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.

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).

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.

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.

scholarly journals SLFAT: Client-Side Evil Twin Detection Approach Based on Arrival Time of Special Length Frames

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Qian Lu ◽  
Haipeng Qu ◽  
Yuzhan Ouyang ◽  
Jiahui Zhang
Keyword(s):  
Arrival Time ◽  
Access Point ◽  
Local Area ◽  
Security Threats ◽  
Wireless Devices ◽  
High Detection Rate ◽  
Malicious Adversary ◽  
Detection Approach ◽  
Client Side ◽  
Very High

In general, the IEEE 802.11 network identifiers used by wireless access points (APs) can be easily spoofed. Accordingly, a malicious adversary is able to clone the identity information of a legitimate AP (LAP) to launch evil twin attacks (ETAs). The evil twin is a class of rogue access point (RAP) that masquerades as a LAP and allures Wi-Fi victims’ traffic. It enables an attacker with little effort and expenditure to eavesdrop or manipulate wireless communications. Due to the characteristics of strong concealment, high confusion, great harmfulness, and easy implementation, the ETA has become one of the most severe security threats in Wireless Local Area Networks (WLANs). Here, we propose a novel client-side approach, Speical Length Frames Arrival Time (SLFAT), to detect the ETA, which utilizes the same gateway as the LAP. By monitoring the traffic emitted by target APs at a detection node, SLFAT extracts the arrival time of the special frames with the same length to determine the evil twin’s forwarding behavior. SLFAT is passive, lightweight, efficient, hard to be escaped. It allows users to independently detect ETA on ordinary wireless devices. Through implementation and evaluation in our study, SLFAT achieves a very high detection rate in distinguishing evil twins from LAPs.

On Stress-Focusing Effect in a Uniformly Heated Solid Sphere

2003 ◽  
Vol 70 (2) ◽  
pp. 304-309 ◽  
Author(s):  
H. J. Ding ◽  
H. M. Wang ◽  
W. Q. Chen
Keyword(s):  
Temperature Rise ◽  
Stress Responses ◽  
Constant Pressure ◽  
Integral Transform ◽  
External Surface ◽  
Separation Of Variables ◽  
Solid Sphere ◽  
Uniform Temperature ◽  
Focusing Effect ◽  
Isotropic Solid

By using the separation of variables technique, the dynamic thermal stress responses in an isotropic solid sphere subjected to uniform temperature rise all over the sphere and a sudden constant pressure at the external surface are performed successfully. The analytical solutions of the radial and hoop dynamic stresses at the center are also obtained. By means of the present method, integral transform can be avoided. Numerical results denote that a very high dynamic stress peak appears periodically at the center of the isotropic solid sphere subjected to uniform temperature rise all over the sphere and a sudden constant pressure at the external surface.

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.

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