Multishock Compactions of a Die-Contained Copper Powder Medium Analyzed by Improved Theory

1991 ◽  
Vol 113 (4) ◽  
pp. 560-569
Author(s):  
Yukio Sano ◽  
Koji Tokushima ◽  
Tokujiro Inoue
Keyword(s):  
Copper Powder ◽  
Elastic Waves ◽  
Common Factor ◽  
Wall Friction ◽  
Compaction Process ◽  
Medium Length ◽  
Powder Medium ◽  
Compaction Processes ◽  
Initial Medium ◽  
The Waves

In the present paper, the multishock compaction process of a die-contained copper powder medium supported by an elastic plug at one end and impacted by an elastic punch at the other end, is analyzed by means of an improved theory having the effect of elasticity of the punch and plug. The compactions computed first have a constant sum of lengths of the medium and plug S0*=110, a constant ratio of punch mass to powder mass filled in the die M*=20, and an initial punch velocity ν0=50m/s. The computations of the compactions for the medium with very short lengths and the plug with long lengths confirm the existence of the medium length Scr1* corresponding to the first critical plug-length found in the previous study, and support the compaction process and the final mean density ρmean*-initial medium length S* relation of the medium shorter than the length Scr1* which were inferred in the study. Furthermore, the effect of elastic waves in the punch and plug on the process of the medium longer than Scr1* are examined. There are one common factor and one significant different factor in the processes. Explicitly, the waves in the plug exert different influence on compaction processes of the medium with different lengths, whereas the waves in the punch have similar influence on the processes. The elastic waves in the plug and die wall friction cause the medium length Scr2* corresponding to the second critical plug-length inferred in the previous study. Moreover, the waves in the plug make the form of the computed relation curve more complicated than the inferred one. The computed curve has the lengths Scr3* and Scr4* at which the density has an extreme value, respectively. Approximate similarity conditions for the compactions with various values of S0* are given by two fixed parameters M* and ν0 in region S*<Scr1*, three fixed parameters S*/S0*, M*, and ν0 in region from Scr1* to small S* where the wall friction effect can be neglected, and three fixed parameters S*, M*, and ν0 in region S*>(1/2)S0*. The computed ρmean*–S* and ρmean*–S*/S0* relations support these conditions. Furthermore, the computations of the compactions reveal that the waves in the punch, medium, and plug behave in similar manner during the processes, though they have different strengths.

General-Form Solution of Shock Fitting Equation Including Die Wall Friction for the Multishock Powder Compaction

1993 ◽  
Vol 115 (4) ◽  
pp. 424-432
Author(s):  
Y. Sano ◽  
K. Tokushima ◽  
M. Yamashita
Keyword(s):  
Friction Force ◽  
Form Solution ◽  
Wall Friction ◽  
Friction Effect ◽  
Medium Length ◽  
Powder Medium ◽  
Different Types ◽  
The One ◽  
Initial Medium ◽  
Shock Fitting

In this paper, shock fitting equations including wall friction force for predicting the one-dimensional compaction process of a powder medium caused by punch impact are first derived. The medium is assumed to be discontinuously compressed only at a shock wave front both when the front propagates toward an assumed rigid plug and when it propagates back to an assumed rigid punch. The equations suggest that the effect of the friction force on the process becomes large as the front propagates toward the plug. This friction effect suggests that a continuous compression will occur in the medium between the impacted surface and the front if the effect is large. Next, the general-form solution of the shock fitting equations is obtained. This solution is compared with the solution by the pseudo-viscosity method without using the assumption that the medium is compressed only at the front. Both the solutions agree well for the compaction with a short initial medium length where the effect is not remarkable. For the compaction with a long initial medium length where the effect is remarkable, however, the solutions predict different types of the process, especially in its earlier stage. Explicitly, the former predicts the discontinuous compression only at the front, as is clear from the assumption made, while the latter predicts not only the discontinuous compaction at the front but also the continuous compression between the impacted surface and the front due to the remarkable friction effect. In its later stage, they predict the compression only at the front. Thus, the general-form solution is valid for the compaction with short initial medium lengths, but results in errors in the earlier stage for long initial medium lengths.

Experimental Verification of the Similarity of Dynamic Compaction Processes of a Copper Powder Medium in Dies of Elementary Shapes

1987 ◽  
Vol 109 (4) ◽  
pp. 306-313
Author(s):  
Kiyohiro Miyagi ◽  
Yukio Sano ◽  
Takuo Hayashi
Keyword(s):  
Cross Section ◽  
Copper Powder ◽  
Similarity Theory ◽  
Rigid Bodies ◽  
Dynamic Compaction ◽  
Wall Friction ◽  
Simple Type ◽  
One Dimensional ◽  
Powder Medium ◽  
Compaction Processes

The similarity of dynamic compaction processes was investigated theoretically and predicted in our previous report, where powder media in a die were assumed to be of a simple type, and the punch and plug to be rigid bodies. The predictions were based on a set of one-dimensional equations and a set of nondimensionalized one-dimensional equations. The objective of this study is to examine the similarity experimentally and to present the results of compaction experiments in order to verify the existence predicted. The experiments were carried out on a copper powder medium in dies having inner cross-section in elementary shapes such as circle, square and triangle. The pressure of the medium at a point contacting the end of the plug, the density distribution and mean density of the green compacts were measured in the experiment. From the analysis of the experimental data the validity of the dynamic similarity theory was demonstrated and the similarity was verified to exist despite the differences in size and shape between the dies used, which implies that the copper powder medium in the dies of elementary shapes is of a simple type. Relations between the density and the shape coefficients showed that the density reached maximum as the coefficients decreased approaching a certain point with a decreasing influence of the die wall friction, while past that point, contrary to the prediction by the theory, it began to decrease due to an increasing influence of the elastic deformation of the punch and plug.

Effect of Shock and Elastic Waves on Dynamic Compaction Process of Two-Layer Powder Media

1987 ◽  
Vol 109 (4) ◽  
pp. 266-271
Author(s):  
K. Miyagi ◽  
Y. Sano
Keyword(s):  
Elastic Waves ◽  
High Speed ◽  
Lower Layer ◽  
Initial Density ◽  
Dynamic Compaction ◽  
Compaction Process ◽  
Density Distributions ◽  
Layer Arrangement ◽  
Powder Medium ◽  
Compaction Processes

The dynamic compaction processes of copper powder which was filled in two layers into a die and subjected to solid punch impaction were investigated experimentally in order to assess the effect of different initial density distributions of the powder on the compaction process. The compaction experiments were performed for two situations of layer arrangement: in the first situation the upper layer had a lower uniform initial density distribution than the lower layer and in the second this order was reversed. The processes were photographed for the two situations of layer arrangement using a high speed camera in order to analyze the movement of powder medium and punch, the propagation of shock and elastic waves in the powder medium and density distributions. The pressure on the plug supporting the medium in the die was also measured so that the analysis of the photograph would be facilitated. The two compaction processes observed and analyzed differed considerably, but the green density distributions had only a slight difference. The compaction process obtained for the first situation of layer arrangement agreed well with the theoretical prediction reported previously by the authors. The compaction process for the second situation also agreed with the theoretical result, indicating that the amounts of internal energy dissipation during the two processes differ only slight.

Multishock Compactions of Powder Media Influenced by Elastic Waves in Punch and Plug

1991 ◽  
Vol 113 (4) ◽  
pp. 372-381
Author(s):  
Yukio Sano ◽  
Koji Tokushima ◽  
Kiyohiro Miyagi
Keyword(s):  
Experimental Data ◽  
Elastic Waves ◽  
Critical Length ◽  
Wall Friction ◽  
Initial Powder ◽  
Green Density ◽  
Previous Experimental Data ◽  
Powder Medium ◽  
Theoretical Predictions ◽  
The Mean

The previous theoretical predictions of the compaction of a copper powder medium, based on the assumption that the punch and plug were both a rigid body, did not satisfactorily agree with the experimental results obtained for short initial powder lengths and long plug lengths. This type of compaction amounts to cases when the plug length exceeds the second critical length which will be described below. Shock waves in a powder medium and elastic waves in the elastic punch and plug, schematically shown in space coordinate-time diagrams, suggest that the elastic wave in the plug is the probable cause of the inconsistency between the theoretical and experimental data of the previous investigation. In fact, the diagrams indicate that the shock wave transmitted in the medium across the medium-plug interface exerts an effect on the compaction process when the plug length does not exceed what is termed the first critical length. In cases when the effect of die wall friction is neglected, the mean green density-initial powder length relation of the copper medium is obtained from a theoretical approximation based on energy of the medium for the compaction with the sum of the initial powder length and the plug length being constant. This relation indicates that the effect of elasticity of the plug is large as the plug length becomes large. The second critical plug length at which the effect of elasticity becomes balanced with the effect of die wall friction is established by this relation and by the previously computed density-length relation with the effect of die wall friction taken into account. More specifically, these two relations provide a relation involving the first and second critical-plug lengths. The relation inferred as such agrees qualitatively with the previous experimental data in the examined region of the initial powder length. This qualitative agreement suggests that if the effects of elasticity and die wall friction are considered, a satisfactory theoretical and experimental agreement could be obtained. Therefore, the mean green density-initial powder length relation is computed taking into account both the effects. The computed relation agrees quantitatively with the previous experimental data even for short initial powder lengths and long plug lengths.

Multiple Shock Compaction of Simple Type Powders by Punch Impact

1992 ◽  
Vol 114 (2) ◽  
pp. 117-138
Author(s):  
Yukio Sano
Keyword(s):  
Constitutive Relations ◽  
Wall Friction ◽  
Qualitative Behavior ◽  
Simple Type ◽  
Final Density ◽  
Shock Compaction ◽  
Powder Medium ◽  
Compaction Processes ◽  
Shock Fitting ◽  
Multiple Shock

Recently, we have elucidated some mechanical behaviors of powders during the compaction. The elucidation involves the constitutive relations of a powder medium under the multishock compaction, the qualitative behavior such as the similarities of the compaction processes, the die wall friction effect, and the uniformity of the final density distribution of the compact with a high density, and the quantitative behavior analyzed by the pseudo-viscosity method and the shock fitting. This review describes this behavior systematically.

Electromagnetic damping of elastic waves: Experimental results

1968 ◽  
Vol 5 (4) ◽  
pp. 825-829 ◽  
Author(s):  
F. E. M. Lilley ◽  
C. M. Carmichael
Keyword(s):  
Magnetic Field ◽  
Elastic Wave ◽  
Applied Magnetic Field ◽  
Elastic Waves ◽  
Applied Field ◽  
Eddy Currents ◽  
Electrical Conductor ◽  
Electromagnetic Damping ◽  
The Waves ◽  
The Magnetic Field

The passage of an elastic wave causes straining and translation in the transmitting material. If a magnetic field is applied, and the medium is an electrical conductor, some of the energy of the wave is dissipated by the flow of electrical eddy currents. Usually the amount of energy lost is very small, but it may be greatly increased if the applied field is strongly non-uniform.Laboratory experiments are described which demonstrate this effect for standing elastic waves in a metal bar. The applied magnetic field changes from almost zero to its full strength over a distance which is short compared to the length of the standing wave. The result of this strong non-uniformity is that the energy lost due to the translation of the bar in the field greatly exceeds the energy lost due to the straining of the bar in the field.The dependence of the attenuation of the waves by the magnetic field is investigated for variation in frequency of vibration, bar thickness, and field gradient.

scholarly journals Dispersion of waves and transmission–reflection in blood vessels with structured stents

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180816 ◽  
Author(s):  
S. Frecentese ◽  
T. K. Papathanasiou ◽  
A. B. Movchan ◽  
N. V. Movchan
Keyword(s):  
Blood Vessels ◽  
Elastic Waves ◽  
Pulsating Flow ◽  
Numerical Examples ◽  
New Model ◽  
Dispersion Properties ◽  
Transmission Properties ◽  
The Waves

A new model is proposed for elastic waves induced by a pulsating flow in a stenotic artery containing several stents. Dispersion properties of the waves depend on the stent structure—this feature is addressed in the present paper. Several vascular stenting procedures include overlapping stents; this configuration is also included in the model. The dispersion and transmission properties are analysed; the analytical derivations are accompanied by illustrative numerical examples.

STUDIES ON SEISMIC WAVES: III. PROPAGATION OF ELASTIC WAVES IN THE NEIGHBORHOOD OF A FREE BOUNDARY

Geophysics ◽  
1947 ◽  
Vol 12 (1) ◽  
pp. 57-71 ◽  
Author(s):  
C. Y. Fu
Keyword(s):  
Surface Waves ◽  
Elastic Waves ◽  
Seismic Waves ◽  
Classical Method ◽  
Epicentral Distance ◽  
Harmonic Waves ◽  
Inhomogeneous Waves ◽  
Different Types ◽  
Propagation Of Elastic Waves ◽  
The Waves

Continuous and spherical harmonic waves are generated at an internal point of the medium. By use of the classical method of Sommerfeld, the different modes of propagation near a free surface after the arrival of the waves are examined. From the approximate evaluations of the integrals, it is found that in addition to the ordinary types of body and surface waves, there are also inhomogeneous waves and surface waves which are not of the Rayleigh type. The amplitude factors of these latter waves vary inversely as the square instead of as the square root of the epicentral distance. Altogether, there are not less than five different types of waves and they are obtained from integrations in the neighborhood of the singularities of the integrals.

scholarly journals Bending-gravity waves in the sea with an ice cover from moving disturbances

2021 ◽  
pp. 157-161
Author(s):  
Ж.В. Маленко ◽  
А.А. Ярошенко
Keyword(s):  
Gravitational Waves ◽  
Gravity Waves ◽  
Elastic Waves ◽  
Isotropic Plate ◽  
Pure Water ◽  
Three Dimensional ◽  
Ice Cover ◽  
Ship Waves ◽  
Plate Vibrations ◽  
The Waves

В статье проводятся исследования колебаний плавающего ледяного покрова под действием движущихся возмущений. В основу колебаний плавающего ледяного покрова положены линеаризованные уравнения гидромеханики и линейная классическая теория колебаний пластин. Ледяной покров рассматривается как тонкая упругая изотропная пластинка. Анализируются образующиеся при этом трехмерные изгибно-гравитационные волны. Показано, что при движении источника возмущений со скоростью 0<v<v0 изгибно-гравитационные волны не образуются, а наблюдается статический прогиб. Здесь v0 – минимальное значение фазовой скорости. При скорости движения v0<v<v1 образуется одна система изгибно-гравитационных волн. Эти волны распространяются как впереди, так и за источником возмущений. Волны, бегущие впереди источника, обусловлены упругими и массовыми силами пластинки. Волны, распространяющиеся за источником, имеют характер гравитационной волны для чистой воды. При v1<v<(gH)1/2 образуется три системы волн. Упругие волны распространяются впереди источника. Две другие волны распространяются за источником и носят характер поперечной и продольной корабельных волн. При v>(gH)1/2 образуются впереди источника упругие волны, а за источником продольные корабельные волны. Исследовано влияние скорости перемещения нагрузки на амплитуды образующихся волн. The article studies the fluctuations of the floating ice cover under the action of moving perturbations. The vibrations of the floating ice cover are based on the linearized equations of hydro-mechanics and the linear classical theory of plate vibrations. The ice sheet is considered as a thin elastic isotropic plate. The resulting three-dimensional bending-gravity waves are analyzed. It is shown that when the source of disturbances moves at a speed of 0<v<v0, bending-gravitational waves are not formed, but a static deflection is observed. Here v0is the minimum value of the phase velocity. At the speed of motion v0<v<v1, a single system of bending-gravitational waves is formed. These waves propagate both ahead and behind the source of the disturbances. The waves traveling ahead of the source are caused by the elastic and mass forces of the plate. The waves propagating behind the source have the character of a gravitational wave for pure water. At v1<v<(gH)1/2, three wave systems are formed. Elastic waves propagate ahead of the source. The other two waves propagate behind the source and have the character of transverse and longitudinal ship waves. At v>(gH)1/2, elastic waves are formed in front of the source, and longitudinal ship waves are formed behind the source. The influence of the load displacement velocity on the amplitudes of the generated waves is investigated.

Wave Field in Fluid Saturated Porous Media Subjected to Excitations of Multiple Energy Sources

2005 ◽  
Author(s):  
Liming Dai ◽  
Guoqing Wang
Keyword(s):  
Porous Media ◽  
Elastic Waves ◽  
Saturated Porous Medium ◽  
Wave Model ◽  
Energy Sources ◽  
Saturated Porous Media ◽  
Moving Coordinate ◽  
Fluid Saturated Porous Medium ◽  
The Mathematical Model ◽  
The Waves

This research is to investigate the behavior of elastic waves in porous media consisting of fluid and solid. A new methodology for describing the wave motion of a fluid-saturated porous medium is developed with the establishment of a mathematical wave model. Dynamic equations in the form of displacements of the fluid and solid are derived for analyzing the elastic waves propagating in homogeneous and isotropic porous media, which are subjected to excitations of multiple energy sources. Solutions of the wave equation are developed on the basis of the moving-coordinate method. Numerical simulations of the waves propagating in the porous media with multiple energy sources are also performed for demonstrating the application of the mathematical model developed.

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