Wave propagation theory

Wave propagation in an inhomogeneous anisotropic material such as a fiber-reinforced composite material is a very complex subject. However, its study is motivated by many important applications such as the use of fiber-reinforced composites in reentry vehicle nosetips, heatshields, and other protective systems. Chou [6-56] gives an introduction to analysis of wave propagation in composite materials. Others have applied wave propagation theory to shell stress problems. 

A. Kienle, Low-order dynamic models for ideal multicomponent distillation processes using nonlinear wave propagation theory. Chem. 

A. Combustion Wave Propagation Theory in Gasless Systems 120... 

The basic principle of SHPB experiment is the stress wave propagation theory in elastic slender bar, which is based on two basic assumptions that one is one-dimensional assumption (also known as plane assumption) and other is uniform stress assumption. The one-dimensional assumption considered that each cross section in elastic bars always keeps the plane state in the propagation process of the stress wave in the slender bar. Uniform stress assumption assumed that the stress... 

The basis for the flow pattern is the wave propagation theory as known with light waves or flow waves in physics (Figure 2.23). While in simple models the flow... 

FIGURE 2.23 Basis for the flow pattern method the wave propagation theory... 

For mechanical wave measurements, notice should be taken of the advances in technology. It is particularly notable that the major advances in materials description have not resulted so much from improved resolution in measurement of displacement and/or time, but in direct measurements of the derivative functions of acceleration, stress rate, and density rate as called for in the theory of structured wave propagation. Future developments, such as can be anticipated with piezoelectric polymers, in which direct measurements are made of rate-of-change of stress or particle velocity should lead to the observation of recognized mechanical effects in more detail, and perhaps the identification of new mechanical phenomena. 

More recently Equation Of Motion (EOM) methods have been used in connection with other types of wave functions, most notably coupled cluster.Such EOM methods are closely related to propagator methods, and give working equations which are similar to those encountered in propagator theory. 

The theories of elastic and viscoelastic materials can be obtained as particular cases of the theory of materials with memory. This theory enables the description of many important mechanical phenomena, such as elastic instability and phenomena accompanying wave propagation. The applicability of the methods of the third approach is, on the other hand, limited to linear problems. It does not seem likely that further generalization to nonlinear problems is possible within the framework of the assumptions of this approach. The results obtained concern problems of linear viscoelasticity. 

Solids 12, 59 - 65 (1964) "A Generalized Theory of Strain- Rate- Dependent Plastic Wave Propagation in Bars 86) M. Lutzky, "The Flow Field Behind a Spherical Detonation in TNT, Using the Landau- Stanyukovich Equation, USNOL-White Oak, NOLTR 64-40 Dec 1964)... 

H. Papas, Theory of Electromagnetic Wave Propagation, Dover, New York, 1988. 

A more tractable approach to shock wave propagation in water is that of Kirkwood and coworkers. For details of this rather involved analysis, the reader is referred to Ref 1, pp 29—33 and 104—106. The basic assumptions of this theory are that behind the shock front the entropy is constant, ie, ds=0, and that the conversion of the expl to its products occurs at constant volume. With these assumptions, it is then possible to get approximate analytical solutions of the equation of motion in terms of the enthalpy of the system... 

Thomas (T13), 1940 Theory of wave propagation in steep channels. Experimental work on wave profiles in channel in which the wetted wall was moved upwards to keep wave profile stationary. Surface tension effects neglected. 

The pancake theory today is perceived by mathematicians as a chapter contributed by Ya.B. to the general mathematical theory of singularities, bifurcations and catastrophes which may be applied not only to the theory of large-scale structure formation of the Universe, but also to optics, the general theory of wave propagation, variational calculus, the theory of partial differential equations, differential geometry, topology, and other areas of mathematics. 

Let us consider the propagation of a detonation wave in a tube, taking account of heat transfer and braking against the side walls of the tube. We will restrict ourselves to the one-dimensional theory in which heat transfer and drag are uniformly distributed over the entire cross-section of the tube. We denote by x the coordinate measured from the detonation wave front toward the unreacted gas, in the direction of wave propagation. It is in fact on this coordinate alone in the steady and one-dimensional theory that all the following quantities depend ... 

Theoretical analysis of gas detonation leads to the conclusion that a shock wave propagates at the detonation front, compressing and heating the gas mixture. The chemical reaction runs in the already compressed gas, and it is only after completion of the reaction that the state of the explosion products calculated in the classical theory is attained (pressure pc, velocity wc, temperature Tc). In particular, in the wave front the velocity w1 and the pressure p1 of the compressed gas are approximately twice as large as in the reaction products w1 2wc, p1 2pc. The amount of the compressed gas at the pressure px and the thickness of this layer are proportional to the chemical reaction time, r. 

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