Scattering of a Plane Longitudinal Wave by a Spherical Obstacle in an Isotropically Elastic Solid

1956 ◽  
Vol 27 (9) ◽  
pp. 1086-1097 ◽  
Author(s):  
C. F. Ying ◽  
Rohn Truell
Keyword(s):  
Longitudinal Wave ◽  
Elastic Solid ◽  
Plane Longitudinal Wave

Longitudinal wave propagation in an infinite isotropic elastic plate with a penny-shaped crack

1969 ◽  
Vol 66 (2) ◽  
pp. 439-442
Author(s):  
H. S. Paul
Keyword(s):  
Longitudinal Wave ◽  
Elastic Plate ◽  
Mixed Boundary ◽  
Elastic Solid ◽  
Vertical Displacement ◽  
Dual Integral Equation ◽  
Positive Direction ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Plane Longitudinal Wave

The stress distribution, subject to a constant pressure over the entire surface of a penny-shaped crack is discussed by Sneddon(4). Recently, Robertson (3) has considered the diffraction of a plane longitudinal wave by a penny-shaped crack on a semi-infinite elastic solid. In the present analysis, the propagation of longitudinal wave in an infinite isotropic elastic plate with a penny-shaped crack in the middle has been investigated. The plane longitudinal wave is moving in the positive direction of z-azis and is impinging on the surface of the penny-shaped crack. The dual integral equation technique of Noble(l) is utilized to solve the mixed boundary-value problem. The analysis closely follows the method used in the author's previous paper (2). The vertical displacement is analysed numerically.

Diffraction of a plane longitudinal wave by a penny-shaped crack

1967 ◽  
Vol 63 (1) ◽  
pp. 229-238 ◽  
Author(s):  
Ian A. Robertson
Keyword(s):  
Longitudinal Wave ◽  
Constant Pressure ◽  
Elastic Solid ◽  
Entire Surface ◽  
Positive Direction ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Distribution Of Stress ◽  
Plane Longitudinal Wave

Introduction. The distribution of stress produced in the interior of an infinite elastic solid when a constant pressure is applied over the entire surface of a penny-shaped crack has been solved by Sneddon(6), (7). The problem considered here is the closely allied one of a plane longitudinal wave, harmonic in time, moving in the positive direction of the z-axis and impinging on the surface of a penny-shaped crack. The analysis follows the methods adopted for dealing with an axisymmetrical vibrating punch acting on a semi-infinite elastic solid, Robertson (5).

scholarly journals Propagation of Plane Waves in a Thermally Conducting Mixture

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Baljeet Singh
Keyword(s):  
Free Surface ◽  
Longitudinal Wave ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Elastic Solid ◽  
Reflection Coefficients ◽  
Governing Equations ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Thermally Conducting

The governing equations for generalized thermoelasticity of a mixture of an elastic solid and a Newtonian fluid are formulated in the context of Lord-Shulman and Green-Lindsay theories of generalized thermoelasticity. These equations are solved to show the existence of three coupled longitudinal waves and two coupled transverse waves, which are dispersive in nature. Reflection from a thermally insulated stress-free surface is considered for incidence of coupled longitudinal wave. The speeds and reflection coefficients of plane waves are computed numerically for a particular model.

Axisymmetric Scattering of a Plane Longitudinal Wave by a Circular Crack in a Transversely Isotropic Solid

1991 ◽  
Vol 58 (3) ◽  
pp. 695-702 ◽  
Author(s):  
T. Kundu ◽  
A. Bostro¨m
Keyword(s):  
Integral Equation ◽  
Longitudinal Wave ◽  
Legendre Polynomials ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Edge Condition ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Isotropic Solid ◽  
Plane Longitudinal Wave

The scattering of elastic waves by a circular crack situated in a transversely isotropic solid is studied here. The axis of material symmetry and the axis of the crack coincides. The incident wave is taken as a plane longitudinal wave propagating perpendicular to the crack surface. A Hankel transform representation of the scattered field is used, and after some manipulations using the boundary conditions this leads to an integral equation over the crack for the displacement jump across the crack. This jump is expanded in a series of Legendre polynomials which fulfill the correct edge condition and the integral equation is projected on the same set of Legendre polynomials. The far field is computed by the stationary phase method. A few numerical computations are carried out for both isotropic and anisotropic solids. Results for the isotropic solid compare favorably with those available in the literature.

Nonaxisymmetric Dynamic Response of Imperfectly Bonded Buried Fluid-Filled Orthotropic Cylindrical Shells

1996 ◽  
Vol 118 (1) ◽  
pp. 64-73 ◽  
Author(s):  
J. P. Dwivedi ◽  
V. P. Singh ◽  
P. C. Upadhyay
Keyword(s):  
Cylindrical Shell ◽  
Wave Propagation ◽  
Dynamic Response ◽  
Longitudinal Wave ◽  
Orthotropic Cylindrical Shell ◽  
Soil Conditions ◽  
Thick Shell ◽  
Fluid Density ◽  
Acoustic Equation ◽  
Plane Longitudinal Wave

This paper is concerned with the nonaxisymmetric dynamic response of an imperfectly bonded fluid-filled buried orthotropic cylindrical shell excited by a plane longitudinal wave. A thick shell model, including the effect of shear deformation and rotary inertia, has been taken. For the wave propagation in the fluid inside the pipe, linear acoustic equation has been used. The effects of fluid presence on the shell displacements have been studied for different soil conditions and at various angles of incidence of the longitudinal wave. The effects of bond imperfection on the shell response have been compared with the effects realized due to the presence of fluid inside the pipeline. Effects of changes in the fluid density are also discussed. It is found that magnitude of the response of fluid-filled pipeline can become even more than that of an empty pipeline (without fluid), and, hence, it cannot be assumed that a fluid-filled pipeline will always furnish safe and conservative response.

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