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.     

Wave scattering by a horizontal circular cylinder in a two-layer fluid with an ice-cover

In a two-layer fluid wherein the upper layer is of finite depth and bounded above by a thin but uniform layer of ice-cover modelled as a thin elastic sheet and the lower layer is infinitely deep below the interface, time-harmonic waves with a given frequency can propagate with two different wavenumbers. The wave of smaller wavenumber propagates along the ice-cover while wave of higher wavenumber propagates along the interface. In this paper problems of wave scattering by a horizontal circular cylinder submerged in either the lower or in the upper layer due to obliquely as well as normally incident wave trains of both the wave numbers are investigated by using the method of multipole expansions. The effect of the presence of ice-cover on the various reflection and transmission coefficients due to incident waves at the ice-cover and the interface is depicted graphically in a number of figures.     

Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis

We use the semiclassical limit of electromagnetic wave scattering theory to determine the properties of the exterior caustics of a diagonally incident plane wave scattered by an infinitely long homogeneous dielectric circular cylinder in both the near zone and the far zone. The transmission caustic has an exterior/interior cusp transition as the tilt angle of the incident beam is increased, and each of the rainbow caustics has a farzone rainbow/exterior cusp transition and an exterior/interior cusp transition as the incident beam tilt angle is increased. We experimentally observe and analyze both transitions of the first-order rainbow. We also compare the predictions of the semiclassical approximation with those of ray theory and exact electromagnetic wave scattering theory.     

Asymptotic analysis of the torsional modes of wave propagation in a piezoelectric solid circular cylinder of (622) class

An asymptotic method due to “Achenbach” is used to analyze the torsional modes of wave propagation in a solid circular cylinder of piezoelectric material of (622) crystal class. Information obtained in this method is useful for the frequency spectrum at long wavelengths. In this method, the field variables and the frequency are expressed as power series of the dimensionless wavenumber, $\text{? = 2π × R/W}$. Substituting these expansions in the field equations and the boundary conditions, a system of coupled second order inhomogeneous ordinary differential equations with the radial coordinate as independent variable is obtained by collecting the terms of same order $\text{?}{}^{\mathrm{m}}$. Integration of such systems of differential equations yield the various terms in the series expansions for the above modes and for the whole range of frequencies, when the real-valued dimensionless wavenumber less than unity ($\text{0<?<1}$). To test the correctness of the present scheme, the roots of the exact frequency equation are computed in double precision and the results thus obtained are compared with the results obtained in the present analysis. The results agree upto five decimal places.     

Mass sensitivity of thickness-shear modes in an isotropic elastic circular cylinder

Theoretical prediction of the mass sensitivity of axial and tangential thickness-shear modes in an isotropic elastic circular cylinder due to a thin surface mass layer is presented. Results suggest the possibility of new mass sensors with certain advantages.     

Transverse electric scattering by a dielectric biconvex cylinder loaded with a shallow circular trough in a ground plane

The scattering problem of transverse electric wave from a dielectric biconvex cylinder buried in a shallow circular trough of a ground plane is investigated and a rigorous series solution is also derived. Based on the region-matching method, the analysed region is decomposed into two subregions by introducing a semi-circular auxiliary boundary. The magnetic field of each subregion is expressed in terms of cylindrical wave functions with unknown expansion coefficients. After imposing the matching conditions and the boundary condition on the trough surface with the aid of Graf's addition theorem, the unknown coefficients are determined. Comparisons with published data for a dielectric circular cylinder case show very good agreement. Visible effects of depth-to-half-width ratios of a dielectric biconvex cylinder on echo width, far- field pattern and near-field distribution are illustrated in graphical form.     

Rarefaction of the spectrum of H-type whispering-gallery modes in a hemispherical dielectric resonator

A dense spectrum of H-type resonance oscillations (whispering-gallery modes) is observed in a hemispherical dielectric resonator excited by a capacitive slit situated on the equatorial metal mirror surface. The spectrum can be significantly rarefied by exciting the WG modes in the resonator by means of distributed coupling to a dielectric waveguide arranged in a certain special position relative to the hemisphere base.     

Plastic buckling analysis of a circular cylinder considering plastic compressibility

In this study the plastic buckling analysis of a circular cylinder under axial compression is carried out considering plastic compressibility. For the stability analysis, the linearized finite element equation is derived and the general elastic-plastic constitutive equation is formulated. The Drucker-Prager plastic potential is used to describe the plastic compressible yielding and the strength-differential effect. The influence of plastic compressibility on the buckling load is investigated for a circular cylinder.     

Rotating flow in a cylinder with a circular barrier on the bottom

Summary The relative flow of a homogeneous, slightly viscous fluid in a rotating cylinder is induced by differential rotation of the bottom disk, on which a thin circular strip of small height is fixed. The axis of symmetry of the strip coincides with the rotation axis of the cylinder.At the strip a Stewartson layer exists which is partially free, partially attached to the strip. The structure of the Stewartson % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaCa% aaleqabaWaaSGbaeaacaaIXaaabaGaaGinaaaaaaaaaa!3873!\[E^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \]-layer (E being the Ekman number) is not affected by the height of the strip, but the % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaCa% aaleqabaWaaSGbaeaacaaIXaaabaGaaG4maaaaaaaaaa!3872!\[E^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} \]-layer problem has to be solved in the two separate intervals. The fact that both solutions do not match at the strip edge necessitates the presence of an intermediate region that exhibits some characteristic features of an Ekman layer.     

On liquid motion in a circular cylinder with horizontal axis

Summary The flow pattern of the slosh motion of a homogeneous, nonviscous (inviscid) and incompressible fluid with a free surface, contained in a rigid circular canal, has been dealt with analytically and experimentally. The axis of the canal is perpendicular to the direction of gravity. Considered are transverse (lateral to axis) oscillations of the liquid. The shape of the free liquid surface is determined numerically by means of a simple procedure. Theoretically calculated streamlines (path lines) are found to be in good qualitative agreement with experimentally observed trajectories of small spheres, made of plastic material and immersed in the liquid. The plastic particles and the liquid (water with a solution of salt added) have the same density.     

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.     

Thermal stresses and couple-stresses in square cylinder with a circular hole

This article deals with the effect of couple-stresses on thermal stress distribution in a square cylinder with a central circular hole under steady state temperature distribution. The analysis is developed by the point-matching technique.From our calculation, it may be concluded that stress concentration around a circular hole, taking couple-stress into account, results in lower values than those accepted heretofore.     

Longitudinal shear of a crack in a multi-material circular cylinder

This is an article dealing with the longitudinal shear of a crack contained in a circular cylinder, which is embedded in and fixed by perfect bonding to a composed hollow circular cylinder, consisting of a number of hollow sub-cylinders of different materials. A rigorous solution to the problem is developed. With the material and geometric constants of the composed hollow circular cylinder as parameters, numerical values of stress intensity factors for the crack are worked out. The delicate behavior in the variation of the stress intensity factors, when the number of the hollow sub-cylinders becomes large, is analyzed and discussed. The solution is developed by utilizing a simplified and improved technique using complex variables.     

Heat of a layer transversely flowing past a cylinder with circular finning

Results of investigations and generalized relations for calculating heat transfer of a dense layer with transversely finned cylinders are presented. Thermal efficiency is determined and recommendations are given for selecting the geometric parameters of developed surfaces of this type.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.18, No. 1, pp. 52–58, January, 1970.     

Singular stresses in a transversely isotropic circular cylinder with circumferential edge crack

This paper concerns the analysis of the singular stresses arising in a transversely isotropic infinite cylinder having a circumferential edge crack. The problem is reduced to that of solving a singular integral equation of the first kind which is solved numerically by the use of the way proposed by Erdogan, Gupta and Cook[1]. The singular stresses are expressed in closed form and the influence of transverse isotropy upon the stresses is clarified numerically for some practical materials.     

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.     

Viscous oscillations in a circular cylinder with an elastic cover on the free surface

The effects of an elastic membrane on the viscous oscillations of liquid filling a circular cylindrical container are studied by using the natural viscous complex eigenfunctions of the problem. The free surface of the liquid is assumed to be fully covered by the membrane. By projecting the governing equations onto an appropriate basis, a nonlinear eigenvalue problem for the complex frequencies is obtained. This is then solved to obtain the modal frequencies as a function of the Reynolds number Re, the tension parameter τ, the mass parameter ζ and the liquid depth h. The zero velocity conditions on both the side and bottom walls are satisfied unlike in earlier studies where either only the sidewall or only the bottom wall conditions were met. Results are presented for the four lowest non-axisymmetric modes as a function of Re, h, τ and ζ. The elastic cover increases the slosh frequencies but only in comparison with an uncovered free surface with a contact line that is free to move; the frequencies are lower when compared with those of a free surface with pinned contact line. There are ranges of Re, h, τ and ζ for which the oscillations are overdamped and the sloshing is aperiodic. Though the frequencies and damping rates decrease for an increasing mass of the elastic cover, there exist ranges of Re, h and τ for which the heavier cover produces higher slosh frequencies.     

速度剪切流中圆柱体绕流特性的数值模拟

采用由速度梯度、圆柱半径以及圆柱中心平面上的来流平均速度定义的无量纲剪切参数β来描述速度剪切的强度。在雷诺数Re=60-1000范围内,运用三维直接数值模拟(DNS)和大涡模拟(LES)两种方法对速度剪切流中的圆柱体的绕流特性进行了数值模拟。研究了驻点、高速和低速两侧分离点、圆柱表面压力分布以及不稳定尾流结构随剪切参数的变化及其对雷诺数的依赖性,从而得到了剪切流中圆柱体的气动力以及脱落特性,并对其机理进行了详细探讨。