JP3845838B2 - Viscoelastic damper, method for manufacturing the same, and damping structure using the same - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a viscoelastic damper, a manufacturing method thereof, and a vibration control structure using the same.
[0002]
[Prior art]
Conventionally, various means are known as a vibration control means for buildings. In particular, seismic dampers that are easy to install and can be used for seismic retrofitting work on existing buildings have become very popular in recent years.
Damping dampers are installed as braces, for example, in a frame surrounded by pillars and beams in the frame of the building, dissipating the energy of disturbances when the braces are deformed due to the tension or compression of the braces, resulting in earthquakes, strong winds, etc. It is intended to attenuate vibrations due to external forces. A viscoelastic damper is a damping damper that uses a viscoelastic body that easily consumes energy even with a relatively small external force.
As viscoelastic dampers used for building damping dampers, for example, there are those described in JP-A-11-280294 and JP-A-11-303448.
[0003]
[Problems to be solved by the invention]
However, in the conventional viscoelastic damper as described above, consideration must be given so that the viscoelastic damper does not buckle when receiving a compressive load.
For example, in the viscoelastic brace described in Japanese Patent Application Laid-Open No. 11-280294, the core material is composed of a shape steel, a square steel pipe, a circular steel pipe, etc., and the buckling strength is improved. For this reason, the viscoelastic brace becomes thick, and there is a problem in that it cannot be adopted in terms of design and appearance of the living space when it is used in a bare glass building or the like.
In the brace described in JP-A-11-303448, during compression, the shaft-shaped brace body is buckled and deformed in a box material filled with a viscoelastic body, thereby realizing the consumption of disturbance energy. Since the brace body is covered with the box material and the amount of deformation is regulated, the brace body does not cause buckling failure unless the box material is deformed. Therefore, there is no risk of buckling in the specified load range, but since the vibration control effect is produced by buckling deformation, in order to withstand a higher load in preparation for a large earthquake, the strength of the box material can be increased, It is necessary to increase the buckling load by thickening the brace body. For this reason, there are problems that the brace becomes thicker and the vibration control effect is reduced at low loads.
[0004]
The present invention has been made in view of such a problem. By adopting a configuration that does not buckle even when subjected to a compressive force, the present invention is capable of forming a thin shape without being influenced by a buckling load. An object is to provide an elastic damper and an earthquake-resistant structure using the elastic damper. Moreover, it aims at proposing the manufacturing method of such a viscoelastic damper.
[0005]
[Means for Solving the Problems]
In order to solve the above problems, in the invention according to claim 1, a cylindrical outer cylinder member, and a cylindrical inner cylinder member joined to an inner peripheral portion of the outer cylinder member via a viscoelastic body In a state where one end portion is exposed from the outer cylinder member, the end portion is locked so as to move integrally with the inner cylinder member in a direction in which the end portion is pulled in the axial direction from the outer cylinder. A shaft member provided to move separately from the inner cylinder member in the reverse direction, an end portion exposed from the outer cylinder member of the shaft member, and the outer cylinder member on the opposite side in the axial direction The viscoelastic damper which provided the to-be-attached member is used for the edge part of each.
Therefore, when the viscoelastic damper is attached to a vibration control target such as a building frame by a mounted member, when the shaft member is pulled by the relative displacement of the vibration control target, the viscoelastic damper is moved together with the shaft member. The locked inner cylinder member moves, the viscoelastic body between the inner cylinder member and the outer cylinder member is deformed, and energy is consumed. In addition, when the shaft member moves in the opposite direction, the shaft member moves separately from the inner cylinder member, and therefore does not receive resistance from the inner cylinder member. No load is applied.
[0007]
In the invention according to claim 2 , a predetermined gap is provided inside the cylindrical outer cylinder member, and the cylindrical inner cylinder member is arranged, and the hot-melt viscoelastic body is placed in the gap by bringing them into a high temperature state. After the cooling, a shaft member provided with a locking portion for locking with the inner cylinder member is arranged at one end inside the inner cylinder member, and the other end of the shaft member is moved in the axial direction. A viscoelastic damper manufacturing method is used in which both ends of the outer cylinder member are sealed in a state where the outer cylinder member is exposed.
Therefore, according to such a manufacturing method, the viscoelastic damper according to claim 1 can be manufactured.
[0008]
Control in the invention according to claim 3, the frame of the building surrounded by beams and columns, using a visco-elastic damper comprising mounting in a direction intersecting with each other at least two viscoelastic damper according to claim 1 Use seismic structure.
For this reason, when the building frame is deformed by an external force such as an earthquake or strong wind, a tensile force acts on at least one viscoelastic damper, so that a seismic control effect can be exhibited.
[0009]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In addition, the same code | symbol is attached | subjected to the member which is the same or it corresponds through all the drawings.
First, an embodiment of a viscoelastic damper according to the present invention will be described.
Fig.1 (a) is sectional drawing of the axial longitudinal direction which shows schematic structure of the viscoelastic damper which concerns on this embodiment. FIGS. 1B and 1C are an AA cross-sectional view and a BB cross-sectional view of FIG. 1A, respectively.
[0010]
The viscoelastic damper 1 is attached to a vibration control target such as a building, and mainly includes an outer cylinder member 2, a viscoelastic body 3, an inner cylinder member 4, a shaft member 5, a front end cover 6, and a rear end cover 7. .
[0011]
The outer cylinder member 2 is made of, for example, a steel pipe and is a cylindrical member that extends straight and has both ends opened. Two perforated plates 2a extending in the radial direction from the outer periphery are provided in the vicinity of each opening. The perforated plate 2a is a plate in which a steel plate or the like provided with a mounting hole 2b through which a fastening member such as a bolt can pass is attached to the outer cylinder member 2 by welding or the like.
[0012]
An inner cylinder member 4 made of, for example, a steel pipe is provided on the inner side of the outer cylinder member 2, for example, a steel pipe whose outer peripheral portion is in close contact with a viscoelastic body 3 made of a polymer material having a hot melt property that liquefies by heating. Yes. The outer cylinder member 2 and the inner cylinder member 4 are disposed substantially coaxially.
[0013]
A sealing material 9 made of cured rubber or the like is provided at one end of the outer cylinder member 2 in contact with the entire circumference of the end, and a rear end cover 7 is provided via the sealing material 9.
The rear end cover 7 has substantially the same diameter as the outer cylindrical member 2 and plugs one end of a cylindrical tube in which a shaft member movable space 7c having a predetermined length is formed in the axial direction, and a perforated plate on the outer peripheral surface in the axial direction. A U-shaped plate 7a provided so as to be aligned with 2a and 2a is fixed by welding or the like.
[0014]
The perforated plates 2a and 2a and the U-shaped plate 7a are connected to the sealing member 9 with the outer cylinder member 2 and the rear end cover 7 through the splice plates 8 and 8, for example, by bolting. It is fixed. The predetermined length of the shaft member movable space 7 c is set to be longer than the designed allowable compression length of the viscoelastic damper 1.
[0015]
A sealing material 9 is brought into contact with the other end portion of the outer cylinder member 2, and a tip cover 6 is provided through the sealing material 9. The front end cover 6 is provided with a guide hole 6c penetrating through the center of the bottom surface of the cylindrical tube having the same diameter as the outer cylinder member 2 and having an appropriate length, and is provided so as to be aligned with the perforated plates 2a and 2a on the outer periphery. The perforated plates 6a, 6a are fixed by welding or the like. The tip cover 6 and the outer cylinder member 2 are fixed to the perforated plates 2a and 2a and the perforated plates 6a and 6a by splice plates 8 and 8, respectively.
[0016]
The sealing materials 9 and 9 are provided so as not to be washed out of the viscoelastic damper 1 even when the viscoelastic body 3 is liquefied due to, for example, a fire.
[0017]
A shaft member 5 made of, for example, a steel rod is disposed on the inner diameter side of the inner cylinder member 4. The end of the shaft member 5 on the side of the rear end cover 7 has an outer diameter that fits inside the rear end cover 7 by, for example, a steel plate, and abuts against the end from the outer side of the inner cylinder member 4 to be locked. A disc-shaped end plate 5a (locking portion) that can be fixed is fixed.
[0018]
The other end of the shaft member 5 extends through the guide hole 6c of the tip cover 6 and extends a predetermined length so as to be movable in the axial direction. At the tip, an appropriate attachment hole 5c is provided in a steel plate or the like, and an attachment portion 5b fixed by welding or the like is provided.
[0019]
As long as the shaft member 5 can smoothly move in the axial direction inside the guide hole 6c and the inner cylinder member 4, there is no restriction on the thickness of the shaft or the shape of the shaft cross section. Moreover, you may arrange | position an appropriate bearing and a lubrication material between the shaft member 5 and each. Furthermore, you may provide the appropriate guide member which supports the axial member 5 so that it can move smoothly to the edge part or the inside of the inner cylinder member 4. FIG.
[0020]
The U-shaped plate 7a and the attachment portion 5b are attached members that are attached to the vibration control object by, for example, bolting or the like via the attachment holes 7b and the attachment holes 5c when the viscoelastic damper 1 is attached to the vibration control object. is there.
[0021]
Next, the operation of the viscoelastic damper according to the present invention will be described.
FIG. 2 is a schematic cross-sectional view in the axial longitudinal direction for explaining the operation of the viscoelastic damper according to the present invention. FIGS. 2A, 2B, and 2C schematically show a state in which the viscoelastic damper is in a neutral position, receives a tensile force, and receives a compressive force, respectively.
[0022]
When in the neutral position, the end plate 5 a is in contact with the end of the inner cylinder member 4, and no external force other than the weight of the inner cylinder member 4 acts on the viscoelastic body 3.
As shown in FIG. 2B, when the shaft member 5 receives a tensile force in the direction of the arrow, the end portion of the inner cylinder member 4 is pressed and moved by the end plate 5a. Shear deformation occurs. Then, as time elapses, the deformation energy of the viscoelastic body 3 is converted into heat and consumed.
[0023]
On the other hand, as shown in FIG. 2C, when the shaft member 5 receives a compressive force in the direction of the arrow, the shaft member 5 is not locked in the compression direction and has no resistance load. In the range of the compression amount, the shaft member is moved while being pushed in the movable space 7c. Therefore, since the compressive force does not act on the shaft member 5 from both ends, it does not buckle regardless of its length and thickness.
[0024]
Next, an example of the load displacement characteristic of the viscoelastic damper 1 will be described. FIG. 3A shows a model for numerically calculating the load displacement characteristic of the viscoelastic damper 1. The building to be controlled is modeled by the building mass 10 and the building stiffness 11, and when the building mass 10 is displaced by an external force such as an earthquake or strong wind, the viscoelastic damper 1 is deformed in conjunction with the displacement. The viscoelastic damper 1 was modeled by connecting a viscoelastic body model 12 based on a forked model composed of a spring and a dashpot, and a spring 13 that is rigid only on the tension side in series.
[0025]
The spring 13 which is rigid only on the tension side is a spring model in which no force is generated by the spring even if it is deformed in the compression direction, and any drag force is generated in the tension direction so that the deformation in the tension direction is zero. If it represents, it will become like FIG.3 (b). Here, the horizontal axis represents the amount of deformation of the spring 13 rigid only on the tension side (the amount of elongation is positive and the amount of compression is negative), and the vertical axis represents the spring force generated on the spring 13 rigid only on the tension side. In the compression deformation area, a linear compression direction characteristic 15b in which the spring force is always 0 is shown, and in the tensile deformation area, a linear tension direction characteristic 15a in which the elongation amount is always 0 is shown.
[0026]
In FIG. 4, the example of the load deformation relationship of the viscoelastic damper 1 obtained analytically by said model is shown. A restoring force characteristic 16 is plotted when a periodic external force whose amplitude changes is applied to the viscoelastic damper 1. Here, the horizontal axis indicates the displacement from the neutral position in which the positive direction is the extension direction, and the unit is (cm). The vertical axis represents the restoring force, and the unit is (kN).
[0027]
The restoring force characteristic 16 first shows a linear change in which an elastic restoring force is generated and abruptly rises from the origin when a tensile force is applied from a neutral position (curve 16a), and then the inclination is increased as the load reaches a peak. As the restoring force decreases, the displacement returns (curve 16b) while dulling and drawing an approximately elliptical curve. The characteristics so far are the same as the restoring force characteristics of the conventional viscoelastic damper, but in the present invention, when the horizontal axis is reached, the horizontal axis is directed toward the origin (straight line 16c). Since the restoring force does not work even if it is further compressed, it returns to the origin by reciprocating on the horizontal axis as shown by the straight line 16d. On the other hand, when the viscoelastic body is unloaded, it returns to the initial state without leaving any residual strain, so that it does not show a so-called slip-type restoring force characteristic, and repeats the above cycle when a tensile force is applied again. The restoring force characteristic 16 is different from the conventional viscoelastic damper in that the restoring force characteristic 16 is not an elliptical loop passing through the first to fourth quadrants of the graph, but is closed within the first quadrant of the graph.
[0028]
As described above, the viscoelastic damper 1 does not resist during compression and causes deformation of the viscoelastic body during tension. Therefore, the viscoelastic damper 1 has a function as a damper that consumes energy while being extended from the neutral position. I understand that.
It should be noted that the result of analyzing an example for explanation is shown, and it is natural that the shape of the restoring force characteristic 16 differs if the modeling of the viscoelastic body, the material constant used, and the like are different. Even in that case, the loop is limited to the range of the first quadrant.
[0029]
Next, the manufacturing method of the viscoelastic damper 1 which concerns on this invention is demonstrated. 5 and 6 are perspective explanatory views for explaining each step of manufacturing the viscoelastic damper 1.
First, as shown in FIG. 5 (a), a perforated plate 2a is attached to the outer periphery of both ends of a cylindrical steel pipe by welding or the like to prepare an outer cylinder member 2. Further, an inner cylinder member 4 is prepared in which spacers 4a for attaching the cylindrical steel pipe to the outer cylinder member 2 in a substantially coaxial position are arranged on both ends of the cylindrical steel pipe having a smaller inner diameter. And the inner cylinder member 4 is put in the outer cylinder member 2, and a double pipe structure is made.
[0030]
The spacers 4a can be provided by welding, for example, a steel plate as shown in the figure. However, if the clearance between the outer cylinder member 2 and the inner cylinder member 4 is kept constant, the thickness of the viscoelastic body 3 can be provided uniformly. For example, a bolt is attached to the inner cylinder member 4 and a bolt head is used. A suitable clearance may be secured, or an appropriate jig that fixes the clearance only until the viscoelastic body 3 is provided may be used.
[0031]
Next, as shown in FIG. 5 (b), a sealing material 22 for preventing the viscoelastic body 3 from flowing out is disposed under the outer cylinder member 2 and the inner cylinder member 4, and the leakage prevention plate 23 is removed from the outer cylinder member 2. Stop and fix to the cylindrical member 2. Specifically, for example, the mounting brackets 21 and 21 may be temporarily fixed to the perforated plates 2a and 2a, and the leakage preventing plate 23 may be fastened together with the bolts 24 and 24.
[0032]
A silo-shaped bucket 20 for pouring the viscoelastic body 3 into the gap between the outer cylinder member 2 and the inner cylinder member 4 is disposed above. In this state, the viscoelastic body 3 liquefied by hot melt property is poured from the bucket 20 of the shape portion into a suitable high-temperature furnace and heated. After a predetermined amount is filled in the gap, it is cooled and waits for the viscoelastic body 3 to solidify, and then the bucket 20, the leakage prevention plate 23, the mounting bracket 21, and the sealing material 22 are removed.
[0033]
Next, as shown in FIG. 6C, the shaft member 5 is passed through the inner cylinder member 4. A rear end cover 7 is arranged on the side where the end plate 5a is located, and a front end cover 6 is arranged on the opposite side, with sealing materials 9 and 9 being sandwiched between the outer cylinder member 2 and the end cover 5 respectively. Then, each is connected to the perforated plate 2a with bolts via the splice plates 8.
[0034]
Next, as shown in FIG. 6D, the attachment portion 5b is attached to the end portion of the shaft member 5 exposed from the tip cover 6 by welding or the like.
The viscoelastic damper 1 can be manufactured by sequentially performing the above steps.
[0035]
According to the manufacturing method described above, unlike the case where the solid viscoelastic body is adhered and fixed to the member, the non-uniformity of tension on the outer cylinder member 2 and the inner cylinder member 4 does not occur, and thus excellent adhesion. Can be obtained. Therefore, there is an advantage that the viscoelastic body 3 can be restrained uniformly, and as a result, the damping effect can be enhanced.
[0036]
Next, a modified example of the viscoelastic damper 1 will be described. FIG. 7 is an axial longitudinal sectional view for explaining a schematic configuration of a modified example of the viscoelastic damper 1. Below, only a different part from the above is demonstrated.
In this modification, instead of the inner cylinder member 4 described above, the locking plate is provided with a through hole of a size that the shaft member 5 penetrates through one end of the cylindrical steel pipe but the end plate 5a catches. 26a uses the inner cylinder member 26 provided by welding or the like. And it arrange | positions so that the end plate 5a may be stored in the inside of the inner cylinder member 26. FIG. Further, a rear end cover 25 in which a U-shaped plate 7a is attached to a disc instead of the rear end cover 7 is used.
[0037]
If comprised in this way, since the end plate 5a will move inside the inner cylinder member 26 if the shaft member 5 receives a compressive force, the shaft member movable space 7c provided in the rear-end cover 7 will become unnecessary. Moreover, the length of the shaft member 5 can be shortened. Therefore, the viscoelastic damper 1 can be shortened and reduced in weight while having equivalent damping characteristics, and the size and cost can be reduced.
[0038]
Next, an embodiment of a vibration control structure using the viscoelastic damper according to the present invention will be described. Fig.8 (a) is explanatory drawing which shows embodiment of the damping structure using the viscoelastic damper which concerns on this invention.
In the present invention, the above-described viscoelastic dampers 1 and 1 according to the present invention are attached to a frame 30 surrounded by beams 17 and 17 and pillars 18 and 18 forming a part of a building.
[0039]
A gusset plate 19a having a mounting hole (not shown) is provided at the approximate center of one beam 17 constituting the frame 30, and a mounting hole (not shown) is formed at the intersection of the other beam 17 and the columns 18,18. Each is provided with gusset plates 19b, 19b provided with an illustration. The viscoelastic dampers 1 and 1 are fixed by bolting the end plate 5a to the gusset plate 19a and the U-shaped plate 7a to the gusset plate 19b. Accordingly, the viscoelastic dampers 1 and 1 are arranged in a square shape and are in a positional relationship in which the longitudinal directions of the axes intersect at a predetermined angle.
[0040]
Next, the operation of this embodiment will be described. According to such a configuration, when an external force is applied to the building and bending deformation occurs, one of the viscoelastic dampers 1 is in the compression direction and one of the other is in the compression direction, as indicated by a two-dot chain line in the drawing. The viscoelastic damper 1 is deformed in the tensile direction. Therefore, vibration energy is consumed by the viscoelastic damper 1 deformed in the tensile direction, and the vibration is attenuated. Since the viscoelastic damper 1 does not buckle even when compressed, the shaft member 5 can be designed to be thin. As a result, the entire viscoelastic damper 1 can be made thinner than before, and the viscoelastic damper 1 can be made slimmer and better-looking than the beam 17 and the column 18. Therefore, for example, even if the viscoelastic damper 1 is exposed and provided in the living space such as a glass-walled building, it is possible to finish the design with a good appearance.
[0041]
Such an action can be obtained by fixing at least two viscoelastic dampers 1 to the frame 30 in a direction crossing each other. Therefore, as a modification of the present embodiment, for example, as shown in FIG. Are provided with gusset plates 19c, 19c, 19d and 19d at the four corners of the frame 30 where the beam 17 and the pillar 18 intersect, and end plates 5a and 5a and U-shaped plates 7a and 7a are attached to the respective corners. The dampers 1 and 1 may be fixed so as to cross each other on the diagonal of the frame 30. If comprised in this way, if the deformation | transformation of a building is the same, since the deformation amount of the viscoelastic damper 1 will become larger than the case of Fig.8 (a), a bigger damping | damping will be provided. According to the viscoelastic damper 1 of the present invention, since there is no concern about buckling, the configuration in which the viscoelastic damper 1 becomes long can be kept thin.
[0042]
Further, since the viscoelastic damper 1 can be thinned, two or more viscoelastic dampers 1 may be arranged on one frame 30 to give a larger attenuation.
[0043]
In the above description, the cross section of the viscoelastic damper 1 has been described as being cylindrical. However, since the viscoelastic body 3 is liquefied and poured, the viscoelastic body 3 can be wound around any cross section. The outer cylinder member 2 and the inner cylinder member 4 may be in a cylindrical shape having any cross section such as an ellipse, a square shape, or a star shape, as long as the member 5 can be enclosed. By doing so, various designs can be realized, and a relatively wide restraint area of the viscoelastic body 3 compared to the thickness of the viscoelastic damper 1 can be secured, so that the viscoelastic damper having a higher damping effect can be secured. Can be configured.
[0044]
【The invention's effect】
As described above, in the invention according to the first aspect, the shaft member can be configured not to buckle even when subjected to compression by locking the shaft member to the inner cylinder member in only one direction. The thickness can be designed regardless of the buckling strength. As a result, it is possible to configure a viscoelastic damper having a thin shape, and it is possible to arrange it in a place where it can be seen in the living space where the appearance of the design becomes a problem.
[0046]
In the invention according to claim 2 , the viscoelastic damper according to claim 1 can be manufactured, and in particular, there is an effect that a viscoelastic damper having good adhesion of the viscoelastic body can be easily manufactured even in a complicated cross section. .
[0047]
In the invention according to claim 3 , even if it is a viscoelastic damper that does not attenuate in the compression direction, it is possible to exert a vibration control effect. As a result, a vibration control structure using a thin viscoelastic damper is provided. There is an effect that can be provided.
[Brief description of the drawings]
FIG. 1 is a cross-sectional view in the axial longitudinal direction and in the lateral direction showing a schematic configuration of an embodiment of a viscoelastic damper according to the present invention.
FIG. 2 is a schematic sectional view in the longitudinal direction of the shaft for explaining the operation of the viscoelastic damper according to the present invention.
FIG. 3 is an explanatory diagram for illustrating a model for numerically calculating a load displacement characteristic of a viscoelastic damper according to the present invention.
FIG. 4 is a graph showing an example of a result of numerical calculation of load displacement characteristics of a viscoelastic damper according to the present invention.
FIG. 5 is a perspective explanatory view for explaining a manufacturing process of the viscoelastic damper according to the present invention.
6 is a perspective explanatory view for explaining a manufacturing step subsequent to FIG. 5. FIG.
FIG. 7 is a cross-sectional view in the axial longitudinal direction showing a schematic configuration of a modified example of the viscoelastic damper according to the present invention.
FIG. 8 is an explanatory view showing an embodiment of a vibration control structure using a viscoelastic damper according to the present invention.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Viscoelastic damper 2 Outer cylinder member 3 Viscoelastic body 4, 26 Inner cylinder member 5 Shaft member 5a End plate (locking part)
5b Mounting part (member to be mounted)
6 Front cover 7, 25 Rear cover 7a U-shaped plate (attached member)
9 Sealing material 12 Viscoelastic body model 13 Spring that is rigid only on the tension side 16 Restoring force characteristic 17 Beam 18 Columns 19a, 19b, 19c, 19d Gusset plate 30 Frame

Claims (3)

A cylindrical outer cylinder member;
A cylindrical inner cylinder member joined to the inner periphery of the outer cylinder member via a viscoelastic body;
In a state where one end portion is exposed from the outer cylinder member, the end portion is locked so as to move integrally with the inner cylinder member in a direction in which the end portion is axially pulled out from the outer cylinder, and the opposite direction. A shaft member provided so as to move separately from the inner cylindrical member,
A viscoelastic damper, wherein a member to be attached is provided at each of an end portion of the shaft member exposed from the outer cylinder member and an end portion of the outer cylinder member on the opposite side in the axial direction. A predetermined clearance is provided inside the cylindrical outer cylinder member, and the cylindrical inner cylinder member is disposed,
Pour hot melt viscoelastic body into the gap with them in a high temperature state,
After the cooling, a shaft member provided with a locking portion for locking with the inner cylinder member at one end is disposed inside the inner cylinder member,
A method for manufacturing a viscoelastic damper, wherein the other end of the shaft member is exposed so as to be movable in the axial direction, and both ends of the outer cylinder member are sealed. A vibration control structure using a viscoelastic damper in which at least two viscoelastic dampers according to claim 1 are attached to a frame of a building surrounded by beams and columns in a direction crossing each other.

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