Oblate Spheroidal Cavity Research Articles

Surface-enhanced Raman scattering from metal films containing dielectric cavities

The electromagnetic field mechanism is applied to Raman scattering by molecules embedded in small cavities within metal films. Very strong enhancements, due to excitation of dipolar surface plasmons, may be obtained for appropriately oriented oblate spheroidal cavities, as has been suggested in connection with experiments with coldly deposited Ag films.

Natural frequencies of circular disks

The natural frequencies or the singularity expansion method (SEM) poles are computed for circular disks. We treat the acoustically soft disk, i.e, the Dirichlet boundary condition, and the perfectly conducting disk. The poles are found by an application of the T -matrix method by searching the zeros of a determinant. The poles associated with the first values of the azimuthal index m are shown in both cases, and numerical values are given in tables and figures. The internal resonances are also computed for the thin oblate spheroidal cavity and comparisons are made with the thin circular cylindrical cavity.

Nondestructive evaluation of subsurface flaws

Ultrasonic NDE is a convenient tool for detecting subsurface flaws in structural parts since the eddy currents technique is unsuitable when the flaw is more than a millimeter below the surface. Further, in most applications it is not possible to make measurements by bonding the transducer directly to the part to be tested due to difficult geometry. In this paper we propose an analytical method to study the scattering of waves from a subsurface flaw in an elastic half‐space that interferes a fluid half‐space (i.e., the part to be tested is immersed in water). The numerical results so obtained will be compared with experimental results for subsurface oblate spheroidal (flat cracks) cavities and the results will be critically analyzed to obtain information about the size and depth of the flaw.

Stresses in a Semi-Infinite Elastic Body Containing an Oblate Spheroidal Cavity or an Internal Penny-Shaped Crack Subjected to an Axisymmetric Pressure

偏平回転だ円体状空かあるいは円形き裂面に軸対称圧力を受ける半無限体の問題を三次元弾性論に基づいて厳密に解析した.解析においてはBoussinesqの応力関数に偏平回転だ円体調和関数および円柱調和関数を与え,両者を互いに座標変換して半無限体表面ならびに空か面の境界条件を同時に満足させた.さらに特別の場合として円形き裂の問題を扱った.そして空か周辺の応力分布および応力集中係数,応力拡大係数を求めた.

Axisymmetric Thermal Stresses in a Thick Plate Having an Oblate Spheroidal Cavity

Axisymmetric Thermal Stresses in a Thick Plate Having an Oblate Spheroidal Cavity

Stresses in an Elastic Thick Plate Having an Oblate Spheroidal Cavity or an Internal Penny-Shaped Crack Subjected to an Axisymmetric Internal Pressure

Stresses in an Elastic Thick Plate Having an Oblate Spheroidal Cavity or an Internal Penny-Shaped Crack Subjected to an Axisymmetric Internal Pressure

Stress analysis of a penny-shaped crack locted between two oblate spheroidal cavities in an infinite solid

The problem of a penny-shaped crack located between two oblate spheroidal cavities in an infinite solid subjected to uniaxial loads is considered. Using transformations between harmonic functions in cylindrical coordinates and those in oblate spheroidal ones, the problem is reduced to non-homogeneous linear equations. The obtained equations are solved numerically and the stress intensity factors at the penny-shaped crack tip under the influence of the two oblate spheroidal cavities are shown graphically.

Stresses in an Elastic Circular Cylinder with an Oblate Spheroidal Cavity or an Internal Penny-Shaped Crack under Torsion

偏平回転だ円体状空かあるいは円形き裂を有する円柱がねじりモーメントを受ける問題を, 三次元弾性論に基づいて厳密に解析した. 解析においては Dougall の応力関数に偏平回転だ円体調和関数および円柱調和関数を与え, 両者を互いに座標変換して円柱側面ならびに空か面の境界条件を同時に満足させた. さらに特別の場合として円形き裂の問題を扱った. そして空かあるいはき裂周辺の応力分布および応力集中係数, 応力拡大係数を求めた.

Stresses in an Elastic Circular Cylinder with an Oblate Spheroidal Cavity or an Internal Penny-shaped Crack Under Tension

This paper contains an exact solution for the stresses arising in an elastic circular cylinder with an oblate spheroidal cavity or an internal penny-shaped crack under tension. The solution is represented by a combination of the solution which is regular in the outside of a cavity and the solution which is regular in an infinite circular cylinder, and is deduced with the aid of Dougall's stress functions. Two sets of harmonic stress functions are given by simple expressions referred to the cylindrical and oblate spheroidal coordinates. The boundary conditions on the surfaces of the cylinder and of the cavity are satisfied by using the relations between the cylindrical and oblate spheroidal harmonics. And the solution for the internal penny-shaped crack is given for a limiting case of the solution for the oblate spheroidal cavity. Numerical results for stress distributions, stress concentration factors and stress intensity factors are shown graphically.

Scattering matrix for elastic waves. III. Application to spheroids

Using the scattering matrix approach to elastic wave scattering, numerical results are presented for the scattering of P and S waves from prolate and oblate spheroidal cavities and inclusions embedded in an elastic solid for a wide range of wavelengths. The incident waves are plane harmonic waves incident obliquely to the axis of revolution of the spheroid.

Stresses in an Elastic Circular Cylinder with an Oblate Spheroidal Cavity or an Internal Penny-Shaped Crack under Tension

Stresses in an Elastic Circular Cylinder with an Oblate Spheroidal Cavity or an Internal Penny-Shaped Crack under Tension

A simple approximation for the stress concentration factor at the equator of an oblate spheroidal cavity

A simple approximation for the stress concentration factor at the equator of an oblate spheroidal cavity

Torsional Waves in an Infinite Elastic Solid Containing a Spheroidal Cavity

A low-frequency analysis is presented here for the axisymmetric problem of diffraction of torsional waves by an oblate spheroidal cavity in an isotropic homogeneous elastic medium. The method used gives a complete low-frequency expansion of the scattered field in terms of associated Legendre functions, instead of spheroidal wave functions that one gets by the method of separation of variables. This makes the numerical computation much simpler. Graphs and tables are presented for the displacement distribution on the cavity surface and the nonzero shear stress at the end of the major axis of the spheroid. It is found that for low frequencies and for the values of the ratio (b/a) of the minor and major axes of the spheroid considered here the absolute value of the ratio of the nonzero dynamic and static shear stress evaluated at the end of the major axis is independent of b/a for confocal spheroids. An estimate is also given for the radius of convergence of the low-frequency expansion.

The collapse time of a closed cavity

The collapse time of a closed cavity that is initially at rest in an incompressible, inviscid fluid of density ρ and ambient pressurep∞has the form\[ t_1 = \{\rho/(p_{\infty} - p_c)\}^{\frac{1}{2}}\ell, \]wherepcis the internal pressure, which is assumed to remain constant during collapse, and [ell ] is a length that depends only on the geometry of the cavity. A variational formulation of the dynamical problem is constructed from Jacobi's statement of the principle of least action. A single-degree-of-freedom approximation is developed from the similarity hypothesis that the cavity collapses through a family of similar surfaces with volume as the generalized co-ordinate. Two-degree-of-freedom approximations are given for both prolate and oblate spheroidal cavities and are used to obtain error estimates for the similarity approximation (approximately 2% for the limiting case of a needle-like, prolate spheroid and approximately ½ % for a disk-like, oblate spheroid). A perturbation analysis is developed for an approximately spherical cavity, which is found to have the same collapse time as a spherical cavity of equal volume within a factor 1 +O(e4), whereeis a representative eccentricity. A first-order correction for surface tension is obtained.

Modes in Spherical-Mirror Resonators

This work is the examination of a cavity mode approach to the mode structure of a laser. Solutions of the vector wave equation for electromagnetic fields in and between perfectly conducting oblate spheroidal cavities are examined for the case of wavelengths much less than cavity dimensions. These solutions are the field modes in Fabry—Perot type resonators with equal-radius concave spherical mirrors, or with concave—convex spherical mirrors, when the parameters of the oblate spheroids are chosen so that the radii of curvature and spacing on the axis of rotation match those of the resonator mirrors. Expressions for the transverse and longitudinal mode structures are derived. The eigenvalue equations are written, and are solved for the case of the two lowest-order modes.

On the motion of a liquid in a spheroidal cavity of a precessing rigid body. II

AbstractIt is supposed that a viscous incompressible fluid is contained in an oblate spheroidal cavity (major axes a, eccentricity e) in a rigid body, and that, up to time t = 0, both fluid and container rotate together with angular velocity ω about the minor axis LB of the spheroid, which is fixed in space. At t = 0, the axis of rotation is moved impulsively, and is given a motion of precession (angular velocity Ω) about an axis LS fixed in space, which makes an angle α with LB. It is required to find the ultimate state of motion of the fluid relative to the container. In a previous paper (Stewartson and Roberts (4)), this problem was solved for arbitrary α under the assumptions thatwhere v is the kinematic viscosity. In the present paper, it is shown how the problem may be solved for arbitrary e (including zero) under the assumptions that

Electric stresses in gaseous cavities in solid dieletrics

Gaseous cavities of two simple geometrical shapes are considered: (a) an elliptic cylindrical cavity with the minor axis of its elliptic cross-section parallel to the field, and (b) an oblate spheroidal cavity with its axis parallel to the field. Circular cylindrical and spherical cavities are treated as special cases.When a cavity of each of these forms is located in an infinite dielectric, which is subjected to an electric stress that is uniform at very large distances from the cavity, the electric stress in the cavity is also uniform, and the relation between the two stresses is well known. When, however, the dielectric is contained between two infinite plane parallel electrodes whose distance apart is not great compared with the dimensions of the cavity, the electric stress in the cavity is no longer uniform, and the problem does not yet appear to have been rigorously studied.In the paper, the electric stresses existing at points on the minor and major axes of the cross-section of the elliptic cylindrical cavity and on the axis and radius of the oblate spheroidal cavity have been calculated, in both alternating- and direct-voltage conditions, in terms of the stress in the solid dielectric, using a technique devised by Rayleigh for solving the Laplace equation. It is shown that the electric stress is greatest in the elliptic cylindrical cavity at the extremities of the major axis and in the oblate spheroidal cavity around its periphery. Formulas for the mean electric stress along the minor axis of the elliptic cylindrical cavity and the axis of the oblate spheroidal cavity are also derived.

Electric stresses at conducting surfaces located in the field between plane parallel electrodes

In the preceding paper, electric stresses in elliptic cylindrical and oblate spheroidal gaseous cavities located in a dielectric contained between infinite plane parallel electrodes were calculated, using a technique devised by Rayleigh for solving the Laplace equation. The same methods give the maximum electric stresses at conducting surfaces of similar geometrical shapes located in the field between plane parallel electrodes, only very slight modifications to the equations developed previously being necessary. The formulas that have been derived in the present paper can be applied to calculate, for example, the maximum stress between successive turns of a long conducting helical coil subjected to a uniform voltage gradient and the maximum stress at the surface of the ellipsoid in an ellipsoidal voltmeter.