Singular solution of a water wave problem in an ocean of finite depth

The Green's Function of a Water Wave Problem for an Ocean of Finite Depth, bounded internally by a circular cylinder, has been obtained by the use of an appropriate Fourier Series. The technique employed in this investigation may be used when the liquid is internally bounded by cylindrical regions of the form D × I where D is any two dimensional region in the undisturbed free surface and I is the linear interval [0, h].     

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.     

Application of the exact solution for scattering by an infinite cylinder to the estimation of scattering by a finite cylinder

A new algorithm for cylindrical Bessel functions that is similar to the one for spherical Bessel functions allows us to compute scattering functions for infinitely long cylinders covering sizes ka = 2πa/λ up to 8000 through the use of only an eight-digit single-precision machine computation. The scattering function and complex extinction coefficient of a finite cylinder that is seen near perpendicular incidence are derived from those of an infinitely long cylinder by the use of Huygens's principle. The result, which contains no arbitrary normalization factor, agrees quite well with analog microwave measurements of both extinction and scattering for such cylinders, even for an aspect ratio p = l/(2a) as low as 2. Rainbows produced by cylinders are similar to those for spherical drops but are brighter and have a lower contrast.     

Green's function solution of a water wave problem in a stratified ocean of finite depth

A stratified ocean consisting of two layers of immissible fluids of finite thickness is considered. The waves are generated by a point source of oscillatory strength lying in the fluid. The Green's function solution is obtained by the use of an appropriately defined Fourier series. The same technique is used to study the waves, when the fluid is bounded internally by a cylinder.     

On the thermal stresses in a finite circular cylinder

Summary A solution is presented for the determination of thermal stresses in a finite cylinder heated axisymmetrically over the curved surface. The solution is obtained by constructing the thermoelastic displacement potential and the biharmonic Love function to satisfy all the boundary conditions. It considers the steady state stresses as well as the transient stresses.Based on a doctoral thesis in applied mechanics submitted by the first author to Kansas State University, Manhattan, Kansas.     

Strip theory for underwater vehicles in water of finite depth

This paper addresses the need to know the unsteady forces and moments on an underwater vehicle in finite-depth water, at small enough submergences for it to be influenced by sea waves. The forces are those due to the waves themselves, as well as the radiation forces due to unsteady vehicle motions. Knowledge of these forces and the mass distribution of the vehicle allow solution of the equations of motion at a single-frequency. Since the theory is linear, any incident wave field can be decomposed into the sum of many individual single-frequency sinusoidal waves. The motions due to each frequency component can then be added together to obtain the total predicted vehicle motions. The wave forces are due to the undisturbed sea wave plus those due to the diffracted wave necessary to satisfy boundary conditions on the vehicle. The long-used strip theory for ships, with the inviscid-flow approximation, is modified for finite depth and inclusion of lift forces on the vehicle fins. The two-dimensional solutions for the forces on each strip are found by a different method than is commonly used for strip theory. This form of the theory is easier to deal with and requires much less computing time than a fully three-dimensional approach. Experiments are conducted and their results are compared with the theory. Excellent agreement is found between the theoretical and experimental wave forces, including the diffracted wave. It is shown that inclusion of the forces on the fins not only improves the theoretical wave forces, but also brings the results of theory for the radiation forces and moments due to vehicle motions much closer to the experimental values that the theory without inclusion of fin lift forces.     

Wave scattering by a circular cylinder half-immersed in water with an ice-cover

The problem of scattering of water waves obliquely incident on a fixed long circular cylinder half-immersed in deep water with an ice-cover is investigated here. The ice-cover is modelled as an elastic plate of very small thickness. The problem is formulated using the method of multipoles. This leads to an infinite system of linear equations which are solved numerically by truncation. The reflection and transmission coefficients are obtained and depicted graphically against the wave number for various values of the angle of incidence and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. The effect of ice-cover is seen to increase the reflection coefficient and to decrease the transmission coefficient.     

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.     

On a dynamic problem in finite elastic shear

Large amplitude oscillations of cylindrical and prismatic bodies are investigated resulting from a generalized shear deformation in the longitudinal direction. The medium is considered perfectly elastic, isotropic and incompressible. Several results applicable to the entire class of such materials are obtained. For the neo-Hookean body the equation of motion becomes linear so that the solution is easily gained by classical methods.     

Equilibrium of an elastic finite cylinder: Filon's problem revisited

This paper deals with an analytical solution of the axisymmetric boundary-value problem of the theory of elasticity for a finite circular cylinder with free ends and arbitrary loaded curved surface. The object of this paper is to employ the method of superposition to obtain accurate values of the stress field near the boundaries. The classical Filon (1902) problem of uniformly distributed tangential load applied along two rings at the curved surface is addressed in full detail. The distribution of stresses along some typical sections of the cylinder are shown graphically.     

High-Reynolds-number flow about a submerged circular cylinder induced by free-surface travelling waves on finite depth

We consider the fluid flow induced when free-surface travelling waves, on fluid whose depth is finite and uniform in its undisturbed state, pass over a submerged circular cylinder. The wave amplitude is assumed to be small, and a suitably defined Reynolds number large. Thus, the inviscid flow may be pursued by perturbation methods, as may viscous effects that are confined to thin boundary layers on the cylinder and bed beneath it. Particular attention is focused on the steady streaming motion, which induces a circulation about the cylinder. The consequences of this on bed scouring beneath the cylinder, when the bed is erodible, are considered.     

Waves generated by a source below a free surface in water of finite depth

The free-surface flow due to a submerged source in water of finite depth is considered. The fluid is assumed to be inviscid and incompressible. The problem is solved numerically by using a boundary integral equation formulation due to Hocking and Forbes [6]. The numerical results show that there is a train of waves on the free surface in accordance with the results of Mekias and Vanden-Broeck [5]. For small values of the Froude number, the amplitude of the waves is so small that the free surface is essentially flat in the far field. These waveless profiles agree with the calculations of Hocking and Forbes [6].     

Steady heat-conduction problem for a double cylinder

An analytical solution of the problem stated in the title is obtained for various conditions at the ends of the cylinder. The method of asymptotic solution of boundary-value problems for elliptic equations in thin domains is translated to the case of boundary conditions of the third kind.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 26, No. 2, pp. 339–348, February, 1974.     

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.     

Cracked semi-infinite cylinder and finite cylinder problems

This work considers the analysis of a cracked semi-infinite cylinder and a finite cylinder. Material of the cylinder is assumed to be linearly elastic and isotropic. One end of the cylinder is bonded to a fixed support while the other end is subjected to axial tension. Solution of this problem can be obtained by superposition of solutions for an infinite cylinder subjected to uniformly distributed tensile load at infinity (I) and an infinite cylinder having a penny-shaped rigid inclusion at z = 0 and two penny-shaped cracks at z = ±L (II). General expressions for the perturbation problem (II) are obtained by solving Navier equations with Fourier and Hankel transforms. When the radius of the inclusion approaches the radius of the cylinder, the end at z = 0 becomes fixed and when the radius of the cracks approach the radius of the cylinder, the ends at z = ±L become cut and subject to uniform tensile load. Formulation of the problem is reduced to a system of three singular integral equations. By using Gauss–Lobatto and Gauss–Jacobi integration formulas, these three singular integral equations are converted to a system of linear algebraic equations which is solved numerically.     

Coupled conduction-convection problem for a cylinder in an enclosure

The coupled heat conduction/convection problem for a solid cylinder in either a rectangular or a circular enclosure filled with air is solved by an operator-splitting pseudo-time-stepping finite element method, which automatically satisfies the continuity of the interfacial temperature and heat flux. The temperature distribution in the cylinder and in the fluid is obtained showing that the usual practice of prescribing a uniform heat flux boundary condition at the interface may not lead to an accurate solution. From the profile of the local Nusselt number, which is strongly dependent on the Rayleigh number but weakly dependent on the thermal conductivity ratio, it is concluded that most of the heat transfer takes place in the lower half of the cylinder through a convective mode.     

Solution to the problem of transient asymmetric heat conduction in a two-layer hollow cylinder of finite length

The problem is solved by the method of finite integral transformations with asymmetric initial and boundary conditions, when heat is generated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 5, pp. 871–878, November, 1972.     

Axisymmetric contact problem for a semiinfinite cylinder and a half space

This paper is concerned with the elastostatic contact problem of a semi-infinite cylinder compressed against a half space. It is assumed that the contact between the cylinder and the half space is frictionless and that only compressive normal tractions can be transmitted through the interface. The problem is reduced to a system of singular integral equations of the second kind using the transform technique. The order of stress singularity at the corner is determined and the integral equations are solved numerically. Numerical results for contact pressure, stress intensity factor and interface slope are given in graphical form for various material pairs.     

On the thermal problem for composite beams using a finite element semi-discretisation

The paper deals with steady state thermo-elastic problems in beam-like structures and it is composed of three theoretical sections. The first part presents a two-dimensional finite element procedure to compute the temperature distribution within a beam cross section subjected to prescribed boundary conditions. It allows the beam cross section to be modelled taking into account any kind of thermal anisotropy or inhomogeneity.

The second part is devoted to the structural thermo-elastic problem in a beam having arbitrary non-homogeneous, anisotropic material properties over the cross section but constant along the axis; the extension of a well-known semi-discretisation procedure to take into account anisotropic thermal expansion coefficients is presented. In this way it is possible to compute strains and stresses related to temperature distributions on the cross section computed, using the method outlined in the first part of the paper.

The third part describes the procedure to evaluate thermal equivalent loads suitable for a three dimensional frame analysis.

Some examples are presented and the results are compared either with their theoretical counterparts or with numerical results obtained from a full three-dimensional finite element analysis.