylinder is evaluated and expressed in terms of two parametersK andK. The effects of the variation of the frequency parameter, eccentricity parameter and relaxation time parameter on the drag parametersK, K is studied numerically.     

The axisymmetric thermoelastoplastic state of a circular two-layer hollow cylinder taking account of frictional heating

We state and solve the axisymmetric thermoelastoplastic problem for a circular two-layer hollow cylinder taking account of frictional heating under the condition that the mechanical and thermophysical characteristics of the materials are independent of temperature. Translated fromMatermatichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 100–106.     

Radiation instability of a circular cylinder in a uniform flow of a two-layer fluid

A solution of the plane linear problem of the oscillations of a horizontal circular cylinder in a uniform flow of a two-layer unbounded fluid is obtained using the method of multipole expansions. The direction of the flow is perpendicular to the cylinder axis. The whole cylinder Ges in the upper or lower layer. The fluid is assumed to be ideal and incompressible, the flow in each layer being a potential one. All the components of the radiation load (the apparent masses and damping coefficients) are determined and the regions of existence of radiation instability are found, depending on the flow velocity for a cylinder suspended by horizontal and vertical elastic links. By solving the integro-differential equation numerically the relative oscillations of the body under specified initial conditions are found.     

Flow of a micropolar fluid through a circular cylinder subject to longitudinal and torsional oscillations

The internal flow of a micropolar fluid inside a circular cylinder which is subject to longitudinal and torsional oscillations is investigated. Analytical expressions of the fluid velocity and micro-rotation are obtained. Explicit expressions of the shear stresses and drag force acting at the wall of the cylinder are derived as well. A numerical analysis followed to examine the effect of the micropolar fluid on the two components of the velocity field through graphical curves. In addition, the magnitude of the tangential drag is computed and compared with the case of a classical fluid.     

Stationary stressed state of an elliptical cylinder

The theory of functions of a complex variable is used to construct an approximate solution for the stationary oscillations of an elliptical cylinder with longitudinal elliptical cavities. Some numerical results are presented for a cylinder with a single cavity. Donetsk State University. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 132–137, 1999.     

Predicting vortex-induced vibration from driven oscillation results

Two-dimensional simulations of flow past both an elastically-mounted cylinder and an externally-driven oscillating cylinder were performed at a Reynolds number of Re = 200. The results were compared to determine if the oscillations of the driven-oscillation model were consistent with the oscillations observed in the elastically-mounted system. It was found that while this is the case, there is considerable sensitivity to input forcing. This sensitivity could explain observed discrepancies between experimental results for the two systems.     

Flow due to the longitudinal and torsional oscillation of a cylinder

Summary An exact solution is obtained for the motion of a fluid contained in an infinité circular cylinder which is undergoing both torsional and longitudinal oscillations. An analytical expression is obtained for the viscous drag on the cylinder and the velocity is depicted graphically. Where possible, comparisons are made with corresponding results for the external problem.     

The antiplane problem of electroelasticity for a cylinder with a tunnel crack excited by an arbitrary system of surface electrodes

The antiplane mixed boundary-value problem of electroelasticity of the oscillations of an infinite piezoceramic cylinder, weakened by a curvilinear tunnel crack, is considered. Using special integral representations of the solution, the boundary-value problem is reduced to a system of singular integro-differential equations of the second kind with discontinuous kernels. The results of a numerical realization of the algorithm, characterizing the amplitude-frequency characteristics of a piecewise-uniform cylinder and the behaviour of the components of the electroelastic field in the region and on the boundary of the cylinder under conditions of the inverse piezoelectric effect, are presented.     

Numerical simulation of vortex induced vibrations and its control by suction and blowing

The vortex formation and shedding behind bluff structures is influenced by fluid flow parameters such as, Reynolds number, surface roughness, turbulence level, etc. and structural parameters such as, mass ratio, frequency ratio, damping ratio, etc. When a structure is flexibly mounted, the Kármán vortex street formed behind the structure gives rise to vortex induced oscillations. The control of these flow induced vibrations is of paramount practical importance for a wide range of designs. An analysis of flow patterns behind these structures would enable better understanding of wake properties and their control. In the present study, flow past a smooth circular cylinder is numerically simulated by coupling the mass, momentum conservation equations along with a dynamical evolution equation for the structure. An active flow control strategy based on zero net mass injection is designed and implemented to assess its efficacy. A three actuator system in the form of suction and blowing slots are positioned on the cylinder surface. A single blowing slot is located on the leeward side of the cylinder, while two suction slots are positioned at an angle α = 100°. This system is found to effectively annihilate the vortex induced oscillations, when the quantum of actuations is about three times the free stream velocity. The dynamic adaptability of the proposed control strategy and its ability to suppress vortex induced oscillations is verified. The exact quantum of actuation involved in wake control is achieved by integrating a control equation to decide the actuator response in the form of a closed loop feed back system. Simulations are extended to high Reynolds number flows by employing eddy viscosity based turbulence models. The three actuator system is found to effectively suppress vortex induced oscillations.     

Vibrations of a cylinder in a concentric vessel filled with a two-layer fluid

A hybrid vibrational system containing a solid (a cylinder) with an elastic connection to a coaxial cylindrical cavity, completely filled with a heavy ideal stably stratified two-layer fluid, is considered. The combined self-consistent vibrations of the body and the fluid (of the internal waves) are studied. An explicit solution of the internal boundary value problem of an inhomogeneous liquid in an annular domain for a specified motion of the body is obtained. An integrodifferential equation of the Newton type is constructed on the basis of this. This equation describes the self-consistent oscillations of the cylinder. In the case of weak coupling of the interaction between the solid and the medium, an approximate solution is obtained using asymptotic methods and an analysis is carried out. Qualitative effects of the mutual effect of the motions of the cylinder and the fluid are found.     

Modelling of a Switching Control Hydraulic System

Modelling of a hydraulic system featuring a specific type of switching control is presented. Despite conventional hydraulic drive technology where rather smooth changes of pressure and flow rate are intended and where oscillations constitute undesired phenomena, switching control provokes oscillations as an indispensable element to achieve high energetic efficiency with valve control. The system under study is one which comprises a novel switching valve, a long line with considerable wave propagation dynamics, a hydraulic cylinder, and the valve's dynamics.     

Optimization of the two-dimensional temperature fields in inhomogeneous bodies with constraints on the phase coordinates

We state a problem of speed-optimal control of the two-dimensional nonstationary temperature regime in inhomogeneous bodies with constraints on the control (the temperature of the heating medium) and the phase coordinates (the temperature of the body, the temperature range, and the heat flux on the surface of the body), and we propose a method for solving the problem numerically. We give as an example the computation of the optimal control of heating of a hollow infinite cylinder under constraints on the temperature range. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 119–123.     

Thermomechanical behavior of nonmetallic electrical conductors during high-temperature treatment

We give a mathematical statement and initial relations for the problem of determining the temperature fields and stresses in nonmetallic electrical conductors under induction heating to high temperatures. We study the influence of the temperature dependence of the characteristics of the material and the radiant heat transfer with the surrounding medium on the thermomechanical behavior of a cylinder. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 74–79.     

On the hydrodynamic interaction of two circular cylinders oscillating in a viscous fluid

The present paper deals with the plane flow fields induced by two parallel circular cylinders with radiia andb oscillating in a direction which is i) parallel or ii) perpendicular to the plane containing their axes. The effect of the cylinders' hydrodynamic interaction on steady streaming has been studied analytically at high frequency by the method of matched asymptotic expansions.It is found that ifa=b the steady streaming is directed symmetrically to the cylinders while whenab (in the case i)) the secondary steady flow is directed towards the larger cylinder and one of the outer steady vortices disappears.It is shown in case i) that the drag force acting on each cylinder is smaller than the same force experienced on a single cylinder with the same radius which is placed in an unbounded oscillating flow. When the cylinder radii are equal, the drag is greater on the forward cylinder than on the rear one.In contrast, in case ii), wherea=b, it is shown that the drag on each of the two cylinders is greater than the drag acting on a single cylinder with the same radius placed in an unbounded oscillating stream and also each of the cylinders experiences a repulsive force in a direction perpendicular to the oscillating flow.     

Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains

The solvability in Sobolev spaces is proved for divergence form complex-valued higher order parabolic systems in the whole space, on a half-space, and on a Reifenberg flat domain. The leading coefficients are assumed to be merely measurable in one spacial direction and have small mean oscillations in the orthogonal directions on each small cylinder. The directions in which the coefficients are only measurable vary depending on each cylinder. The corresponding elliptic problem is also considered.     

Pattern formation in microwave heated ceramics: cylinders and slabs

Analyses of microwave heating of a thin ceramic cylinder and a thin ceramic slab in a single mode, highly resonant cavityare presented. Realistic assumptions regarding the effectiveelectrical conductivity, thermal parameters, and physical dimensionsare adhered to throughout. Consequently, the models developedherein incorporate most of the features of actual experiments.They incorporate both the effects of cavity detuning and alocal electric field perturbation on the heating process. The models presented take the form of one- and two-dimensionalreaction–diffusion equations which contain a functionaland an inhomogeneous source term for the cylinder and slab,respectively. The development of these equations is the product of a systematic modelling process that involves S-matrix theory,a small Biot number asymptotic analysis, and a matched asymptotic analysis of a non-standard electromagnetic scattering problem.The one-dimensional equation for the cylinder reveals boththe mathematical structure and physical mechanism for the formationof hot-spots. The two-dimensional equation supports a hot stripe pattern, due to preferential electromagnetic heating, whichbecomes unstable and evolves into an oval-like spot. Accuratenumerical methods which approximate the solutions of theseequations and their stability are presented and these agreequalitatively with experiments and predict observed trends. Received 1 June, 1999. ⁺ antoine@mip.ups-tlse.fr     

The thermally stressed state of a thickwalled hollow composite cylinder

We propose an approach to the determination of the temperature, stress, and displacement, fields in laminated hollow composite cylinders. The cylinders are studied in three-dimensional formulation; the material of each lamina has the properties of thermal and elastic orthotropy. We study the influence of the heat flow passing through the end surfaces and nonuniform heating of the cylinder to its thermally stressed state. We exhibit peculiarities in the stress and displacement distributions caused both by anisotropy of the mechanical and thermophysical properties and by the nature of the thermal actions applied. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 14–18     

On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets

A singularly perturbed eigenvalue problem for the Laplacian in a cylinder is considered. The problem is characterized by frequent nonperiodic alternation of boundary conditions imposed on narrow strips lying on the cylinder’s lateral surface. The width of the strips is an arbitrary function of a small parameter and can oscillate rapidly, with the nature of the oscillations being arbitrary. Sharp estimates are derived for the convergence rate of the eigenvalues and eigenfunctions in the problem.