Neck propagation as a shock wave

Neck propagation in the stretching of elastic solid filaments having a yield point was analyzed using the space one-dimensional thin filament governing equations developed previously by the authors and other researchers. Constitutive model for the filament was assumed to be expressible as engineering tensile stress(X) (tensile force) given as a function of elongational strain with the(X) curve having a yield point maxima followed by a minima and a breaking point greater than the yield point maxima. Also incorporated into the model is the hysteresis of irreversible plastic deformation. When inertia is taken into consideration, the thin filament equations were found to reduce to the nonlinear wave equation ² (X)/ ² =C ₁ ² X/ ² where is Lagrangean space coordinate, is time, andC ₁ is inertia coefficient. The above nonlinear wave equation yields a solutionX(, ) having a stepwise discontinuity inX which propagates along the axis. The zero speed limit of the step wave solution was found to describe the above neck propagation occurring in solid filaments. Furthermore, it was recognized that the nonlinear wave equation was known for many years to also govern the plastic shock wave which propagates axially within a metal rod subjected to a very strong impact on its end. The one-dimensional atmospheric shock wave also was known to be governed by the nonlinear wave equation upon making certain simplifying assumptions. The above and other evidences lead to the conclusion that neck propagation occurring in the extension of solid filament obeying the above(X) function can be formally described as a shock wave.     

Fatigue-crack propagation in metals

Cyclic-tension tests between constant limits of stress-intensity factor and at constant speed have been conducted on aluminum alloy RR 58 and mild steel BS 15. The resulting crack propagation was monitored against the number of cycles. The results, together with those obtained by other workers on similar metals, have been examined in the light of linear elastic fracture-mechanics concepts and two simple crack-propagation laws assessed. A typical linear relationship between crack length and number of cycles was observed, the relationship between crack growth and stress intensity was found to exhibit three separate regions and a law based on mean levels of the stress intensity found to adequately describe the results. There was evidence of a threshold value of stress intensity below which fatigue cracks may not grow.     

Quasi-kinematic flood wave propagation

Summary In the flood waves of natural streams, the plot of discharge versus simultaneous water level values at a river station usually show a little shift from the socalled steady rating curve. In other terms, natural flood waves normally have small loops and may be considered to be quasi-kinematic. Very often, on the basis of the steady rating curve and of the observed hydrograph at an upstream gage station, we can quickly and easily forecast the values and time of flood peaks at one or more downstream channel sections. This article describes a set of very simple formulas first to check whether the flood wave may be considered to be quasi-kinematic, and then to estimate the speed and the attenuation with which it moves downstream. For a number of prismatic channels, the results were compared with those obtained with equally simple, currently used formulas (Jones, Henderson) and with the exact solutions. The comparisons showed that the formulas proposed in this article are more general and accurate than the other known simple formulas and that, for flood loops of less than 10%, give results that are very near to being exact.

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Sommario Nei fenomeni di piena dei corsi d'acqua naturali la successions nel tempo dei valori di portata e livello idrometrico in una sezione d'alveo presenta, nella gran parte dei casi, modesti scostamenti dalla cosiddetta scala di deflusso di moto permanente: in altri termini normalmente le onde naturali di piena hanno cappi modesti e possono ritenersi quasi cinematiche. Molto spesso, data una stazione di monte in cui sia nota la scala di deflusso el'drogrammadei livelli, occorre prevedere semplicemente e rapidamente i valori e gli istanti dei colmi di portata e livello in una o più sezioni a valle. In questo articolo vengono presentate formule molto semplici per verificare dapprima che l'onda di piena possa ritenersi quasi cinematica, e stimare quindi la velocità e l'attenuazione con cui i colmi si propagano verso valle. I confronti fatti, per alcuni alvei cilindrici, con la soluzione esatta e con i risultati ottenibili con formule altrettanto semplici e di uso corrente (Jones, Henderson), mostrano che le formule proposte sono più generali e corrette di queste ultime, e danno risultati quasi esatti finchè i cappi di piena relativi sono inferiori al 10%.

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List of symbols P(x, z) steady rating curve - Q volumetric rate of discharge - q=Q-P flood loop - g gravitational acceleration - I water surface slope - c=dP/dA kinematic wave velocity - y water depth - p, s time and space steps - x, t channel distance starting upstream; time - z water surface height above datum - A, B channel cross section area and surface width - F=B Q ²/gA ³ Froude number - L,L ₀,L ₁,L ₂,L ₃ characteristic lengths of the channel - T=L/c characteristic time of the channel - f _x =f/x, f _f =f/t etc for the partial derivatives - Df/Dt,Df/Dx for the derivatives of functionf following the discharge peak     

非均匀吸收介质中地震波的广义传播矩阵解法

本文在复频域内,通过应用混合变量粘弹性波方程和线性常微分方程组的指数矩阵解法,给出了一种计算非均匀吸收介质中地震波传播的广义传播矩阵解法。该方法适用于各种粘弹性模型,可模拟任意震源及所产生的各种体波、面波,数值结果表明具有很高的计算精度。     

Ultrasound propagation in cancellous bone

Wave propagation in fluid-saturated cancellous bone is studied on the basis of two approaches: The thermodynamic-consistent Theory of Porous Media (TPM) and Biot’s theory. Phase velocities in the low-frequency range, calculated with the Biot-Gassmann relations, Wyllie’s equation and the TPM, are demonstrating that a simple, so-called hybrid biphasic TPM model is able to capture the main acoustical effects in cancellous bones. Furthermore, an extension towards high-frequency wave propagation is discussed on the basis of the constitutive relations for the momentum exchange of the fluid and the solid phases. Further numerical results show that, in the high-frequency (ultrasound) range a viscous correction as well as an added mass effect (tortuosity) needs to be taken into account to explain experimentally obtained results.     

激波的传播与干扰

激波的传播特性既取决于激波的产生条件,也与所处的传播环境密切相关。驱动条件、几何边界、介质的物理化学属性等发生变化时,都会引起激波传播特性的改变,而激波的变化反过来又会对其波及的流场产生影响。尽管激波传播及其干扰现象广泛存在于自然界和人类科技活动之中,其复杂机理的认识、规律的描述乃至应用潜力的挖掘仍有漫长的路要走。本文根据气体中激波传播和干扰现象以及与之相关的理论描述特征,在对激波传播以及反射、折射等基本现象进行简要阐述的基础上,重点围绕目前的热点问题,包括激波/激波干扰、激波/边界层干扰、激波与湍流作用、激波的聚焦与点火以及激波作用下气体界面不稳定性等研究进行了介绍和讨论,旨在对近年来该领域的进展及获得的成果做一个概述和归纳,期望对将来的深入研究有一个鉴借意义。     

Wave propagation in earth-ionosphere waveguide

Summary In this paper, wave propagation in a stratified medium which consists of earth, atmosphere and ionosphere, is studied. The ionosphere is described by a compressible plasma model where the earth magnetic field is neglected. The earth is considered as a highly conducting medium. The modal solutions due to the excitation of a vertical dipole have been obtained, where characteristic waves are analytically discussed and numerically determined.This work was supported by National Aeronautics and Space Administration under Grant NSG-395.     

Shock wave propagation and interactions

激波的传播特性既取决于激波的产生条件,也与所处的传播环境密切相关.驱动条件、几何边界、介质的物理化学属性等发生变化时,都会引起激波传播特性的改变,而激波的变化反过来又会对其波及的流场产生影响.尽管激波传播及其干扰现象广泛存在于自然界和人类科技活动之中,其复杂机理的认识、规律的描述乃至应用潜力的挖掘仍有漫长的路要走.本文根据气体中激波传播和干扰现象以及与之相关的理论描述特征,在对激波传播以及反射、折射等基本现象进行简要阐述的基础上,重点围绕目前的热点问题,包括激波/激波干扰、激波/边界层干扰、激波与湍流作用、激波的聚焦与点火以及激波作用下气体界面不稳定性等研究进行了介绍和讨论,旨在对近年来该领域的进展及获得的成果做一个概述和归纳,期望对将来的深入研究有一个鉴借意义.     

An analysis of brittle-fracture propagation

Brittle-fracture propagation tests were carried out to find relations among the speed of crack propagation, the dynamic-stress distribution, the test temperature and the applied stress. These tests were performed at low temperatures so that the behavior of the crack propagation was fully elastic. The test results were compared with the theoretical calculations and some considerations were made on the surface plastic work.     

坑道内化爆冲击波的传播规律

装药在坑道内部爆炸时将产生沿坑道传播的空气冲击波,由于受到坑道洞壁的限制,空气冲击波在坑道内的传播规律异于在自由大气中的传播。利用三维数值模拟计算程序,对长坑道中的化爆流场进行了数值计算,归纳出空气冲击波沿坑道方向的传播规律。计算结果与试验结果符合较好。     

Wave propagation in elastic shells

The problem of wave propagation in shells within the framework of a simplified linear shell theory is treated using the method of Hadamard. Speeds of propagation, wave shape and decay, as well as coupling effects, are obtained for longitudinal, transverse and bending waves. The theory is applied to wave propagation on a spherical shell.

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Résumé On traite la problème de la propagation des ondes dans les voiles minces en utilisant la méthode de Hadamard. Les vitesses de la propagation, la forme de l'onde, et aussi les effets d'accouplement sont obtenus pour les onides longitudinales, transversales et fléchissantes. On applique cette théorie à la propagation des ondes dans une coque sphérique.

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This work was supported in part by funds from the National Research Council of Canada, under Grant Number A 3805.     

Wave propagation in elastic membranes

The problem of wave propagation in linear elastic membranes is treated using the method of Hadamard. Speeds of propagation, wave shape and decay, as well as coupling effects, are obtained for longitudinal and transverse waves. Examples are considered which illustrate the features of the theory.

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Résumé On traite la problème de la propagation des ondes dans une membrane lineare et elastique, utilisant la mèthode de Hadamard. Les vitesses de la propagation, la forme del'onde, et les effets d'accouplement sont obtenus en cas des ondes longitudinales et transversales. Les exemples sont presentés qui demontrent les points essentiales de la theorie.

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This work was supported in part by funds from the National Research Council of Canada, under grant number A3805.     

Wave propagation in elastic plates

The problem of wave propagation within the framework of a complete linear theory of elastic plates is treated using the method of wave curves. A complete classification of the various extensional and bending waves is obtained, along with the corresponding speeds of propagation. These are shown to correspond to the phase velocities of harmonic waves for infinite wave number. The decay and coupling equations are found, and the problem of waves due to a punch applied to the plate surface is treated.

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Résumé On a étudié le problème de la propagation des ondes en utilisant la méthode des courbes ondiales et assumant la théorie linéaire et complète des plaques minces. On obtient une classification totale des ondes diverses, de l'extension et de la flexion, avec des vitesses de la propagation. On prouve aussi, que celles-ci correspondent avec des vitesses des phases de la propagation, en cas de nombre infinite des ondes. Les équations de la décadence et de l'accouplement sont derivées, et on a étudié le problème d'une onde, qui est produite par une emporte-pièce appliquée sur la surface d'une plaque.

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This work was supported in part by funds from the National Research Council of Canada, under Grant Number A3805.