On the torsional vibration of a finite circular cylinder of non-homogeneous material by a particular type of twist on one of the plane ends

Summary In this paper the torsional vibration of a finite circular cylinder of non-homogeneous material whose rigidity and density vary linearly with the depth has been considered. One end of the cylinder is fixed while a periodic shearing force acts along the circumference of a circle on the other end.     

On the vibratory motion of a non-homogeneous cylinder having a periodic shearing force prescribed on the plane end

Summary In this paper the torsional vibrations of a semi-infinite circular cylinder of nonhomogeneous material, when there is a periodic shearing force prescribed on the plane end, has been discussed.     

Torsional vibration of a solid finite cylinder having transverse isotropy

Summary Stress and displacement components in a solid circular cylinder of transversely isotropic material under the torsional vibration set up by an impulsive twist applied at one and while the other end remains fixed, have been obtained by the application of Laplace transformation.     

Torsional vibration of a composite truncated conical bar

Summary Torsional vibration of a body composed of two conical bars, the upper one being made of non-homogeneous material and the lower of a homogeneous material, by the application of a shearing stress on the upper end has been considered in the problem. It is assumed that the lower end of the composite body is fixed and the lateral surface is free from shearing stress.     

On forced torsional oscillation of a cylindrical shell of non-homogeneous material by the application of a periodic shearing force at one end

Summary In the present note the author has considered the torsional vibration of a cylindrical shell of non-homogeneous material whose rigidity and density vary linearly with distance from the axis of the shell. It is assumed that one end of the shell is fixed while the other end is acted on by a periodic shearing force, both the inner and the outer curved surface being free from stress at all times.     

Exact solution of the source problem for a finite threedimensional source

Summary In this note the surface displacement for an elastic half-space due to a finite cylindrical source has been calculated in exact terms. The source consists of outward body forces acting on the surface of the right circular cylinder, one end of which is parallel to the free surface of the half-space.     

On twisting of a non-homogeneous circular disk,due to a tangential traction of the boundary of a concentric circular hole

Summary In this note, the stresses and displacements due to tangential traction on the inner boundary of a nonhomogeneous annular circular disk, the outer boundary of the disk being kept fixed have been investigated. Some numerical results are given at the end.     

Thermoelastic response of a cylinder in the generalised dynamical theory of thermoelasticity

Summary Using the generalised dynamical theory of thermoelasticity, thermoelastic problem for an isotropic infinite circular cylinder has been solved by approximate techniques. A two dimensional harmonic problem for a cylinder has also been considered and small amplitude vibrations of the circular cylinder have been studied further.     

Dynamic thermoelastic response of a cylinder

Pure and Applied Geophysics - In this paper, dynamic thermoelastic response of an infinite solid circular cylinder has been studied when the surface of the cylinder is kept at zero temperature...     

On the transition from the laminar to disordered flow in a precessing spherical-like cylinder

We investigate, through both asymptotic analysis and direct numerical simulation, precessionally driven flow of a homogeneous fluid confined in a fluid-filled circular cylinder that rotates rapidly about its symmetry axis and precesses about a different axis that is fixed in space. A particular emphasis is placed on a spherical-like cylinder whose diameter is nearly the same as its length. At this special aspect ratio, the strongest direct resonance occurs between the spatially simplest inertial mode and the precessional Poincaré forcing. An asymptotic analytical solution in closed form describing weakly precessing flow is derived in the mantle frame of reference for asymptotically small Ekman numbers. We also construct a nonlinear three-dimensional finite element model – which is validated against both the asymptotic solution and a constructed exact solution – for elucidating the nonlinear transition leading to disordered flow in the precessing spherical-like cylinder. Properties of both weakly and strongly precessing flows are investigated with the aid of a complete inertial-mode decomposition of the fully nonlinear solution. Despite a large effort being made, the well-known triadic resonance is not found in the precessing spherical-like cylinder. The energy contained in the precessionally forced inertial mode is primarily transferred, through nonlinear effects in the viscous boundary layers, to the geostrophic flow that becomes predominant when the precessional Poincaré force is sufficiently large. It is found that the nonlinear flow evolutes gradually and progressively from the laminar to disordered as the precessional force increases.     

绕流对称性破缺诱发柔细结构振动研究——以Tacoma大桥风振致毁事故为例

绕流对称性破缺往往对柔细结构产生很大的作用效应,诱发结构振动,严重影响其可靠性和安全性。基于圆柱平面绕流模型,系统分析了实际流体圆柱绕流纵向对称性破缺以及各种情况的横向对称性破缺现象。为了更加深入地理解理论分析的结果,利用Fluent软件对圆柱绕流模型进行了计算机模拟,详细分析了雷诺数为10、20、40、100、200、2000、20000时的绕流情况,结果显示,当雷诺数为200时,流场开始出现横向对称性破缺。在此基础上,以Tacoma大桥风振致毁事故为例,分情况探讨了旋涡同步交替脱落导致的桥面起伏性振动,以及旋涡异步交替脱落导致的桥面扭振。分析结果表明,绕流对称性破缺是诱发大桥振动破坏的直接原因。     

一种新的实时电磁逆散射方法

为解决介质圆柱体逆散射问题,提出一种新的在线逆散射方法,通过支持向量机将逆散射问题转化成一个回归估计问题. 该方法可应用于各种逆散射方面, 尤其是目标的几何与电磁参数重构和埋地目标探测. 文中首次将支持向量机方法应用到该领域,设置多个散射场的观测点,通过提取散射场的不同信息作为样本信息训练支持向量机, 建立了介质圆柱体的逆散射模型, 利用该模型重构了介质圆柱体的电磁参数,同时探测了埋地位置. 数值结果显示了该方法的有效性和准确性,为目标的实时逆散射研究提供了一种有效方法.     

The evaluation ofHeuman's Lambda function and its application to calculate the gravitational effect of a right circular cylinder

Summary A computational scheme has been derived to generateHeuman's Lambda function. This has been applied to compute the gravitational attraction of a right vertical circular cylinder. Test computations show that the error introduced by assuming a semifinite cylinder in place of a finite one of depth 30 times its radius is 1.77%.     

The gravitational attraction of a right vertical circular cylinder at points external to it

Summary In this paper a general and exact expression of the gravitational attraction of a right vertical circular cylinder at points external to it is developed. This expression is derived in terms of complete elliptic integrals of the first and second kind and the Neumann's Lambda function. Since the solution involves only tabulated functions, it is well suited for rapid desk calculations with any degree of accuracy at any points, including the points in the plane of the cylinder (outcroping cylinder). For this case, the corresponding master curve is given. Finally, a relation between the abscissa of the inflexion point of the g curve and the depth of the cylinder is established.     

Some problems of rotation and equilibrium of transversely isotropic elastic bodies

Summary The present discussion is concerned with the rotation of a few problems of aeolotropic elastic solids. The symmetry of the material considered in the discussion is transverse-isotropy. The problems solved are: (i) rotation of a circular cylinder with axle-hole, (ii) rotation of a circular disc with axle-hole, (iii) a cylindrical tube under external and internal pressures. Complete cylinder and complete disc are the particular cases of the above.     

The instability of precessing flow

Abstract

An explanation is put forward for the instability observed within a precessing, rotating spheroidal container. The constant vorticity solution for the flow suggested by Poincaré is found to be inertially unstable through the parametric coupling of two inertial waves by the underlying constant strain field. Such resonant couplings are due either to the elliptical or shearing strains present which elliptically distort the circular streamlines and shear their centres respectively. For the precessing Earth's outer core, the shearing of the streamlines and the ensuing shearing instability are the dominant features. The instability of some exact, linear solutions for finite precessional rates is established and used to corroborate the asymptotic analysis. A complementary unbounded analysis of a precessing, rotating fluid is also presented and used to deduce a likely upperbound on the growth rate of a small disturbance. Connection is made with past experimental studies.     

Quasilinear infiltration from an elliptical cavity

We develop analytic solutions to the linearized steady-state Richards equation for head and total flowrate due to an elliptic cylinder cavity with a specified pressure head boundary condition. They are generalizations of the circular cylinder cavity solutions of Philip [Philip JR. Steady infiltration from circular cylindrical cavities. Soil Sci Soc Am J 1984;48:270–8]. The circular and strip sources are limiting cases of the elliptical cylinder solution, derived for both horizontally- and vertically-aligned ellipses. We give approximate rational polynomial expressions for total flowrate from an elliptical cylinder over a range of sizes and shapes. The exact elliptical solution is in terms of Mathieu functions, which themselves are generalizations of and computed from trigonometric and Bessel functions. The required Mathieu functions are computed from a matrix eigenvector problem, a modern approach that is straightforward to implement using available linear algebra libraries. Although less efficient and potentially less accurate than the iterative continued fraction approach, the matrix approach is simpler to understand and implement and is valid over a wider parameter range.     

Analysis of magnetic anomalies due to some two-dimensional bodies using the Mellin transform

An interpretation technique using the Mellin transform is suggested for the analysis of magnetic anomalies due to some two-dimensional structures namely (i) a vertical sheet of both finite and infinite depth extent, (ii) a thick dyke and (iii) a horizontal circular cylinder. The Mellin transformed magnetic anomalies resemble gamma functions which are amenable to an easy interpretation. This procedure is illustrated with a small number of synthetic examples in each case. The practicality of the method is exemplified with the well-known vertical magnetic anomalies of Kursk (USSR) in the case of an infinite sheet model and Karimnagar magnetic anomaly (India) in the case of a horizontal circular cylinder. The results are compared with the techniques already available and found to be reliable.     

Disturbance produced in a semi-infinite anisotropic elastic medium by an impulsive twist applied on the plane surface

Summary In this paper the displacement due to an impulsive twist produced by impulsive shearing stresses acting on a finite circular area on the plane surface of a semi-infinite solid of homogeneous anisotropic material has been found.Paper presented by Dr. A. K. Mitra of Jadavpur University.     

Elastic waves from a circular disc source

Summary Elastic waves radiated by a finite circular disc source are compared for two models by treating it as the limit of an explosion inside a cavity in the form of a circular cylinder of small height or an oblate spheroid of small minor axis.Now on leave at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England (Priv. Address: 19 Marlowe Road, Cambridge, England).