US20060207913A1

US20060207913A1 - Granular container protector for protecting impulse

Info

Publication number: US20060207913A1
Application number: US11/375,864
Authority: US
Inventors: Jongbae Hong
Original assignee: Seoul National University Industry Foundation
Current assignee: Seoul National University Industry Foundation
Priority date: 2005-03-15
Filing date: 2006-03-15
Publication date: 2006-09-21
Also published as: KR20060099795A; KR100763351B1

Abstract

The present invention discloses a granular container protector for protecting impulse comprising a plurality of granular media each having a certain elastic property and a certain mass; wherein the plurality of granular media is arranged one-dimensionally into a plurality of sections, each section including one or more granular medium having same elastic property and same mass; wherein the plurality of sections is arranged in a manner that a ratio of mass to elastic property of the granular media in each section decreases toward a central section from both side sections; wherein the plurality of sections is arranged to be a mirror image about the central section; and wherein the side sections and the central section form walls of the granular container protector.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to Korean Patent Application No. 10-2005-0021244 filed on Mar. 15, 2005, which is incorporated in its entirety by this reference.

TECHNICAL FIELD

The present invention relates to a granular container protector for protecting impulse. More specifically, the present invention relates to a granular container protector for protecting impulse which lessens a big external impulse effectively by disintegrating it into a plurality of small impulses and releasing the small impulses little by little with time lag, using propagation characteristics of the impulse in a granular chain.

DISCUSSION OF RELATED TECHNOLOGY

Generally, it is a very important problem in a daily life to protect lives and personal properties from fatal disasters such as automobile collision, and gas explosion, etc. It becomes high interests in terms of an industrial aspect to lessen various kinds of mechanical impacts coming from outside as can be seen from various kinds of sports appliances such as a protective helmet or a tennis racket. In addition, it is also very important in an army to lessen impulses caused by a bomb explosion or military arms.
One possible effective protection method against an external impulse is to confine the impulse into a specific region. However, it is practically impossible to confine the impulse in a specific region perfectly and permanently. In the meanwhile, it is possible that one may construct an effective protector that confines a strong impulse inside it for a short time, makes the strong impulse into a plurality of weak impulses, and then releases them outside from the protector little by little with time lag. This kind of protection mechanism may be realized in a specially prepared granular chain.
Granular matter is ubiquitous around us and in our daily life. However, fundamental research has not been made much because of its complication and nonlinear nature. It has been proved analytically and numerically that the propagating mode in the granular chain with power-law type contact force, i.e., F ∝ δ^P, where δ is the squeezed distance between neighboring grains, is a solitary wave. The solitary wave in a granular chain with Hertzian contact force having p= 3/2 can be described by a soliton in a continuum limit. Some of soliton properties predicted by theory have been demonstrated by experiments.
Interestingly, this soliton or the solitary wave in a granular chain shows anomalous features of propagation when it passes an interface of a granular chain composed of different granules, which are discriminated by mass and elastic property. A known anomalous feature of the wave propagation in the granular chain is the total transmission of a solitary wave along with disintegration of the solitary wave into many smaller solitary waves when it passes the interface from the region of heavy granules to that of light granules where “heavy” means a larger value of m/η (where m is mass of a granule and η is an elastic property) and “light” means a smaller value of m/η, while neither disintegration nor total transmission occurs when it passes the interface from the region of light granules to that of heavy granules. The number of disintegrated solitary waves depends on the strength of pre-compression. An example of disintegration of a big solitary wave into smaller solitary waves is illustrated in FIG. 1. More specifically, FIG. 1 shows an example where the ratio of the quantity m/η of each region is 10. The leading solitary wave after transmission is highest and fastest, and the following solitary waves are lower and slower gradually.

SUMMARY OF THE INVENTION

By using the above anomalous behaviors of total transmission which are propagating features of an impulse in a granular container composed of inhomogeneous granular chains, it is possible to confine incident impulse inside the granular container protector and to make a big solitary wave into a plurality of smaller solitary waves using the property of disintegration of an impulse at an interface. Thus, it is possible to reduce a strong impulse into many weak impulses inside the granular container protector thereby lessen the strong impulse effectively.
Therefore, the present invention is to provide a novel protector for protecting impulse by constructing a granular container having a specific arrangement. More specifically, a first aspect of the present invention is to provide a granular container protector for protecting impulse comprising a plurality of granular media each having a certain ratio of mass to elasticity; wherein the plurality of granular media is arranged one-dimensionally into a plurality of sections, each section composing of the same ratio of mass to elasticity; wherein the plurality of sections is arranged in a manner that a ratio of mass to elasticity of the granular media in each section decreases toward a central section from both side sections; wherein the plurality of sections is arranged to be a mirror image about the central section; and wherein the side sections form walls of the granular container protector; and wherein the central section can be replaced by materials that change the energy of impulse into heat.
A second aspect of the present invention is to provide a granular container protector for protecting impulse comprising a plurality of granules each having certain elasticity and a certain mass; wherein the plurality of granules is arranged one-dimensionally into a plurality of sections, each section having the same ratio of mass to elasticity; wherein the plurality of sections is divided into a first zone ranging from one side section to a central section and a second zone ranging from the other side section to the central section; wherein the plurality of sections is arranged in a manner that a ratio of mass to elasticity of the granules in the each section decreases in one same direction in the first zone and the second zone, respectively; and wherein the side sections and the central section form walls of the granular container protector.
Yet a third aspect of the present invention is to provide a three-dimensional granular container protector for protecting impulse, wherein the three-dimensional granular container protector is structured by stacking a plurality of the granular container protectors in accordance with the first and the second aspects described above in up and down directions and left and right directions.
Further features and advantages of the present invention, as well as the structure and operation of various embodiments of the present invention, are described in detail below with reference to the accompanying drawings where same or similar reference numerals refer to the same structural elements.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example of disintegration of a big solitary wave into many smaller solitary waves when it passes the interface from the region of large m/η to small one. The ratio of the value m/η of two regions is 10.
FIGS. 2 (a) and 2(d) illustrate a schematic diagram of a granular container protector for protecting impulse in accordance with the present invention.
FIG. 2 (b) illustrates a schematic diagram of a granular container protector for protecting impulse in accordance with the present invention.
FIGS. 2(c) and 2(e) illustrate schematic diagrams in order to compare with a granular container protector for protecting impulse illustrated in FIGS. 2 (a) and 2(d).
FIG. 3 illustrates a snap shot of granule velocity which shows energy leakage of an incident big impulse in the form of a smaller solitary waves from a granular container protector for protecting impulse of the present invention illustrated in FIG. 2(a).
FIG. 4 illustrates a behavior of an impulse energy remaining inside each granular container protector for protecting impulse of the present invention as time passes therein respectively illustrated in FIGS. 2(a) to 2(e).

EMBODIMENTS OF THE PRESENT INVENTION

Hereinafter, the present invention is described in more detail with reference to preferred embodiments.
First, FIGS. 2(a) and 2(d) illustrate a schematic diagram of a standard form of the granular container protector for protecting impulse in accordance with the present invention. Further, FIGS. 2 (b), 2(c), and 2(e) illustrate schematic diagrams in accordance with the present invention in order to compare with a standard form of the granular container protector for protecting impulse illustrated in FIGS. 2 (a) and 2(d).
In FIGS. 2(a) to 2(e), circles, hatched octagons, and squares indicate p=1.5, p=2, and p=1, respectively and the ratio of mass to elastic property (i.e., m/η) is indicated as mass m of granules by setting the elasticity thereof to be a fixed value. In FIG. 2, FIG. 2(a) or FIG. 2(d) is a standard type granular container protector for protecting impulse in accordance with the best modes of the present invention.
Referring to FIG. 2, the present invention provide a granular container protector for protecting impulse comprised of a plurality of granular sections or linear medium sections, each of which contains a plurality of granules, as illustrated in FIG. 2(a). In the granular sections which are a structural element of the granular container protector for protecting impulse of the present invention as illustrated in FIG. 2(a), three linear medium sections (p=1) as indicated squares in left, central, and right positions, respectively, form walls of the granular container protector for protecting impulse and the granular container protector for protecting impulse of the present invention is constructed by these walls. Further, the arrangement of other non-linear granular sections (p=1.5 and p=2.0) thereof is a mirror image about the linear medium section (p=1.0) at the central position. The ratio of mass to elastic property (m/η) of granules contained in each and every section is the same, while it has different values for respective sections.
In an embodiment described above, although it is described and illustrated that three sections are included between walls of the granular container protector for protecting impulse of the present invention, it may be easily understood by a skilled person in the art that the number of section between the walls thereof may be any number having one or more when desired.
Further, in an embodiment illustrated in FIG. 2(a), although the number of granules in each section are the same due to a mirror image (e.g., if the number of granules in a section with p=1.5 and m=0.1 is 20, then the number of granules in a section with p=2.0 and m=1.0 is 20), the number of granules in each section may vary from section to section in another embodiment of the present invention. However, even in the latter case, the granules contained in each section must have the same ratio of mass to elastic property (m/η) and the value of m/ηin each section must become smaller from both outer walls toward a central wall.
FIGS. 2(b) and 2(c) are an example for performing a comparing experiment with a standard type granular container protector for protecting impulse as illustrated in FIG. 2(a) and thus are modified embodiments, each having a different arrangement. It is obvious to a skilled person in the art that these modified embodiments should fall upon a scope of the present invention. Furthermore, FIG. 2(e) is another comparative embodiment for comparing a various embodiments depicted in FIGS. 2(a) to 2(d). More specifically, in FIG. 2(b), an arrangement of three non-linear (p≠1) medium sections is placed between one side wall and a central wall of the granular container protector for protecting impulse of the present invention (hereinafter “First Zone”), while another arrangement of three non-linear medium sections is placed between the central wall and the other side wall thereof (hereinafter “Second Zone”), where the order of the sections in First Zone is identical to that in Second Zone. Therefore, each section does not have a mirror image to the corresponding section about the central section (or the central wall) in FIG. 2(b). In the meanwhile, FIG. 2(c) depicts one section having same kind of granules, unlike FIGS. 2(a) and 2(b) where First Zone and Second Zone respectively have three non-linear medium sections. Furthermore, FIG. 2(d) illustrates a case that each section has 50 granules in FIG. 2(a). FIG. 2(e) illustrates a case that every section including walls has same kind of granules.
Hereinbelow, an effective protecting mechanism for protecting impulse in a granular container protector for protecting impulse in accordance with the present invention will be described. In a granular container protector for protecting impulse in accordance with the present invention illustrated in FIG. 2(a), an impulse reaching one end side wall thereof proceeds up to the central section (wall) without reflection. However, the impulse disintegrates into a plurality of small solitary waves when it passes through each interface between the sections, because the ratio value of mass to elastic property (m/η) of granules decreases toward the central section (wall) in each section of FIG. 2(a). This impulse disintegration lasts until the leading solitary wave reaches the edge of the central section (wall). A first reflective wave occurs at the edge of the central section (wall) and then the solitary wave proceeds from the central section (wall) to both side walls of the granular container protector for protecting impulse. In this case, both transmission and reflection occur simultaneously at each interface, while only transmission occurs for the reflective wave toward the central section (wall) where the reflective wave again disintegrates into a plurality of small solitary waves. These disintegrated impulses having different peak heights leave from the granular container protector for protecting impulse of the present invention at different times, i.e., with time lag.
The granular container protector for protecting impulse in accordance with the present invention must be practically a three-dimensional structure. However, a usual three-dimensional granular system has complicated distribution of force chains through which impulse may transmit. Accordingly, the nature of propagation of an impulse inside a three-dimensional granular container protector for protecting impulse does not show features appeared in a force chain system of one-dimensional granular container protector for protecting impulse of the present invention illustrated in FIG. 2. Thus, in order to provide a three-dimensional granular container protector for protecting impulse to retain the peculiar propagation features of a solitary wave described above, an artificial three-dimensional granular container protector for protecting impulse can be structured by stacking granular chains of one-dimensional granular container protector for protecting impulse illustrated in FIG. 2(a). For example, in case that the granular chains of one-dimensional granular container protector for protecting impulse illustrated in FIG. 2(a) are oriented in x-direction, a three-dimensional granular container protector for protecting impulse of the present invention may be obtained by staking the same granular chains of one-dimensional granular container protector for protecting impulse in y-axis and z-axis.
A protection from an impulse through a granular container protector for protecting impulse in accordance with the present invention may be understood by a numerical simulation on an equation of motion (1) of a grain written below:
mü _n=η[{δ₀−(u _n −u _n−1)}^p−{δ₀−(u _n+1 −u _n)}^p] (1)
where δ₀is the displacement under pre-compression; u_iis the displacement of the i-th grain from its initial equilibrium position due to an external perturbation; m is the mass of the grain; and η is the elastic constant of the grain depending on its radius, Young's modulus, and Poisson's ratio. The only parameter governing Equation (1) for a given pre-compression is the ratio m/η. As in the embodiments of the present invention, if a fixed value of η is given for all grains, different granules can be discriminated only by masses thereof. Therefore, light and heavy granules mean small and large values of m/η, respectively. Thus, it is easily understood by a skilled person in the art how masses of granules, an elastic property of granular medium, and a geometrical structure of granules may affect the results of the present invention.
In the embodiments of the present invention, most granules are chosen to be Hertzian contact force (i.e., p=3/2) which corresponds to a spherical shape. However, any skilled person in the art may understand that granules with irregular surfaces such as sand are close to another nonlinear contact, p=2. Further, a linear medium, p=1, is introduced in order to use for the walls of a granular container protector for protecting impulse. The properties of a propagating solitary wave inside a granular container protector for protecting impulse have been already studied in the art. In addition, a variety of modified type of a granular container protector for protecting impulse as illustrated in FIGS. 2(b) to 2(e) is provided in the present invention.
FIG. 3 illustrates a snap shot of granule velocity which shows energy leakage of an incident big impulse in the form of a smaller solitary waves in a granular container protector for protecting impulse of the present invention illustrated in FIG. 2(a). In FIG. 3, the mass of a granule in three linear sections (p=1) is changed into m=10 instead of m=2. To see the leaking solitary waves from the granular container protector for protecting impulse, heavy Hertzian grains of m=100 in either outside thereof are placed in the present invention. Then, an initial impulse to the right outside end of the granular chain thereof is applied to a grain of mass 100 with velocity 10 (with the arbitrary program units used in the present invention). A large solitary wave produced by the impact at the right outside end thereof propagates along the chain and passes the right wall thereof without reflection. The incident impulse reaches up to the central section (wall) without any reflection, even though a large incident solitary wave is disintegrated into a plurality of small solitary waves.
When using a stainless steel ball of diameter 1 mm as a grain, the value of η is 2.618×10⁹(N/m^3/2), the mass m=100 corresponds to a value of 2.36×10⁻³(Kg), and the velocity 10 corresponds to a value of 5.4×10⁶(m/s) in Equation (1). In this embodiment, the time interval of snap shot is 0.40 μs and thus, the snap shot illustrated in FIG. 3 is one that 0.112 ms (millisecond) has lapsed after collision. Under the conditions described above, an interesting result is obtained when seeing the energies of small solitary waves leaving out of the granular container protector for protecting impulse. The energy of a solitary wave is the sum of the mechanical energies of grains participating in the small solitary waves. The number of grains composing a solitary wave is approximately 5 for any height thereof. This is a unique property of the Nesterenko soliton appearing in a granular chain.
The energies of leading solitary waves leaving the granular container protector for protecting impulse appearing at the right and left ends of the snap shot illustrated in FIG. 3 are 3.3% and 7.7% of the energy of the incident solitary wave, respectively. From this result, it can be seen that a strong initial impulse incident on the granular container protector for protecting impulse is disintegrated into small solitary waves whose individual energy is less than 10% of the original energy when they leave the granular container protector for protecting impulse. Therefore, it is possible to protect an external impact effectively by designing a granular container protector for protecting impulse having a specific arrangement of grains.
The protection can be improved when the linear materials of the central section (wall) can be replaced by some dissipative materials that can transform the mechanical motions (i.e., mechanical energy) of granules into heat effectively. A typical dissipative material to be used for the present invention is sand or plastic. In case of plastic, it must be pulverized into particles, each having a coarse surface. Since the arrangement shown in FIG. 2 (a) (the standard one) is designed for all the solitary waves transmitted or reflected to reach the central section eventually, the dissipative material of the central section improves the effect of protection.
Meanwhile, FIG. 4 illustrates a behavior of an impulse energy remaining inside each granular container protector for protecting impulse of the present invention as time passes therein respectively illustrated in FIGS. 2(a) to 2(e). More specifically, FIG. 4 illustrates a change of energy remaining inside the granular container protector for protecting impulse as time elapses for the modified types illustrated in FIGS. 2(b), 2(c) and 2(e) as well as for the standard types illustrated in FIGS. 2(a) and 2(d). In FIG. 4, the time axis is indicated as a unit of 0.40 μs. That is, 600 in the time axis indicates 600×0.40 μs=240 μs. As can be seem from FIG. 4, FIG. 2 (d) where the number of granules in each section is increased to 50 shows slower leaking of energy than FIG. 2 (a) where the number of granules in each section is 20, while FIG. 2(a) shows the slowest leaking of energy among FIGS. 2(a), 2(b), 2(c), and 2(e) where the numbers of granules are the same.
An effective protection against an external impact may be accomplished by using a granular container protector for protecting impulse of the present invention having an appropriate arrangement of m/η with a plurality of interfaces, because a big solitary wave can be disintegrated into a plurality of small solitary waves when it passes through an interface from a large granular medium having a larger value of m/η to a small granular medium having a smaller value of m/η. That is, it is possible to protect a big external impact by confining energy transmitted by a solitary wave inside the granular container protector and then releasing the energy in the form of a plurality of weak solitary waves little by little thereby disintegrating the big external impact effectively.
Although the present invention describes a granular container protector using a phenomenon of confining an impact appearing in a grain chain, it is easily conceivable by a skilled person in the art that other systems such as a electromagnetic system and a molecular biological chain may also possibly protect an external impact as accomplished by the granular container protector of the present invention, if non-linear interactions with a power-law type between structural elements of a system exist. Therefore, the spirit of the present invention is not only applied to a granular container protector, but also applied to any system with a power-law type described in the present invention.
As various modifications could be made in the constructions and method herein described and illustrated without departing from the scope of the present invention, it is intended that all matter contained in the foregoing description or shown in the accompanying drawings shall be interpreted as illustrative rather than limiting. Thus, the breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims appended hereto and their equivalent.

Claims

1. A granular container protector for protecting impulse comprising a plurality of granules each having certain elasticity and a certain mass;

wherein said plurality of granules is arranged one-dimensionally into a plurality of sections, each section including a number of granules having the same elasticity and mass;

wherein said plurality of sections is arranged in a manner that a ratio of mass to elasticity of said granules in each section decreases toward a central section from both side sections;

wherein said plurality of sections is arranged to be a mirror image about said central section; and

wherein said side sections and said central section form walls of said granular container protector.

2. The granular container protector as claimed in claim 1, wherein the number of section between said both side sections and said central section is three, respectively, and the number of said granules in each section are the same.

3. The granular container protector as claimed in claim 2, wherein said ratio of mass to elasticity of said granules in said plurality of sections is assigned to be 2.0, 1.0, 0.3, 0.1, 2.0, 0.1, 0.3, 1.0, and 2.0 starting from either one of said both side sections.

4. The granular container protector as claimed in claim 1, wherein each of said plurality of sections includes 20 granules.

5. The granular container protector as claimed in claim 2, wherein each of said plurality of sections includes 20 granules.

6. The granular container protector as claimed in claim 3, wherein each of said plurality of sections includes 20 granules.

7. The granular container protector as claimed claim 1, wherein each of said plurality of sections includes 50 granules.

8. The granular container protector as claimed claim 2, wherein each of said plurality of sections includes 50 granules.

9. The granular container protector as claimed claim 3, wherein each of said plurality of sections includes 50 granules.

10. The granular container protector as claimed in claim 1, wherein said central section can be replaced by a dissipative material changing energy of said impulse into heat.

11. The granular container protector as claimed in claim 10, wherein said dissipative material is sand or plastic.

12. A granular container protector for protecting impulse comprising a plurality of granules each having certain elasticity and a certain mass;

wherein said plurality of sections is divided into a first zone ranging from one side section to a central section and a second zone ranging from the other side section to said central section;

wherein said plurality of sections is arranged in a manner that a ratio of mass to elasticity of said granules in said each section decreases in one same direction in said first zone and said second zone, respectively; and

13. The granular container protector as claimed in claim 12, wherein the number of section between said both side sections and said central section is three, respectively.

14. The granular container protector as claimed in claim 13, wherein said ratio of mass to elasticity of said granules in said plurality of sections is assigned to be 2.0, 1.0, 0.3, 0.1, 2.0, 0.1, 0.3, 1.0, and 2.0 starting from either one of said both side sections.

15. The granular container protector as claimed in claim 12, wherein each of said plurality of sections includes 20 granules.

16. The granular container protector as claimed in claim 13, wherein each of said plurality of sections includes 20 granules.

17. The granular container protector as claimed in claim 14, wherein each of said plurality of sections includes 20 granules.

18. The granular container protector as claimed in claim 15, wherein each of said plurality of sections includes 20 granules.

19. The granular container protector as claimed in claim 12, wherein each of said plurality of sections includes 50 granules.

20. The granular container protector as claimed in claim 13, wherein each of said plurality of sections includes 50 granules.

21. The granular container protector as claimed in claim 14, wherein each of said plurality of sections includes 50 granules.

22. The granular container protector as claimed in claim 15, wherein each of said plurality of sections includes 50 granules.

23. The granular container protector as claimed in claim 12, wherein said central section can be replaced by a dissipative material changing energy of said impulse into heat.

24. The granular container protector as claimed in claim 23, wherein said dissipative material is sand or plastic.

25. A three-dimensional granular container protector for protecting impulse, wherein said three-dimensional granular container protector is structured by stacking a plurality of said granular container protectors recited in claim 1 in up and down directions and left and right directions.

26. A three-dimensional granular container protector for protecting impulse, wherein said three-dimensional granular container protector is structured by stacking a plurality of said granular container protectors recited in claim 12 in up and down directions and left and right directions.