Propagation of a Shock Wave Front Across a Curved Fluid-Solid Interface

1976 ◽  
Vol 43 (4) ◽  
pp. 589-593 ◽  
Author(s):  
B. E. Bennett ◽  
G. Herrmann
Keyword(s):  
Shock Wave ◽  
Cross Section ◽  
Pressure Pulse ◽  
Center Line ◽  
Ray Theory ◽  
Reflection And Transmission ◽  
Solid Interface ◽  
Circular Arcs ◽  
Acoustic Fluid ◽  
Special Case

Geometric optics, or the ray theory, is used to investigate the effect of pulse reflection and transmission at a curved fluid-solid interface. In particular, the problem of a plane pressure pulse, supported by an acoustic fluid, impinging on a plane symmetrical elastic body whose cross section is delineated by circular arcs is considered. The response of the solid is determined along its center line to reflection at the back interface with another fluid. Consideration of the special case in which the fluid densities are zero indicates that special care must be exercised in dealing with the in vacuo problem, and particularly in specifying the boundary conditions in that instance.

Wave-Front Analysis in Composite Materials

1969 ◽  
Vol 36 (3) ◽  
pp. 497-504 ◽  
Author(s):  
T. C. T. Ting ◽  
E. H. Lee
Keyword(s):  
Wave Front ◽  
Pressure Pulse ◽  
Spherical Inclusion ◽  
Stress Gradient ◽  
Back Surface ◽  
Ray Theory ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Linear Elastic ◽  
Elastic Composite

The propagation of an initially sharp plane pressure pulse through a linear elastic composite medium is analyzed. Wave front and ray theory analogous to geometrical optics is shown to determine the change in shape of the leading wave front and also the stresses immediately behind it. For certain circumstances the stress amplitudes on this front, or the corresponding tensile stresses on its reflection at the free back surface of a slab, may be critical in design. Examples are presented of an initially sharp plane pressure pulse transmitted through an elastic circular cylinder and an elastic spherical inclusion. The method can be applied to more general composite configurations, and can be extended to determine the stress gradient behind the front. For the latter, general formulas are derived by which the reflection and transmission coefficients can be determined for the stress gradient and the higher-order derivatives at an arbitrary interface.

Propagation of a Shock Wave Front Through a Lens-Shaped Elastic Body

1974 ◽  
Vol 41 (3) ◽  
pp. 691-696 ◽  
Author(s):  
T. C. T. Ting ◽  
G. Herrmann
Keyword(s):  
Wave Front ◽  
Elastic Body ◽  
Cross Section ◽  
Pressure Pulse ◽  
Time History ◽  
P Wave ◽  
Back Surface ◽  
Ray Theory ◽  
S Wave ◽  
Discontinuous Pressure

Ray theory is used to solve the problem of a plane pressure pulse with a discontinuous pressure front striking an elastic body whose cross section has the shape of a lens. Both plane-strain and axisymmetric motions are considered. The front and back surfaces of the lens are assumed to be circular. The velocity and acceleration at the P-wave front and the discontinuity in acceleration at the S-wave front are obtained explicitly for points along the axis of the lens and at the center of the back surface where reflections occur. The purpose of this study is to assess the effect of the curvatures of the lens on the velocity-time history at the center of the back surface of the lens which can be measured experimentally. Comparison with a laboratory test shows excellent agreement between analytical and experimental results.

The Uniform Flexure of an Incomplete Tore

1949 ◽  
Vol 2 (4) ◽  
pp. 469
Author(s):  
W Freiberger ◽  
RCT Smith
Keyword(s):  
General Solution ◽  
Cross Section ◽  
Harmonic Functions ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Derivatives Of ◽  
Special Case

In this paper we discuss the flexure of an incomplete tore in the plane of its circular centre-line. We reduce the problem to the determination of two harmonic functions, subject to boundary conditions on the surface of the tore which involve the first two derivatives of the functions. We point out the relation of this solution to the general solution of three-dimensional elasticity problems. The special case of a narrow rectangular cross-section is solved exactly in Appendix II.

The Effect of Initial Forces on the Hydroelastic Vibration and Stability of Planar Curved Tubes

1974 ◽  
Vol 41 (2) ◽  
pp. 355-359 ◽  
Author(s):  
J. L. Hill ◽  
C. G. Davis
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Constant Curvature ◽  
Elastic Limit ◽  
Center Line ◽  
Finite Element Technique ◽  
Line Shapes ◽  
Circular Arcs ◽  
Out Of Plane ◽  
Element Technique

The effect of initial forces on the vibration and stability of curved, clamped, fluid conveying tubes is analyzed by the finite-element technique. The tubes are initially planar with general center-line shapes approximated by constant curvature arcs. The effect of internal pressure is included. Numerical results are presented with, and without, the effects of the initial in-plane forces, for circular arcs S, L, and spiral configurations. Neglecting initial forces results in out-of-plane buckling, while including these forces prevents buckling within the elastic limit, in all configurations studied.

scholarly journals WAVE TRANSMISSION THROUGH TRAPEZOIDAL BREAKWATERS

1978 ◽  
Vol 1 (16) ◽  
pp. 129 ◽  
Author(s):  
Ole Secher Madsen ◽  
Paisal Shusang ◽  
Sue Ann Hanson
Keyword(s):  
Energy Dissipation ◽  
Approximate Method ◽  
Cross Section ◽  
Wave Energy ◽  
Graphical Form ◽  
Dissipated Energy ◽  
Simple Method ◽  
Reflection And Transmission ◽  
Transmission Coefficients

In a previous paper Madsen and White (1977) developed an approximate method for the determination of reflection and transmission characteristics of multi-layered, porous rubble-mound breakwaters of trapezoidal cross-section. This approximate method was based on the assumption that the energy dissipation associated with the wave-structure interaction could be considered as two separate mechanisms: (1) an external, frictional dissipation on the seaward slope; (2) an internal dissipation within the porous structure. The external dissipation on the seaward slope was evaluated from the semi-theoretical analysis of energy dissipation on rough, impermeable slopes developed by Madsen and White (1975). The remaining wave energy was represented by an equivalent wave incident on a hydraulically equivalent porous breakwater of rectangular cross-section. The partitioning of the remaining wave energy among reflected, transmitted and internally dissipated energy was evaluated as described by Madsen (1974), leading to a determination of the reflection and transmission coefficients of the structure. The advantage of this previous approximate method was its ease of use. Input data requirements were limited to quantities which would either be known (water depth, wave characteristics, breakwater geometry, and stone sizes) or could be estimated (porosity) by the design engineer. This feature was achieved by the employment of empirical relationships for the parameterization of the external and internal energy dissipation mechanisms. General solutions were presented in graphical form so that calculations could proceed using no more sophisticated equipment than a hand calculator (or a slide rule). This simple method gave estimates of transmission coefficients in excellent agreement with laboratory measurements whereas its ability to predict reflection coefficients left a lot to be desired.

Experiment on the Attenuation Characteristics of Shock Wave Interacting with Open and Closed Foam

2014 ◽  
Vol 1035 ◽  
pp. 445-452
Author(s):  
Jian Wang ◽  
Bao Gui Wang ◽  
Gang Tao
Keyword(s):  
Shock Wave ◽  
Internal Friction ◽  
Dynamic Behavior ◽  
Solid Phase ◽  
Experimental Results ◽  
Reflection And Transmission ◽  
Attenuation Characteristics

For understanding the dynamic behavior of open and closed foam subject to a shock wave, this paper through experiments, to gain a deeper understanding of the incidence, reflection and transmission of a shock wave when it interacted with cellular foam. Moreover, by analyzing the loss of the peak overpressure and positive impulse, we were able to respectively know the positive impulse of the incidence, reflection and transmission shock wave. The experimental results indicated that the attenuation capability for foam to the shock wave was caused by the internal friction and deformation of solid phase, which would absorb the energy of the shock wave. From the results we gain an understanding that the mechanical phenomenon of open foam to shock wave are not fully consistent with those of closed foam , while the attenuation of open foam to shock wave is more effective than that of closed foam.

scholarly journals DEVELOPMENT OF A POLYGONIZATION METHOD FOR RAIL STRUCTURES OF MONORAIL BY USING CENTER LINE AND CROSS SECTION

2016 ◽  
Vol 72 (2) ◽  
pp. I_156-I_166 ◽  
Author(s):  
Nao HIDAKA ◽  
Takashi MICHIKAWA ◽  
Nobuyoshi YABUKI ◽  
Tomohiro FUKUDA ◽  
Ali MOTAMEDI
Keyword(s):  
Cross Section ◽  
Center Line

Enskog-Boltzmann-Equation for a Fluid of Nonspherical Particles

1982 ◽  
Vol 37 (7) ◽  
pp. 660-664
Author(s):  
H. Thurn ◽  
S. Hess
Keyword(s):  
Boltzmann Equation ◽  
Differential Cross Section ◽  
Cross Section ◽  
Differential Cross ◽  
Position Vector ◽  
Nonspherical Particles ◽  
Fixed Orientation ◽  
General Relations ◽  
The Impact ◽  
Special Case

Abstract The Enskog-Boltzmann-equation is generalized to fluids of nonsperical particles with fixed orientation, i.e. for overdamped rotational motion. General relations between the interparticle position vector at the instant of contact, the impact parameter and the differential cross section are derived. The dependence of these quantities of the orientations of the colliding particles is studied for the special case of hard ellipsoids.

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