Guided ultrasonic waves in composite cylinders

The ultrasonic nondestructive evaluation of composite cylinders requires a thorough understanding of the propagation of waves in these materials. In this paper, the propagation of flexural and longitudinal guided waves in fiber-reinforced composite (FRC) rods with transversely isotropic symmetry properties is studied. The frequency equations obtained for free cylinders and the effect of increased fiber volume fraction (increased anisotropy) on the dispersion characteristics of the rod are explored. The numerical results reveal a number of previously unnoticed characteristics of dispersion curves for composite cylinders. The mode shapes of longitudinal waves propagating in glass/epoxy cylinders are also plotted. These plots can be used to choose an appropriate strategy for inspecting composite cylinders by ultrasonic nondestructive evaluation techniques. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 411–426, May–June, 2007.     

Longitudinal flow past cylinders arranged in a triangular array

The longitudinal viscous flow past arranged in a triangular array of cylinders is studied through boundary perturbation. The velocity distribution is found to 3rd order. Accurate analytic formula for permeability is derived for arbitrary solid fractions. A variety of cylinder shapes are considered. The results are useful in modelling convective heat transfer, porous media, and composite manufacturing.     

Fully developed incompressible flow between non-coaxial circular cylinders

Exact formulae which relate the rate of mass flow to the constant axial pressure gradient in fully developed flow between non-coaxial circular cylinders are obtained for the first time. Of the two formulae which are presented, that which corresponds to the case of fully eccentric cylinders is particularly simple, being in structure no more complicated than the well known result for coaxial cylinders. Attention is also given to the wall shear stresses and to the drag which the fluid exerts on unit length of each cylinder. Exact formulae provides results which describe the dependence of these quantities on the ratio of the diameters of the cylinders and on the eccentricity.

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Résumé On a trouvé pour la première fois les formules exactes qui mettent en relation le flux de la masse au gradient de la pression pour le mouvement d'un fluide dans l'espace entre deux longs cylindres non coaxiaux. Quant les cylindres se touchent nous trouvons un résultat très simple. Nous dérivons aussi les formules exactes pour la tension de frottement à la paroi et la résistance visqueuse par unité de longueur de chaque paroi.

     

On the flow of a viscous incompressible fluid between two coaxial rotating porous cylinders

Exact solution of the Navier-Stokes equations for the laminar flow of a viscous incompressible fluid between two coaxial rotating porous cylinders, kept at constant temperatures, has been studied. The rate of injection at one cylinder is taken to be the same as the rate of suction at the other. Expressions for the velocity and temperature distributions and for the torque required to turn the outer cylinder are obtained. The effects of λ (injection parameter), σ (the ratio of the radii of the cylinders) and Pé (Péclet number = λPr) on them are shown graphically.     

Vibrational mixing of a fluid between two quasiconcentric cylinders

We consider the possibility of intense mixing of a viscous fluid in the gap between two quasiconcentric cylinders, with one of the cylinders performing high-frequency vibrations about its axis. The motion of the fluid is described by Navier-Stokes equations for the axisymmetric case. The stream function is represented by a generalized Fourier series. The small parameter is the ratio of the vibration amplitude to the radius of the external cylinder. Calculations carried out in the zeroth approximation produced the pattern of stream lines for various Reynolds numbers, vibration amplitudes, and ratios of external and internal radii. The mixing intensity was found to increase substantially with the reduction of the gap between the cylinders, whereas variation of the ratio of the vibration amplitude to the Reynolds number did not produce marked qualitative changes. The fluid flow in this system generates a contraction semigroup, which makes it possible to derive the ergodicity criterion for the stream function.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 35–39, 1986.     

Two-dimensional viscous flow between circular cylinders: application to damping devices for seismic isolation

A detailed analysis of the fluid dynamics of the two-dimensional viscous flow between circular cylinders is dealt with in this paper. Analytic solutions are found on the basis of asymptotic expansions with respect to a small parameter defined by the ratio between the difference of the radii and the radius of the internal cylinder. The analysis is related to the study of recently developed devices for seismic isolation of buildings based on modified pile foundation, separated from the soil, in which a viscous fluid is inserted in the void space between the pile and the lining of the surrounding soil. The availability of this analytical solution contributes to obtaining accurate predictions of the force on the pile.     

Long nonlinear waves in anisotropic cylinders

Small-amplitude plane nonlinear waves in anisotropic cylinders are considered in the case of longitudinal and torsional waves having close velocities. Anisotropy corresponding to this condition can take place in specifically plaited ropes and in the case of anisotropy of other nature. The characteristic velocities are found, and simple waves are studied.     

Numerical studies of time-independent and time-dependent scattering by several elliptical cylinders

A numerical solution to the problem of time-dependent scattering by an array of elliptical cylinders with parallel axes is presented. The solution is an exact one, based on the separation-of-variables technique in the elliptical coordinate system, the addition theorem for Mathieu functions, and numerical integration. Time-independent solutions are described by a system of linear equations of infinite order which are truncated for numerical computations. Time-dependent solutions are obtained by numerical integration involving a large number of these solutions. First results of a software package generating these solutions are presented: wave propagation around three impenetrable elliptical scatterers. As far as we know, this method described has never been used for time-dependent multiple scattering.     

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.     

Torsional vibrations of piezoceramic hollow cylinders with circular polarization

A problem of natural torsional vibrations of hollow piezoceramic cylinders is considered. The piezoceramic is polarized in the circular direction. The lateral surfaces of the cylinder are covered with shortcircuited thin electrodes. The method of solution of the problem is based on the combination of the spline collocation methods along the longitudinal coordinate and the stepwise search method along the radial coordinate. We present results of a numerical analysis of a cylinder made from PZT 4 ceramic in a wide range of change in the geometrical characteristics of the cylinder.     

Packing cylinders on a cylinder with contact constraints

The problem of cylinder packing is investigated. The specific problem is to determine the maximum number of congruent cylinders that can be packed around a core cylinder of arbitrary dimensions. The constraint is that their circular face must keep in contact with the core cylinder and there may be no overlapping. Only right circular cylinders are considered. Mathematically, a lower and upper bound is determined. A quantitative result is also found using a modified genetic algorithm. The algorithm was found to reproduce the published results for the top and bottom circular faces of the core which reduces to the problem of packing congruent circles within a circle. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimizing the packing of cylinders into a rectangular container: A nonlinear approach

The container loading problem has important industrial and commercial applications. An increase in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of economic importance. In this work, a procedure based on a nonlinear decision problem to solve the cylinder packing problem with identical diameters is presented. This formulation is based on the fact that the centers of the cylinders have to be inside the rectangular box defined by the base of the container (a radius far from the frontier) and far from each other at least one diameter. With this basic premise the procedure tries to find the maximum number of cylinder centers that satisfy these restrictions. The continuous nature of the problem is one of the reasons that motivated this study. A comparative study with other methods of the literature is presented and better results are achieved.     

Generalized holomorphic orthogonal function systems over infinite cylinders

In this paper we construct two distinct generalized holomorphic orthogonal function systems over infinite cylinders in . Explicit representation formulae and properties of the obtained basis functions are given. As an application, we present some plot simulations that illustrate the results of this work. Copyright © 2014 John Wiley & Sons, Ltd.     

Abelian quotients of monoids of homology cylinders

A homology cylinder over a surface consists of a homology cobordism between two copies of the surface and markings of its boundary. The set of isomorphism classes of homology cylinders over a fixed surface has a natural monoid structure and it is known that this monoid can be seen as an enlargement of the mapping class group of the surface. We now focus on abelian quotients of this monoid. We show that both the monoid of all homology cylinders and that of irreducible homology cylinders are not finitely generated and moreover they have big abelian quotients. These properties contrast with the fact that the mapping class group is perfect in general. The proof is given by applying sutured Floer homology theory to homologically fibered knots studied in a previous paper.     

Exact solutions of functionally graded piezoelectric material sandwich cylinders by a modified Pagano method

The three-dimensional (3D) coupled analysis of simply-supported, functionally graded piezoelectric material (FGPM) circular hollow sandwich cylinders under electro-mechanical loads is presented. The material properties of each FGPM layer are regarded as heterogeneous through the thickness coordinate, and obey an exponent-law dependent on this. The Pagano method is modified to be feasible for the study of FGPM sandwich cylinders. The modifications are as follows: a displacement-based formulation is replaced by a mixed formulation; a set of the complex-valued solutions of the system equations is transferred to the corresponding set of real-valued solutions; a successive approximation method is adopted to approximately transform each FGPM layer into a multilayered piezoelectric one with an equal and small thickness for each layer in comparison with the mid-surface radius, and with the homogeneous material properties determined in an average thickness sense; and a transfer matrix method is developed, so that the general solutions of the system equations can be obtained layer-by-layer, which is significantly less time-consuming than the usual approach. A parametric study is undertaken of the influence of the aspect ratio, open- and closed-circuit surface conditions, and material-property gradient index on the assorted field variables induced in the FGPM sandwich cylinders.     

Second order wave loads on large monolithic offshore structures

This paper considers the wave loads on large monolithic offshore structures. The second order wave force formulae developed by Rahman and Heaps, applicable to large circular cylinders in waves, are extended to evaluate the overturning moments on large circular cylinders. The theory is then applied to square section caissons in waves, to predict the wave loads on these structures. These calculations are performed using the exact form of the second order velocity potential, φ₂, with arbitrary wave number, k₂, and the approximate form of φ₂, with twice the value of the wave number of the first order velocity potential. The second order analytical predictions are compared with available experimental data for various ranges of wave parameters for both circular and square caissons in large amplitude waves.     

Contact interaction between elastic cylinders with axis misalignment

The three-dimensional problem of frictionless contact between semi-infinite elastic cylinders with the axes misaligned at small angles is examined. An approximate solution yielding the simplest scheme possible for practical calculations is constructed as a result of investigation of the contact zone near the edge and a number of asymptotic simplifications. The results obtained from this scheme and possible restrictions placed on its applicability are analyzed in specific examples of a roller bearing with misaligned rings and gearing.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 32–39, 1988.     

Efficient modelling of rotating disks and cylinders using a cartesian grid

Calculations are presented of flow characteristics in the vicinity of disks and cylinders rotating at speeds typical of those found in modern mechatronics machinery. The rotational speeds are slow or intermittent, and the generated boundary layers are laminar and transitional. Comparison is made with existing experimental data and exact, though idealised, analytical solutions. A three-dimensional finite volume procedure with time dependence was employed as the solution method, and two grid geometries were used, namely, axisymmetric and cartesian. Use of a cartesian grid is very important, as it is compatible with the design of the interiors of mechatronics machinery, and present practice is to model these interiors with computationally economical cartesian grids. Expanding grids were generated normal to surfaces for each of the grid geometries so as to capture the thin boundary layers. To alleviate numerical difficulties, when using the cartesian geometry, an expanding and contracting grid was generated normal to the axis of the disks and cylinders with the grid spacing based on a shifted Chebyshev polynomial.     

Solution of an axisymmetric problem of free vibrations of piezoceramic hollow cylinders of finite length by the spline collocation method

An axisymmetric problem of longitudinal free vibrations of piezoceramic hollow cylinders for some types of boundary conditions on the end faces is considered. The lateral surfaces of the cylinder are covered with thin short-circuited electrodes. The polarization of piezoceramics is directed along the axis of the cylinder. Using the method of separation of variables and method of spline collocation along the length of the cylinder, we reduce the problem to a system of ordinary differential equations, which is solved by the method of step-by-step search. We present results of calculations for a PZT 4 piezoceramic cylinder.     

Effects of radial temperature gradient on the stability of flow of a viscous incompressible fluid between two rotating cylinders

Stability of the flow of a viscous incompressible fluid in a narrow gap between two concentric cylinders rotating in opposite directions is studied. Exact values of critical Taylor number for the first and second modes are derived by a numerical procedure and these are compared with the known results. It is observed that the value of the critical Taylor number T_crit decreases with increasing the values of a parameter $\text{N (N =}\text{Ra}\text{T}\text{,}\text{Ra = Rayleigh number, T = Taylor number}\text{)}$, and the rate of decrease in the value of T_crit is more when the two cylinders rotate in the opposite directions.