Behavior Of Acceleration Waves Research Articles

МОДЕЛИРОВАНИЕ РАСПРОСТРАНЕНИЯ УПРУГИХ ВОЛН В ТРЕХКОМПОНЕНТНОЙ СРЕДЕ ПРИ ФОРМИРОВАНИИ КОМПОЗИТНОГО ПОКРЫТИЯ ПЛАЗМЕННЫМ НАПЫЛЕНИЕМ

In a three-component medium, when it is de-formed, acceleration waves propagate longitudi-nally on the wave surface. In this paper, the be-havior of acceleration waves and their influence on the quality of the propagation medium during the formation of composite coatings during plasma spraying were investigated. A flowchart has been compiled to create a software product that promotes theoretical studies of wave pro-cesses in a three-component environment.

Asymptotic solution of a non-linear wave motion in an electron plasma

The theory of high-frequency waves has been used to calculate first and second-order asymptotic solutions for the propagation of non-linear waves in a cylindrical symmetric flow of an electron plasma. The behaviour of acceleration waves and weak shock waves has been analysed through these solutions and Whitham's rule for a weak shock wave on any wavelet has been confirmed through the first-order solution. The appearance of a weak shock wave on any wavelet has been determined and its strength, the location, and the speed of propagation have been found from the asymptotic solution presented in this paper. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.

Growth and Decay of Acceleration Waves in Incompressible Saturated Poroelastic Solids

AbstractIn the present paper the evolution of the amplitudes of acceleration waves in incompressible saturated poroelastic solids within the framework of the geometrically linear theory is examined. The incompressible porous media model by Bowen is adopted to describe the mechanical behaviour of an incompressible two‐phase system. The underlying assumption made is that the amplitudes do not change tangentially to the wave fronts. The differential equations governing the amplitudes of acceleration waves are derived and the explicit solutions are obtained. The results indicate that the amplitudes of acceleration waves may either decay to vanish or grow to infinity in finite time, which depends on the geometrical property of the initial shapes of the wave fronts and the diffusion effect between the two phases. In particular, the longitudinal acceleration waves in the liquid are completely carried by the solid skeleton. The behaviour of acceleration waves in the porous medium is similar to that in isotropic elastic non‐porous solids.

The behavior of acceleration waves in radiation magnetogasdynamic flow

The method of characteristics is used to study the propagation of acceleration waves in a radiation magnetogasdynamic flow, which is induced by the motion of a piston advancing with a finite acceleration into a constant state of rest. The analysis assumes an azimuthal magnetic field produced by a constant current flowing along the axis. The characteristic solutions have been obtained in the neighborhood of leading forward characteristics. The critical values of the initial amplitude and critical time for breakdown of an acceleration wave at the cusp of the envelope of intersecting forward characteristics have been obtained. It has been shown that the effect of coupling of the radiation and the magnetic field on compression waves, which are emanating from piston movement, is to slow down the motion of a breakdown point, and thus to increase the cylindrical shock formation time, while the effect on expansion waves is to enhance the decay rate.

Propagation of mechanical and temperature acceleration waves in thermoelastic materials

The behaviour of acceleration waves in the nonlinear theory of thermoelasticity of Green and Lindsay [1] is investigated systematically. It is shown that two coupled waves may propagate with different finite wavespeeds. For waves entering isothermal homogeneously strained regions, explicit results are obtained for the wavespeeds and wave amplitudes, and the possibility of shock-wave formation is discussed.

On the Behavior of Acceleration Waves in Elastic Dielectrics With Internal State Variables

On the Behavior of Acceleration Waves in Elastic Dielectrics With Internal State Variables

Acceleration waves in a mixture of chemically reacting materials with memory

In this paper we consider a mixture of chemically reacting materials with memory. After stating the constitutive assumptions we adopt the usual postulate of fading memory and determine the restrictions which the Second Law of Thermodynamics places on the response functions. Subsequently, we examine the behavior of acceleration waves propagating in such a mixture which is initially in a state of thermochemical equilibrium. We also distinguish between the cases when the equilibrium state is weak or strong, and determine their effects on the wave behavior.

Acceleration Wave Propagation in a Nonlinear Viscoelastic Solid

In this study the growth and decay of one-dimensional acceleration waves in nonlinear viscoelastic solids are considered. The conditions governing the growth and decay, including the concept of a critical acceleration level derived by Coleman and Gurtin, are discussed in terms of certain relevant material functions. It is shown that these material functions can be determined from the results of experimental shock wave-propagation studies. The experimental methods used to generate and observe acceleration waves in solids are discussed and applied to the propagation of acceleration waves in the polymer, polymethyl methacrylate (PMMA). It was found that the conditions derived by Coleman and Gurtin accurately predict the experimentally observed behavior of acceleration waves in PMMA.

Propagation of acceleration waves in a binary nonreacting mixture

In this work, the behavior of acceleration waves in a two-constituent mixture is examined. This examination is based on a purely mechanical theory that does not consider reactions. Each of the constituents is assumed to behave in a quasielastic manner, and no restriction is placed on the amplitude of the waves.

On the Behavior of Acceleration Waves in Deformed Elastic Nonconductors

In this paper, we consider one-dimensional acceleration waves propagating in an elastic nonconductor of heat which is at rest in a nonhomogeneous configuration. We show that there exists a number called the critical initial amplitude which either vanishes or is finite depending on the nature of the strain field just ahead of the waves and the material properties, and that under various physically reasonable circumstances the behavior of the waves can be quite different.

On the local and global behavior of acceleration waves: Addendum, asymptotic behavior

On the local and global behavior of acceleration waves: Addendum, asymptotic behavior

On the local and global behavior of acceleration waves

where t denotes the time. Formula (1.1) is the well-known Bernoulli equation. In general, the coefficients/~ and fl are functions of t. A careful examination of these coefficients reveals that there are two common features. Briefly, (1) the coefficient # depends on the material under consideration and the consequences of the physical assumptions introduced regarding the conditions of the material ahead of the waves, (2) the coefficient fl depends on the elastic response of the material alone. In other words, the coefficient # depends on whether we are considering acceleration waves propagating in, e.g., materials with memory, elastic nonconductors of heat, or inhomogeneous elastic materials, and whether we assume that the material regions ahead of the waves are at rest in homogeneous configurations, in mechanical equilibrium, or in dynamic equilibrium. On the other hand, the coefficient fl depends on the instantaneous elastic response of materials with memory, the isentropic elastic response of elastic non-conductors of heat, or the local elastic response of inhomogeneous elastic materials. In this paper, we shall show that knowing the sign of fl(t) not only allows us to determine the local behavior of amplitudes f rom (1.1) but it also tells us a great deal about their global behavior. Some of our conclusions on the global behavior would not be expected f rom the local behavior alone.