Response of an Elastic Cylindrical Shell to a Transverse, Step Shock Wave

1953 ◽  
Vol 20 (2) ◽  
pp. 189-195
Author(s):  
R. D. Mindlin ◽  
H. H. Bleich
Keyword(s):  
Shock Wave ◽  
Cylindrical Shell ◽  
Wave Front ◽  
Plane Shock Wave ◽  
Elastic Response ◽  
Acoustic Medium ◽  
Elastic Cylindrical Shell ◽  
Plane Shock ◽  
Mathematical Solution ◽  
Long Cylindrical Shell

Abstract A plane shock wave in an acoustic medium encounters a long cylindrical shell whose axis is parallel to the wave front. An approximate mathematical solution is obtained for the elastic response of the shell.

scholarly journals The air pressure on a cone moving at high speeds.—I

1933 ◽  
Vol 139 (838) ◽  
pp. 278-297 ◽  
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Wave Front ◽  
Abrupt Change ◽  
The Body ◽  
Plane Shock Wave ◽  
Plane Shock ◽  
High Speeds ◽  
Air Stream ◽  
Continuous Field

When a body moves through air at a uniform speed greater than that of sound, a shock wave is formed which remains fixed relative to the body. This wave is situated on a surface where a very abrupt change in density and velocity occurs. It can be seen as a sharp line in photographs of bullets in flight. In front of this surface the air is stationary, behind it there is a continuous field of fluid flow which may contain further shock waves. The nature of these shock waves is well known and the equations which govern their propagation were first obtained by Rankine. The work of Rankine, however, seems to have escaped the notice of subsequent writers and it was not till some years later that they were rediscovered by Hugoniot to whom they are usually attributed. Rankine’s equations give the relationship between the conditions in front and behind a plane shock wave. They connect the ratio of the density in front and behind the wave with the components of velocity normal to the wave. They have been applied by Meyer to find the flow in the neighbourhood of an inclined plane or wedge moving at high speeds. Meyer begins with a plane shock wave reduced to rest by giving the whole field a suitable velocity perpendicular to its plane. He then gives the whole field a velocity parallel to the wave front. The system is then a steady one, the shock wave remaining at rest, but the direction of motion of the air, which is now oblique to the wave, suffers an abrupt change at the wave front. By combining two such shock waves intersecting at a point, but not continuing beyond the intersection, a system can be devised in which all the air on one side of the pair of waves is moving with a uniform velocity. The air which passes through one wave is deflected, say, upwards, while that which passes through the other is deflected downwards. This system can evidently be bounded by a solid wedge, the faces of which are parallel to the two parts of the deflected air stream.

Formation of a plane shock-wave front in rods

2009 ◽  
Vol 29 (8) ◽  
pp. 775-777
Author(s):  
D. I. Chernyavskii ◽  
D. D. Chernyavskaya
Keyword(s):  
Shock Wave ◽  
Wave Front ◽  
Shock Wave Front ◽  
Plane Shock Wave ◽  
Plane Shock

The reflection of a plane shock wave over a double wedge

1987 ◽  
Vol 176 (-1) ◽  
pp. 483 ◽  
Author(s):  
G. Ben-Dor ◽  
J. M. Dewey ◽  
K. Takayama
Keyword(s):  
Shock Wave ◽  
Plane Shock Wave ◽  
Plane Shock ◽  
Double Wedge

scholarly journals Elastic Response of Acoustic Coating on Fluid-Loaded Rib-Stiffened Cylindrical Shells

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Christopher Gilles Doherty ◽  
Steve C. Southward ◽  
Andrew J. Hull
Keyword(s):  
Cylindrical Shell ◽  
Cylindrical Shells ◽  
Coupled System ◽  
Elastic Response ◽  
System Response ◽  
Elastic Cylindrical Shell ◽  
Fluid Environment ◽  
Reinforcing Ribs ◽  
Double Index ◽  
Stress Boundary Conditions

Reinforced cylindrical shells are used in numerous industries; common examples include undersea vehicles, aircraft, and industrial piping. Current models typically incorporate approximation theories to determine shell behavior, which are limited by both thickness and frequency. In addition, many applications feature coatings on the shell interior or exterior that normally have thicknesses which must also be considered. To increase the fidelity of such systems, this work develops an analytic model of an elastic cylindrical shell featuring periodically spaced ring stiffeners with a coating applied to the outer surface. There is an external fluid environment. Beginning with the equations of elasticity for a solid, spatial-domain displacement field solutions are developed incorporating unknown wave propagation coefficients. These fields are used to determine stresses at the boundaries of the shell and coating, which are then coupled with stresses from the stiffeners and fluid. The stress boundary conditions contain double-index infinite summations, which are decoupled, truncated, and recombined into a global matrix equation. The solution to this global equation results in the displacement responses of the system as well as the exterior scattered pressure field. An incident acoustic wave excitation is considered. Thin-shell reference models are used for validation, and the predicted system response to an example simulation is examined. It is shown that the reinforcing ribs and coating add significant complexity to the overall cylindrical shell model; however, the proposed approach enables the study of structural and acoustic responses of the coupled system.

Moment solution of comprehensive kinetic model for plane shock wave problem

Shock Waves ◽  
2005 ◽  
pp. 1217-1222
Author(s):  
R. Nagai ◽  
K. Maeno ◽  
H. Honma ◽  
A. Sakurai
Keyword(s):  
Shock Wave ◽  
Kinetic Model ◽  
Plane Shock Wave ◽  
Plane Shock ◽  
Wave Problem

Experimental Investigation of Non-Equilibrium Temperatures in a Plane Shock Wave

1995 ◽  
pp. 289-292
Author(s):  
Yury V. Romanenko ◽  
Oleg P. Shatalov ◽  
Igor E. Zabelinsky
Keyword(s):  
Shock Wave ◽  
Experimental Investigation ◽  
Plane Shock Wave ◽  
Plane Shock ◽  
Non Equilibrium
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