Propagation Of Plane Shock Waves Research Articles

Plane shock wave propagation in partially saturated soil

Considered that the gas content of partially saturated soil would decrease under a shock load, which would cause volumetric plastic deformation, Lyakhov's constitutive model is improved. The P-α state equation is used to describe the volume compression relationship of partially saturated soil. Numerical and experimental results are compared to validate the material model. The peak stress and duration of shock wave are crucial to study the dynamic response of underground structures. Considered the saturation of partially saturated soils under natural conditions increases with depth and both peak stress and duration change when shock waves propagate in inhomogeneous media, several partially saturated soil models with linearly decreasing air content in the depth direction are developed. The propagation law of shock waves with various peak stresses and durations in partially saturated soils is studied. The results show that the peak stress caused by the incident load in partially saturated soil first decreases and then increases under incident loads with a shorter duration, and it increases monotonically under incident loads with a longer duration. The rate of change in the incident peak stress is proportional to the air content at the top of the partially saturated soil. The peak free-field stress reaches its maximum, which is 2.2 to 5.5 times the peak stress of the incident load, in fully saturated soil. Long-duration incident loads such as nuclear explosions are more threatening to underground structures than short-duration incident loads. Underground structures buried in fully saturated soil or below fully saturated soil with higher air contents above are more at risk than underground structures buried in partially saturated soil with smaller air contents.

Underground pipeline reliability under longitudinal impact load

The paper presents the results of numerical solution obtained by the modified finite difference method according to the Wilkins scheme, to a two-dimensional unsteady-state problem of the plane shock wave propagation in an underground elastic pipeline, interacting with surrounding soil. Soil is considered to be an undeformable body moving relative to the pipeline at a given velocity. The value of the friction force depends on radial stress in the pipeline, determined by numerical solution to the problem. Changes in longitudinal and radial stresses over time and pipeline length, of velocity and displacements for fixed sections of the pipeline are obtained. Two times increase in values of longitudinal and radial stresses was detected in the case of active Coulomb friction at the pipeline-soil contact. The increase in stress values occurs due to the friction force acting in the direction of wave propagation. At significant values of the friction force on the outer surface of the pipeline, the hypothesis of flat sections is fulfilled for all its sections. This result justifies the consideration of similar problems of underground pipelines earthquake resistance in a one-dimensional statement. The results also make it possible to identify the mechanisms of the stress state formation in an underground pipeline interacting with soil, which can be used in seismic resistance calculation of underground trunk pipelines.

Propagation of Plane Shock Waves in a Liquid Containing Bubbles of a Conducting Gas

This paper considers the propagation of plane shock waves in a mixture of conducting gas and liquid by taking appropriate equations of continuity, momentum, energy and an equation of state. When the temperature rise, which is small for a very wide range of problems is neglected, across a shock, it is shown that teh shock wave relations assume a simple form. It is also suggested that the relations can be applied to the collision between two normal shock waves.

Ground Shock Resistance of Mechanically Stabilized Earth Walls

A simple analytical method has been developed that characterizes plane shock wave propagation through reinforced soil and the dynamic interaction between soil and retaining wall panels. The shock wave attributable to an explosion in the backfill was modeled as a velocity boundary condition at a standoff distance from the wall. The exact solution to this problem was obtained using the Laplace transform method. Full-scale explosive test data from 4.6-m-high and 24-m-wide reinforced soil walls were used to validate the analytical methodology. The accuracy of the analytical method has further been verified by finite-element analysis. The method is adequate for the response analysis of mechanically stabilized embankment walls under ground shock attributable to an explosion in the backfill.

Reply to ‘‘Comment on ‘Equation of state of aluminum nitride and its shock response’ ’’ [J. Appl. Phys. 78, 5854 (1995)

This reply reinforces the need for examining the internal consistency of longitudinal and lateral stress data under plane shock wave propagation. This was pointed out in an article by Dandekar, Abbate, and Frankel [J. Appl. Phys. 76, 4077 (1994)] to determine the shear strength of a solid. It also shows that shear strength of a crystalline solid under plane shock wave compression can be determined accurately from its reliable Hugoniot and applicable hydrodynamic compression of the solid.

Shear strength of solids and its effect on plane shock wave propagation

Shear strength of solids and its effect on plane shock wave propagation

Propagation of plane relativistic shock waves

Similarity solutions for propagation of plane shock waves in a relativistic gas, where the nucleon number density varies linearly as distance from its edge at near vacuum is obtained. The shock front moves with constant speed and the solutions are applicable only to an isothermal medium or cold gas.

Similarity solutions for plane relativistic flow in a homogeneous medium

Similarity solutions in closed forms for propagation of plane shock waves in a relativistic gas of uniform number density are obtained. The shock moves with constant speed.

Flash Radiographic Study of Shock Wave Propagation in Laminated Composites

The flash radiographic method has been used to study the propagation of plane shock waves in laminated composites consisting of alternate layers of PMMA and aluminium. Experiments were arranged so that the shock waves could propagate in the direction parallel to the laminations. The shock front in each PMMA plate was observed to be slightly curved because of the impedance mismatch between constituents. An abrupt change in the area ratio of constituents was also observed at the section of constituents where the shock front was passing by. The average Hugoniot data obtained for laminated composites have been compared with previous theoretical models.

Effect of Thermal Radiation on the Propagation of Plane Shock Waves

A study is made of the effect of thermal radiation on the propagation of plane shock waves produced by an infinite, plane and moving wall. Governing equations of one-dimensional, nonsteady and radiating gas flow are formulated, and solutions are found by using the perturbation technique and the method of characteristics. To display the essential features of the radiation effect a few cases, optically thick gas, optically thin gas, perfect absorbing wall, and perfect reflecting wall, are studied in detail. For the case of large time and a perfectly absorbing wall, the profiles of temperature, pressure, and density (or shock structure) resemble those of steady radiation-resisted shock waves. Application of these solutions to the shock tube problems is also discussed.

Diffraction of a Shock Wave by a Cylinder

The propagation of plane shock waves around cylinders of various radii was recorded with shadowgrams using a Cranz-Schardin multiple spark camera and with single Mach-Zehnder interferograms. The range of the incident shock Mach numbers extends from 1.04 to 2.2. Regular reflection and transition to Mach reflection are seen as the incident shock proceeds. From shadowgrams made at about 1 μsec intervals during this process the critical angle of transition was measured. The limiting angle of two shock theory fails to agree with the measured value. A theory of Whitham which requires the critical angle as well as the incident shock Mach number as initial values was applied to predict the triple point locus and the contour of the Mach stems. Numerical calculations using both the theoretical and the measured value of the critical angle for a fixed shock Mach number produced triple point loci lying close together. The predicted contour of the Mach stem and the density jump across it agree with the observations to within experimental error.

Shock waves in a liquid containing gas bubbles

Considerations of continuity, momentum and energy together with an equation of state are applied to the propagation of plane shock waves in a gas + liquid mixture. The shock-wave relations assume a particularly simple form when the temperature rise across a shock, which is shown to be small for a very wide range of conditions, is neglected. In particular, a simple relation emerges between the shock propagation speed and the pressure on the high-pressure side of the shock, the density of the liquid and the relative proportions, by mass and volume, of gas and liquid in the mixture. It is shown from entropy considerations that a rarefaction wave cannot propagate itself without change of form, and it is argued that a compression wave can be expected to steepen into a shock wave. Consideration of the collision between two normal shock waves, moving in opposite directions, suggests that the strengths of the two shocks are unaltered by the interaction between them. This implies, in particular, that, when a shock impinges normally on a plane wall, the pressure ratio across the reflected shock is equal to that across the incident shock. When the mass ratio of gas to liquid in the mixture is allowed to tend to infinity, the various shock-wave relations for a mixture, derived with the temperature rise across the shock neglected, assume the same limiting form as the corresponding relations for a perfect gas when the ratio of specific heats tends to unity. The theoretical discussion has been illustrated by experiments with a small gas + liquid mixture shock tube. Samples of the records, obtained when the passage of a shock changes the amount of light transmitted through the mixture to a photoelectric cell, illustrate the steepening of a compression wave and the flattening of a rarefaction wave. Measurements confirm the theoretical relation for the propagation speed of shock waves. Reasonably good experi­mental confirmation is also reported of the theoretical predictions for the pressure which arises following the normal impact of a shock wave on a plane wall.

On Shock-Wave Phenomena: Waterlike Substances

The properties of shock waves in waterlike substances are investigated in detail. A waterlike substance is defined as one for which the intrinsic energy is separable into a sum of two terms, one of which is a function of density only and the second a function of specific entropy. It is known that many substances, including water, behave in this fashion within a large range of pressure variation. The paper consists of six sections. Section I contains some introductory material. Section II consists of a derivation of the basic equations that govern the propagation of plane shock waves in a waterlike substance. Section III is an analysis of one-dimensional interaction of shock waves, rarefaction waves, and contact discontinuities in a medium of this type. It is shown that a number of intrinsic differences exist between the behavior of shock waves in waterlike substances and their behavior in ideal gases. In Section IV, one-dimensional interaction of shock waves in arbitrary fluids is discussed. Section V presents the theory of regular reflection of shock waves in waterlike substances; while Section VI presents the theory of triple-shock intersections. In both instances essential differences between the behavior of shock waves in waterlike substances and ideal gases are noted. The text is supplemented by numerous tables and charts.