Basic Equations for Wave Propagation in Turbulence

1994 ◽  
pp. 19-46 ◽  
Author(s):  
Richard J. Sasiela
Keyword(s):  
Wave Propagation ◽  
Basic Equations

Radial Propagation of Axial Shear Waves in a Finitely Deformed Elastic Solid

1974 ◽  
Vol 41 (1) ◽  
pp. 83-88 ◽  
Author(s):  
M. Kurashige
Keyword(s):  
Wave Propagation ◽  
Method Of Characteristics ◽  
Shear Waves ◽  
Elastic Solid ◽  
Radial Deformation ◽  
Numerical Examples ◽  
Axial Shear ◽  
Cylindrical Bore ◽  
Basic Equations ◽  
Radial Propagation

A study is made of the radial propagation of axial shear waves in an incompressible elastic solid under finite radial deformation. Basic equations are derived on the basis of Biot’s mechanics of incremental deformations, and analysis is made by the method of characteristics. Numerical examples are given by specializing the initial deformation to two cases: (a) an infinite solid with a cylindrical bore is inflated by all-around tension, and (b) a cuboid is rounded into a ring and its ends are bonded to each other. The influence of the inhomogeneities of such deformations upon the laws of shear wave propagation is presented in the form of curves.

scholarly journals Energy Spectrum for Gravitational Waves

2020 ◽  
pp. 24-31
Author(s):  
W. F. Chagas- Filho
Keyword(s):  
General Relativity ◽  
Wave Propagation ◽  
Quantum Mechanics ◽  
Gravitational Field ◽  
Loop Quantum Gravity ◽  
Canonical Quantization ◽  
Minimum Length ◽  
Speed Of Light ◽  
Basic Equations ◽  
Area And Volume

Loop Quantum Gravity (LQG) is a formalism for describing the quantum mechanics of the gravitational field based on the canonical quantization of General Relativity (GR). The most important result of LQG is that geometric quantities such as area and volume are not arbitrary but are quantized in terms of a minimum length. In this paper we investigate the possibility of combining the notion of a minimum length with the basic equations that describe wave propagation. We find that the minimum length, combined with the constancy of the speed of light, induces a natural spectrum for the energy of a gravitational wave.

Vibro-Acoustics Characteristics of Non-Uniform Ring Stiffened Cylindrical Shells Using Wave Propagation Approach

2013 ◽  
Vol 655-657 ◽  
pp. 562-567 ◽  
Author(s):  
Bing Ru Li ◽  
Yue Peng Jiang ◽  
Xuan Yin Wang ◽  
Hui Liang Ge
Keyword(s):  
Wave Propagation ◽  
Cylindrical Shells ◽  
Stiffened Cylindrical Shell ◽  
Various Boundary Conditions ◽  
Structural Loss ◽  
Basic Equations ◽  
Vibration And Sound Radiation ◽  
Uniform Ring ◽  
Thin Shell Theory ◽  
Stiffened Cylindrical Shells

Based on Donnell’s thin shell theory and basic equations, the wave propagation method is discussed here in detail, which is used to investigate the vibration and sound radiation characteristics of non-uniform ring stiffened cylindrical shells under various boundary conditions. The structure damp effects of cylindrical shells are investigated and the ring ribs were considered very narrow, and the rib forces are considered in radial direction. The conclusion are drawn that with the structural loss factor changing large, the whole pressure level are changed little, but the peak of resonance are slacking down obviously; The shell’s resonance frequency can be changed with irregular ring stiffened cylindrical shell .The work will give some guidelines for noise reduction of this kind of shell.

Wave Propagation in an Unbounded Magneto-Thermoelastic Rotating Medium Permeated by a Heat Source

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Nilanjana Gangopadhyaya ◽  
Abhijit Lahiri ◽  
Pulak Patra ◽  
Surath Roy
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Heat Source ◽  
Generalized Thermoelasticity ◽  
Thermoelastic Wave ◽  
Rotating Medium ◽  
Unbounded Medium ◽  
Method Of Solution ◽  
Linear Differential ◽  
Basic Equations

Abstract Matrix method of solution is applied to determine generalized thermoelastic wave propagation in an unbounded medium due to periodically varying heat source under the influence of magnetic field. Green–Lindsay (GL) model of generalized thermoelasticity for finite wave propagation is considered along with a magnetic field for a rotating medium with uniform velocity. Basic equations are solved by eigenvalue approach method after compiling in a form of vector–matrix linear differential equation in Laplace transform domain. Finally inverting the perturbed magnetic field and other field variables by a suitable numerical method, the results are analyzed by depicting several graphs in space–time domain.

BASIC EQUATIONS FOR SYNTHETIC SEISMOGRAMS USING THE z‐TRANSFORM APPROACH

Geophysics ◽  
1968 ◽  
Vol 33 (3) ◽  
pp. 521-523 ◽  
Author(s):  
Enders A. Robinson
Keyword(s):  
Wave Propagation ◽  
Seismic Wave ◽  
Present Note ◽  
Layered Media ◽  
Seismic Wave Propagation ◽  
Synthetic Seismograms ◽  
The Past ◽  
Basic Equations ◽  
Fundamental Equations

In the past few years several papers have been published on the z‐transform approach to the problem of seismic wave propagation in layered media. Although these papers start with the same fundamental equations, small differences in notation make the study of the synthetic seismograms derived in these papers time consuming. In order to aid the reader, the present note gives the basic equations as well as tables which show the correspondence for the main symbols used in the papers of Goupillaud (1961), Kunetz (1964) Sherwood and Trorey (1965), Treitel and Robinson (1966), Robinson (1967), and Claerbout (1968).

A NON-LINEAR THERMOELASTIC SOLID WITH UNIAXIAL WAVE PROPAGATION

1993 ◽  
Vol 17 (2) ◽  
pp. 229-242 ◽  
Author(s):  
M.C. Singh ◽  
D.V.D. Tran
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Initial Conditions ◽  
Constitutive Relations ◽  
Graphical Form ◽  
Simple Waves ◽  
Thermoelastic Solid ◽  
Basic Equations ◽  
Gibb’S Free Energy ◽  
Fundamental Equations

This study is devoted to an examination of wave motion in nonlinear thermoelastic solids. For this purpose, a new materially nonlinear constitutive relation for thermoelastic solids has been developed. The development makes use of the principles of continuum thermomechanics and takes into account Gibb’s free energy. On the basis of the nonlinear constitutive relations so developed the fundamental equations of wave propagation for a nonlinear thermoelastic uniaxial solid have been constructed. These are further simplified for a nonconducting nonlinear uniaxial material. The initial conditions and boundary conditions are stated. The jump conditions for simple waves and shock waves in such a material are derived. Shock amplitude relation has been obtained on the basis of kinematic compatibility relations. Solution of the system of basic equations, with boundary conditions, initial conditions and jump and shock conditions at the wave front has been obtained by the method of characteristics and a combination of finite difference and finite element methods. Numerical results are presented in graphical form for uniaxial waves.

Propagation Characteristics of Ultrasonic Waves in Concrete Medium with Local Damage

2011 ◽  
Vol 255-260 ◽  
pp. 561-568
Author(s):  
Yuan Cao Guo ◽  
Shao Hua Guo
Keyword(s):  
Wave Propagation ◽  
Inverse Analysis ◽  
Propagation Characteristic ◽  
Ultrasonic Waves ◽  
Local Damage ◽  
Propagation Characteristics ◽  
Ultrasonic Wave Propagation ◽  
Basic Solutions ◽  
Basic Equations ◽  
Elastic Dynamics

The theory of ultrasonic wave propagation characteristic in damaged concrete media was studied in this paper. Basing on the fundamentals of classical elastic dynamics and the model of damaged mechanics,the basic equations of elastic wave propagation in damaged media are established and the example analysis and a numerical calculation are displayed. The basic solutions of the equations is deducted. Because the damage exists in the construction, the concrete’s wave response comprised of the shape,the amplitude and the propagated time of the ultrasonic waves in the structure will change obviously. The transformation mentioned above is provided for further study of inverse analysis and nondestructive test of the structure.

Electron Microscopy of Shock Loaded Polycrystalline Beryllium

1974 ◽  
Vol 32 ◽  
pp. 506-507 ◽  
Author(s):  
J. M. Galbraith ◽  
L. E. Murr ◽  
A. L. Stevens
Keyword(s):  
Electron Microscopy ◽  
Wave Propagation ◽  
Structural Change ◽  
Single Crystal ◽  
Diffraction Pattern ◽  
Shock Loading ◽  
Slip Systems ◽  
Compression Tests ◽  
X Ray Diffraction ◽  
X Ray

Uniaxial compression tests and hydrostatic tests at pressures up to 27 kbars have been performed to determine operating slip systems in single crystal and polycrystal1ine beryllium. A recent study has been made of wave propagation in single crystal beryllium by shock loading to selectively activate various slip systems, and this has been followed by a study of wave propagation and spallation in textured, polycrystal1ine beryllium. An alteration in the X-ray diffraction pattern has been noted after shock loading, but this alteration has not yet been correlated with any structural change occurring during shock loading of polycrystal1ine beryllium.This study is being conducted in an effort to characterize the effects of shock loading on textured, polycrystal1ine beryllium. Samples were fabricated from a billet of Kawecki-Berylco hot pressed HP-10 beryllium.

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