Reconsideration of the Stress-Focusing Effect in a Uniformly Heated Solid Cylinder

1994 ◽  
Vol 61 (3) ◽  
pp. 676-680 ◽  
Author(s):  
T. Hata
Keyword(s):  
Free Surface ◽  
Infinite Series ◽  
Stress Waves ◽  
Ray Theory ◽  
Solid Cylinder ◽  
Reflected Waves ◽  
Focusing Effect ◽  
Ray Path ◽  
Very High ◽  
Constant Period

The stress-focusing effect is the phenomenon that, under an instantaneous heating, stress waves reflected from the free surface of the cylinder result in very high stresses at the center. Ho solved the problem by using Laplace transform on time and presented the solution as infinite series summations, which converge very slowly for certain combinations of time and the radius of a cylinder. However, adopting a concept of the ray theory, the solution of stress waves in the cylinder is sorted out into rays according to the ray path of multiply reflected waves. The results expressed in an infinite series reveal that stresses peak out periodically at a constant period and the order of singularity of the stresses in a cylinder is O(ρ−2).

Stress-Focusing Effect in a Uniformly Heated Solid Sphere

1991 ◽  
Vol 58 (1) ◽  
pp. 58-63 ◽  
Author(s):  
Toshiaki Hata
Keyword(s):  
Arrival Time ◽  
Solid Sphere ◽  
Stress Waves ◽  
Ray Theory ◽  
Reflected Waves ◽  
Focusing Effect ◽  
Inverse Transform ◽  
Ray Path ◽  
Very High ◽  
Constant Period

The ray theory is applied to the stress-focusing effects in a uniformly heated solid sphere. The stress-focusing effect is the phenomenon that, under an instantaneous heating, stress waves reflected from the free surface of the sphere result in very high stresses at the center. Using the ray theory, the Laplace transformed solution of stress waves in the sphere is sorted out into rays according to the ray path of multiply-reflected waves. Inverse transform of each ray gives rise to the exact solution of the transient response up to the arrival time of the next ray. The numerical results reveal that stresses peak out periodically at a constant period and, unlike the case of cylinder, the radial stress at the center of the sphere is bounded.

Stress-Focusing Effect in a Uniformly Heated Cylindrical Rod

1976 ◽  
Vol 43 (3) ◽  
pp. 464-468 ◽  
Author(s):  
Chih-Horng Ho
Keyword(s):  
Cross Section ◽  
Temperature Rise ◽  
Dynamic Stress ◽  
Peak Stress ◽  
Stress Waves ◽  
Uniform Temperature ◽  
Focusing Effect ◽  
Tension And Compression ◽  
Very High ◽  
Heating Duration

A long cylindrical rod is considered brought suddenly to a uniform temperature rise over its cross section. Stress-focusing effects occur when stress waves reflect from the outer surface of the rod and proceed radially inward to the axis. The focusing effect can cause a very high peak dynamic stress in both tension and compression in the rod. The magnitude of the peak stress depends upon the magnitude of the temperature rise and the effective heating duration. For instantaneous heating, the infinite peak of stress propagates outward from the center while these peaks are finite for nonzero heating duration. The solutions are carried out by using Laplace transform on time and presented as infinite series summations after the end of heating.

Determination of Transient Responses of a Thick-Walled Spherical Shell by the Ray Theory

1978 ◽  
Vol 45 (1) ◽  
pp. 114-122 ◽  
Author(s):  
Yih-Hsing Pao ◽  
Ahmet N. Ceranoglu
Keyword(s):  
Spherical Shell ◽  
Arrival Time ◽  
Applied Pressure ◽  
Ray Theory ◽  
Multiple Reflections ◽  
Transient Responses ◽  
Reflected Waves ◽  
Ray Path ◽  
The Waves

The dynamic response of a thick-walled elastic spherical shell subject to radially symmetric loadings is studied by applying the theory of rays. The Fourier transformed solution of the waves in the shell is sorted out into rays by following the ray-path of the multiply reflected waves at both surfaces. Inverse transform of each ray, which is obtainable in closed form, gives rise to the exact solution of the transient response up to the arrival time of the next ray. Numerical results are shown for internally applied pressure with a step or a square-time function. The radial stresses are found to be critically large in tension due to multiple reflections at both surfaces of a thick shell.

The role of stress waves reflected from the free surface in rock breaking by blasting

1978 ◽  
Vol 14 (2) ◽  
pp. 165-168 ◽  
Author(s):  
N. E. Trufakin ◽  
V. D. Belyakov
Keyword(s):  
Free Surface ◽  
Rock Breaking ◽  
Stress Waves

The Fresnel volume and transmitted waves

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 653-663 ◽  
Author(s):  
Jesper Spetzler ◽  
Roel Snieder
Keyword(s):  
Wave Equation ◽  
Fresnel Zone ◽  
Wave Theory ◽  
Three Dimensions ◽  
Ray Theory ◽  
Finite Frequency ◽  
Frequency Wave ◽  
Reflected Waves ◽  
Band Limited ◽  
Propagation Of Waves

In seismic imaging experiments, it is common to use a geometric ray theory that is an asymptotic solution of the wave equation in the high‐frequency limit. Consequently, it is assumed that waves propagate along infinitely narrow lines through space, called rays, that join the source and receiver. In reality, recorded waves have a finite‐frequency content. The band limitation of waves implies that the propagation of waves is extended to a finite volume of space around the geometrical ray path. This volume is called the Fresnel volume. In this tutorial, we introduce the physics of the Fresnel volume and we present a solution of the wave equation that accounts for the band limitation of waves. The finite‐frequency wave theory specifies sensitivity kernels that linearly relate the traveltime and amplitude of band‐limited transmitted and reflected waves to slowness variations in the earth. The Fresnel zone and the finite‐frequency sensitivity kernels are closely connected through the concept of constructive interference of waves. The finite‐frequency wave theory leads to the counterintuitive result that a pointlike velocity perturbation placed on the geometric ray in three dimensions does not cause a perturbation of the phase of the wavefield. Also, it turns out that Fermat's theorem in the context of geometric ray theory is a special case of the finite‐frequency wave theory in the limit of infinite frequency. Last, we address the misconception that the width of the Fresnel volume limits the resolution in imaging experiments.

Added Moment of Inertia of Rolling Ship Sections

1982 ◽  
Vol 26 (02) ◽  
pp. 89-93
Author(s):  
P. P. Hsu ◽  
L. Landweber
Keyword(s):  
Free Surface ◽  
Infinite Series ◽  
Laurent Series ◽  
Low Frequency ◽  
Moment Of Inertia ◽  
Section Area ◽  
Family Of Curves ◽  
Section Rolling ◽  
The Given ◽  
Two Parameter

An expression for the added moment of inertia of a ship section rolling at low frequency at a free surface, in terms of the coefficients of the Laurent series of the function which maps the given section into a circle, has been derived. The method is applied to the two-parameter family of Lewis forms and the results are presented as a family of curves which gives the coefficient of the added moment of inertia as a function of the thickness ratio and the section-area coefficient of a form. A second application is to a square section, for which the Laurent expansion is an infinite series.

Near and Far-Field Evaluations of the Free-Surface Multipole Potential

1989 ◽  
Vol 33 (01) ◽  
pp. 10-15
Author(s):  
Stuart B. Cohen
Keyword(s):  
Free Surface ◽  
Integral Representation ◽  
Infinite Series ◽  
Digital Computer ◽  
Velocity Potential ◽  
Series Representation ◽  
Rapid Evaluation ◽  
Far Field ◽  
Small Field ◽  
Significant Figures

The general mth-order, free-surface, multipole velocity potential is considered and found suitable for arrays of spherical devices requiring interactions between the devices. Expansions into an infinite series representation and an integral representation with finite limits are shown. These expressions can be evaluated by digital computer to any degree of accuracy and are formulated for especially rapid evaluation in certain regions: the series representation for small field distances, and the integral representation for large distances. Tables of the potentials and their Cartesian and radial derivatives are given to eight significant figures. Illustrations of multipoles between m = 0 and m = 4 are shown.

Finsler geometry of seismic ray path in anisotropic media

2009 ◽  
Vol 465 (2106) ◽  
pp. 1763-1777 ◽  
Author(s):  
Takahiro Yajima ◽  
Hiroyuki Nagahama
Keyword(s):  
Euclidean Geometry ◽  
Fractal Structure ◽  
Finsler Geometry ◽  
Roughness Parameter ◽  
Anisotropic Media ◽  
Convex Curve ◽  
Ray Theory ◽  
Fractal Curve ◽  
Non Euclidean Geometry ◽  
Ray Path

The seismic ray theory in anisotropic inhomogeneous media is studied based on non-Euclidean geometry called Finsler geometry. For a two-dimensional ray path, the seismic wavefront in anisotropic media can be geometrically expressed by Finslerian parameters. By using elasticity constants of a real rock, the Finslerian parameters are estimated from a wavefront propagating in the rock. As a result, the anisotropic parameters indicate that the shape of wavefront is expressed not by a circle but by a convex curve called a superellipse. This deviation from the circle as an isotropic wavefront can be characterized by a roughness of wavefront. The roughness parameter of the real rock shows that the shape of the wavefront is expressed by a fractal curve. From an orthogonality of the wavefront and the ray, the seismic wavefront in anisotropic media relates to a fractal structure of the ray path.

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