Method for restraining vibration of a floor and apparatus therefor
BACKGROUND OF THE INVENTION 
     The present invention relates to a method and an apparatus for restraining a vibration of a floor. 
     Floors in a building vibrate when the building vibrates due to earthquakes, winds, traffics, and other vibration sources. Floors are induced to vibrate also because of vibration sources located on the floor. Modern buildings generally have more flexibility and less damping compared to conventional buildings by virtue of affluently flexible modern structural members and precise construction techniques. Consequently, modern buildings permit larger displacements than before, and vibration in modern buildings tend to become larger than in conventional buildings. Then, excessive vibration of floors may cause such various inconveniences and problems as misoperation of equipments installed on the floor and uncomfortable feeling of motion induced to the occupants etc. Reduction of vibration is desirable also to reduce vibrational loads exerted on the structural members of the building when the vibration source is located on the floor. 
     In order to resolve some of these inconveniences, present inventors have already proposed a vibration restraining apparatus for buildings by a Japanese Patent Application No. 62-241045, FIG. 1. By the Patent Application, disclosed is a vibration restraining apparatus comprising a tank and a liquid retained in the tank to be installed at a roofing of the building so as to restrain vibration of the building. As the building vibrates, vibrational energy of the building excites the liquid, having a sloshing natural frequency identical to a natural frequency of the building, to slosh in resonance with the building. Consequently, vibration of the building is restrained as the vibrational energy of the building is transmitted to the liquid. It was stated in the specification that the weight of the liquid retained in the tank had better be larger than 1% of the building so as to assure an effectiveness. 
     A problem as to the above-mentioned conventional apparatus and methods for restraining vibration of a building is that the apparatus requires a large space to be installed in and consequently the space is found, in general, only at the top of the building. 
     Another problem in conventional apparatus and methods is that a large number of such tanks have to be installed. It is because that the size of the liquid tank is relatively small in order to make the sloshing frequency identical to that of the building and because effective weight of the liquid has to be larger than 1% of that of the building. Another problem is that it is not easy to make sure that a prescribed amount of liquid is retained in each of the tanks. 
     On the other hand, there is a requirement to suppress vibration of a specific floor where precision instruments are installed such as computers. In some cases, vibration restraint of each floor is more effective or economic, and thus preferable. 
     In some other cases, vibration source is located on a specific floor and the floor had better be isolated so as not to transmit vibration to the building. 
     A conventional technique to reduce vibration of a floor is to support the floor from structural members of the building by resilient means. By virtue of the resilience of the support, natural frequency of the floor is lowered becomes far apart from that of the building. The support of the floor acts as a kind of isolation device. 
     A problem in this case is that relative displacement between the floor and the building tends to become large and cause various inconveniences on pipings and cables passing through the building and the floor. Another problem is that once a vibration occurs the vibration tends to continue long before being stabilized and give uncomfortable feeling to the occupants. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to a method and an apparatus for restraining a vibration of a floor by supporting the floor by a relatively flexible support and providing the floor structure with a reservoir retaining liquid therein and adjusting a sloshing natural frequency of the liquid so that it generally coincides with a natural frequency of the floor structure. 
     In achieving practical application of the present invention, the vibration restraining apparatus, which is to be attached to a floor, may comprise a reservoir defining at least one chamber for retaining a liquid having a free surface. 
     The liquid retained in the chambers slosh as the floor vibrates. Vibrational energy of the floor is transferred to the liquid and generates sloshing thereof. As a result, vibration of the floor is restrained due to the loss of the vibration energy. Vibration of the floor is restrained most effectively when a natural frequency of the sloshing coincides with a natural frequency of the floor structure. In other words, the floor and the liquid form a unitary oscillating system, and a fundamental vibration mode of the system is a mode wherein sloshing occurs together with a displacement of the building. Eigen mode of the oscillating system, as defined in a complex space, comprises a displacement of the sloshing 90 degrees out of phase with respect to the displacement of the floor. The effect is distinct even when an effective mass of the liquid is far less than that of the floor as far as the natural frequency of the sloshing coincides with that of the floor. Displacement of the floor in the fundamental mode of the unitary oscillating system is smaller than that of the floor without the liquid. Consequently, the vibration becomes smaller when the floor is provided with the vibration restraining structure. 
     In a primary aspect of the invention, vibration restraining apparatus comprises (a) a prescribed dimensions and secured to the floor structure; and (b) a liquid retained in the reservoir means, having a prescribed depth and a free surface; whereby making a sloshing natural frequency of the liquid being generally equal to the dry natural frequency of the floor structure corresponding to a condition in which the reservoir means without the liquid and equipments are loaded on the floor structure. In a secondary aspect of the invention, method for restraining vibration of a floor comprises steps of (a) attaching a vibration restraining apparatus to the floor structure, the apparatus comprising a reservoir means of prescribed dimensions; and (b) providing the reservoir means with a prescribed amount of liquid so that the liquid has a prescribed depth beneath a free surface at a top thereof; whereby adjusting a sloshing natural frequency of the liquid generally equal to the dry natural frequency of the floor structure corresponding to a condition in which the reservoir means without the liquid and equipments are loaded on the floor structure. 
     Further objects and advantages of the present invention will appear hereinafter. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows a conventional vibration restraining apparatus. 
     FIG. 2 shows an embodiment of a vibration restraining apparatus for a floor according to the present invention. 
     FIG. 3 is a plan view of the vibration restraining apparatus. 
     FIG. 4 is a vertical section of the vibration restraining apparatus. 
     FIG. 5 is a close-up vertical section of the vibration restraining apparatus. 
     FIG. 6 shows how the amount of water retained in the vibration restraining apparatus is adjusted. 
     FIG. 7 is a perspective view of an example of floor structure to which the vibration restraining apparatus is attached. 
     FIG. 8 is a side elevation view of a modified embodiment of the vibration restraining apparatus, vertically stood up on a floor panel. 
     FIG. 9 is a plan view of a modified embodiment of the vibration restraining apparatus. 
     FIG. 9A is a cross-sectional view of the vibration restraining apparatus of the present invention, taken along line 9A--9A in FIG. 9. 
     FIG. 9B is a cross-sectional view of the vibration restraining apparatus of the present invention, taken along line 9B--9B in FIG. 9. 
     FIG. 10 is an oscillatory system modelizing a floor and a vibration restraining apparatus. 
     FIG. 11 shows transfer functions of a floor with and without a vibration restraining apparatus. 
     FIGS. 12 (A) and (B) show vibration time histories calculated for a floor with and without a vibration restraining apparatus. 
     FIG. 13 shows a modified vibration restraining apparatus. 
     FIGS. 14 to 17 show mechanisms for feeding and draining water to and from the reservoirs. 
     FIGS. 18 to 20 show a modified reservoir. 
     FIG. 21 shows a further modified reservoir. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Preferred embodiments of the present invention will now be explained in detail referring to the attached drawings. 
     FIG. 7 is a perspective view of an example of a floor structure to which a vibration restraining apparatus of the present invention is to be provided. A grid 3 is supported from a concrete slab 40 by means of floor columns 2 which are anchored into the slab 40. The grid 3 comprises longitudinal members and transversal members which are intersecting and connected to each other at their junctions. The grid 3 is connected to the floor columns 2 at the junctions. Floor panels 4 are placed on the grid generally in a detachable manner. The floor structure is one of those which are often used in computer rooms etc. in order to secure a cable space beneath the floor panel. 
     FIGS. 2 and 3 show a first embodiment of the vibration restraining structure according to the present invention together with a floor structure. The floor structure comprises a floor panel 4 supported from a concrete slab 1 of a building by means of four floor columns 2. Beneath the floor panel 4 is attached a vibration restraining apparatus 10. The vibration restraining apparatus 10 comprises four side walls 14 connected to each other at a pair of opposing edges to define a rectangular parallelepiped inner space, and a bottom plate 16 closing a lower end of the inner space. A lower edge of the side walls 14 is connected to each edge of the bottom plate 16. An upper edge of each of the side walls 14 is connected to a lower surface of the floor panel 4. Vertical partition walls 12 and a horizontal partition wall 17 are provided in the inner space to separate the inner space into chambers 18. Communication holes 15 are formed in the vertical separation walls 11 at a lower portion of each chamber 18 so that the chambers 18 located at a same elevation are communicating to each other through the holes 15. Inlet apertures 12 is formed in the floor panel 4 so as to supply and drain liquid, such as water, to and out of the chambers 18. 
     As shown in FIG. 4, a pipe 13 is provided in an upper chamber 18, an upper end thereof being attached to the floor panel 4, a lower end thereof being attached to the horizontal separation plate 17. A leveling aperture 13a is formed at a prescribed position of the pipe. A liquid feeding hole 14 is formed in the horizontal separation plate 17 closing a bottom of the tube 13. Therefore, the upper chamber 18 is communicating with a lower chamber 18 through the tube 13 by means of the leveling aperture 13a and the liquid feeding hole 14. FIG. 5 shows the pipe 13 in more detail. 
     The floor structure has a natural frequency, which is referred to as a dry natural frequency hereinafter, which is a natural frequency of the floor when equipments are installed thereon and the attached vibration restraining apparatus containing no liquid therein. The dry natural frequency is approximately determined by a total stiffness of the floor columns 2 and a total weight supported by the columns 2. 
     Water is supplied to the apparatus as follows. 
     First, a prescribed amount of water is poured in the reservoir through the inlet aperture 12. The water is retained in the upper chambers 18. Then, an edge of the apparatus 10 farthest from the pipe 13 is lifted up to incline the apparatus 10. Consequently, a portion of water is drained through the pipe 13 and retained in the lower chambers, FIG. 6. By selecting the angle of inclination properly as illustrated in, the amount of water drained into the lower chambers 18 is made to be equal to that retained in upper chambers. After resetting the apparatus horizontally, water levels in the upper chambers 18 and lower chambers 18 becomes identical to each other by means of communication holes 15. The water level can be adjusted by determining selectively the amount of water poured to the reservoir and the angle to tilt the apparatus thereafter. 
     Dimension of the chambers 18 and depth of water retained in the chambers 18 are determined so that the sloshing natural frequency of the water is generally equal to the above-mentioned vacant natural frequency of the floor structure. 
     In a modified embodiment, the leveling aperture 13a is located at a level at which the water surface has to be maintained. In such a case, it is enough to simply pour a prescribed amount of water to the reservoir. Redundant water drips from the upper chambers 18 to the lower chambers 18 through the leveling aperture 13a and a prescribed amount of water is retained in both the upper and lower chambers 18 as a result. 
     FIGS. 8 and 9 and 9A and 9B show a further modified embodiment of the vibration restraining apparatus. In the embodiment, a rectangular side wall 21 and a plurality of cylindrical wall reservoirs 20 having a common rectangular bottom plate 75, closing their lower end, are secured to the floor panel 4. As shown in FIG. 8, wall of each reservoir 20 is in contact to each other to form a closed space 71 thereby. Inside the reservoir 20, a plurality of partition walls 73 are provided parallel to the floor panel 4. As illustrated in FIGS. 9A and 9B, each reservoir 20 has a wall surface which includes an upper and a lower end. Notably, the upper and lower ends of the cylindrical wall surface touch the floor panel 4 and the bottom partition walls 73 as shown. Thus a closed space inside the reservoir 20 is divided into a plurality of short cylindrical chambers by virtue of the partition walls 73. Wall of the cylindrical reservoir 20 has first plurality of slits 70, formed at the lower end of each chamber, opening toward the closed space 71. Each chamber is communicating with the closed space 71 through the slit 70. A wall of each reservoir 20 and a pair of intersecting tangential side walls 21 define a generally triangular prismatic closed space 72. The wall of the cylindrical reservoir 20 has a second plurality of slits 74 (not shown) at the upper part of each of the chambers through which the chambers communicate with the prismatic space 72. A feed water line 22 is provided in the prismatic space 72 so that the prismatic closed space 72 is connected to a water supply means (not shown) therethrough. At the opposite corner of the vibration restraining apparatus, another feed water line 22 is provided. The feed water lines 22 are used not only for feeding water to the apparatus 1 but also to drain water from the apparatus 1. 
     Way of supplying a prescribed amount of water to each of the reservoirs 20 is explained hereinafter. 
     First, the vibration restraining apparatus 1 is held in an upright position as shown in FIG. 8, in particular. A prescribed amount of water is supplied to the apparatus through one of the feed water lines 22. Then, the apparatus is turned down so that the horizontal partition walls become vertical. While the apparatus is at this position, as shown in FIG. 8, the water flows into half of the chambers which are lower than the other half of chambers through the plurality of second slits 74. Next, the apparatus is set up again to the upright position. The water having been retained in the lower chamber flows into the other chambers through the plurality of first slits 70. As a result, all chambers have an identical water depth, consequently, an identical sloshing natural frequency. In a still further modified embodiment, a rectangular separation wall replaces four partition walls separating inner space of reservoirs and separates the triangular prismatic spaces also. In this case, abovementioned feed water means 12 are used to provide each triangular prismatic space with water. Method of providing the apparatus with water is similar to the above case. 
     Preferably, flanges 64 are secured to the inner surface of the side wall 20 so as to obstruct any swirling motion of the water. 
     FIGS. 13 to 17 show modified embodiments of the present invention. FIG. 13 shows a vibration restraining apparatus 1 which comprises a cylindrical side wall 40 secured to a floor panel 43 and a bottom plate 41, the wall 40 and the bottom plate 41 defining an inner cylindrical space thereby. Partition walls are provided within the inner space to define thereby chambers 42. Each separation wall 44 and the bottom plate 41 are provided with a pair of feed water apparatus 45 comprising a tubular member 40. The tubular member is attached to the partition wall 44 at its lower end. The tubular member 40 is standing as a cantilever on the attached lower end. There is a gap 47 of a prescribed distance between the upper end of the member 40 and a partition wall above the end, FIGS. 13 and 14. A feed water aperture 46 is formed in the partition walls 44 so that an inner space within the tubular member 40 is communicating with the chamber beneath the partition wall 44 to which the member 40 is attached through the aperture 46. In the floor panel 43, a feed water hole 46 is formed at a location above the tubular member 40. 
     FIG. 15 shows another embodiment of the feed water apparatus which comprises a feed water line 50 passing vertically through the chambers 42. A regulation aperture 51 is formed in the feed water line 50 near an upper partition wall 40 defining each chamber 42. Same as in the above case, the inner space of the feed water line 50 communicates with the chambers 42 through the the regulation chambers 51. 
     For supplying the chambers 42 with prescribed amount of water, sum of the prescribed amount of water is first poured in the vibration restraining apparatus 1 through the feed water hole 46. The water is retained in a or some of the lower chambers 42. Then, the apparatus is rotated by 90 degrees so that the horizontal wall 44 is retained vertically. In the position, one of the tubular member 40 or the feed water line 50 is retained lower than a water surface. Consequently, amount of the water different from a chamber 42 to the other is regulated automatically. The vibration restraining apparatus 1 is restored. Then, the amount of water retained in the chambers 42 remains unchanged. Thus, the feed water apparatus 45 simplifies much the procedure to supply the chambers 42 with a prescribed amount of water. 
     FIGS. 16 and 17 show a plugging apparatus for closing the communication of chambers 42 after a prescribed amount of water is supplied in the chambers 42. The apparatus comprises an elongated elastic tubular member 52 having an inlet (not shown). The tubular member 52 is smaller in diameter than the inner space within the tubular member 40 and the feed water line 50 while it is not inflated and expands in diameter when inflated so that the diameter thereof becomes larger than the inner diameter of the tubular member 40 and the feed water line 52 closing the gap 47 or the regulation aperture 51. 
     When using the plugging apparatus, water is poured in the vibration restraining apparatus 1 and a prescribed amount of water is distributed to each chamber according to a procedure as above-mentioned. Then, the plugging apparatus is inserted in the tubular members 40 or the feed water line 50 as it is not inflated. Then the elastic tubular member 52 is inflated to closely come in contact with an inner surface of the tubular members 40 or the feed water line 50. At a same time, the elastic tubular member 52 plugs the gaps 47 or the regulation apertures 51. Therefore, water retained in the chambers is refrained from moving to the other chambers and to be evaporated. Thus, a reliability of the system is increased. 
     In a further modified embodiment shown in FIG. 18, separation wall 61 has a groove 60 formed in a lower surface thereof diametrically connecting a pair of pertures 22 formed at opposing edges of the all 61. Depth of the groove 60 increases gradually from center thereof to both edges. Therefore, bubbles captured in a chamber are lead by the groove 60 to the apertures 22 and evacuated therethrough. 
     In a still modified embodiment shown in FIGS. 19 and 20, the upper surface of the plate 3 is flat and the thickness thereof decreases from edges to a groove 7 formed diametrically in the lower surface thereof. By virtue of this inclination of the lower surface, bubbles in the chamber can be gathered and evacuated more easily. In this embodiment also, depth of the groove increases from center thereof to the outer edges to lead the bubbles. 
     FIG. 21 shows an embodiment wherein a plurality of flanges 64 are provided inside the chamber so as to obstacle the water flow in the chamber and increase damping coefficient of sloshing. 
     Operation of the embodiment will now be explained. 
     The floor structure including the equipments installed on the floor and the vibration restraining structure are modelized simply as shown in FIG. 10. Vibrational characteristics will be discussed hereinafter with reference to the model of FIG. 10 which is a so called two-degree-of-freedom oscillating system. A mass-spring-dashpot system 30 represents schematically vibrational characteristics of the floor structure. A mass 32, a spring 33 and a dashpot 34 represent effective mass, effective stiffness and effective damping of the mode, respectively, which are determined by the structural property of the floor structure and the weight of the equipments supported by the floor. A mass-spring-dashpot system 31 represent a certain mode of the vibration restraining structure, more specifically, sloshing characteristics of the liquid in the vibration restraining structure. A mass 35 and a spring 36 are determined by an effective mass and an effective spring of the sloshing which are functions of geometrical features of chambers in which the liquid is retained, depth of the liquid, and material of the liquid. Because these values are identical throughout chambers, effect of the sloshing in all the chambers is represented by a single mass-spring-dashpot system 31. Property of dashpot 37 is determined mainly by viscosity of the liquid and geometry of the reservoir. 
     As far as the effective weight of the liquid is lower than 2% of the effective weight of the floor structure, coupling effect on the natural frequencies of the floor structure and sloshing is negligible. Therefore, when the natural frequency of the floor structure coincides with that of sloshing, so does the natural frequency of the coupled two-degree-of-freedom system. Natural frequencies of sloshing Fs are determined as follows. 
     
         Fs=ks g tanh(ks h)/2 pi 
    
     ks: (2n-1) pi/2a 
     n: order of the mode concerned 
     pi: ratio of a circumference to its diameter 
     2a: width of the tank in the direction of oscillation 
     g: gravity 
     h: depth of the water. 
     Natural frequency of the floor structure Fb is determined as follows. 
     
         Fbn=Kn/Mn/2 pi 
    
     wherein 
     Kn: modal stiffness of the floor structure 
     Mn: modal mass of the floor structure. 
     Therefore, it becomes possible to set a natural frequency of sloshing equal to the natural frequency of the floor structure by virtue of the above-mentioned equations. 
     Because the sloshing resonates with the vibration of the floor structure when the floor structure vibrates due to earthquakes etc. and the vibrational amplitude of the floor structure is reduced by virtue of the vibration restraining structure. 
     In the above explanation, vibrational characteristics of the floor structure was represented by the first mode and the effects of the vibration restraining structure were explained on the basis for a simplicity of explanation. But application of the vibration restraining structure is not restricted to restrain the first mode but the vibration restraining structure is also applicable to restrain any other modes. In such cases, the vibration restraining structure had better be installed where the floor structure displaces largely in the mode to be reduced. Consequently, the restraining structure is installed at an or at a plurality of intermediate floors. 
     Natural frequency of the floor structure differs naturally according to the mode. Therefore, geometry of the chamber retaining the liquid is determined so as to equate the sloshing natural frequency to the natural frequency of the floor structure of the concerned mode. 
     Further, because the vibration restraining structure according to the present invention is compact, the structure can be installed under any floor structure. 
     Because the vibration restraining structure contains a considerable amount of liquid, the structure is effective as a sound insulation floor and a fireproof floor also. 
     EXAMPLES 
     Effects of the vibration restraining structure of the present invention have been verified by earthquake response analyses of floor structures with and without the vibration restraining structure. The structure for analyses is a 5-story floor structure model and a vibration restraining structure located at the top of the floor structure as shown in FIG. 1. The building model has a mass of 400 kg at each floor. First natural period (reciprocal of first natural frequency) of the floor structure is 0.41 seconds. Total effective weight of the liquid is 52 kg and the first sloshing period thereof is 0.41 seconds. 
     FIG. 12(A) shows a displacement time history at the fourth mass from bottom of the floor structure without the vibration restraining structure responsive to the El Centro (NS) earthquake record. FIG. 12(B) shows a corresponding time history of the floor structure provided with the vibration restraining structure. Comparison of the earthquake responses elucidates that the response displacement of the floor structure is reduced by virtue of a vibration restraining structure. Yet, vibration stabilizes more rapidly when the floor structure is provided with the restraining structure. 
     Further analytical study shows that the effect of the vibration restraining structure is distinct when the effective mass of sloshing is larger than 0.5% of the effective mass of the floor structure. It is also shown that when the effective mass of sloshing exceeds 2% of that of the floor structure, natural frequency of the coupled system becomes different from the uncoupled structures and the vibration restraining effect decreases. In such cases, it is required to adjust sloshing frequency taking into account of the coupling effect of the structures. When the sloshing natural frequency is correctly adjusted, the vibration restraining effect can be obtained also in these cases. 
     FIG. 11 shows a Fourier spectrum of the response time histories. When the floor structure is not provided with the apparatus, the transfer function has a distinct peak which means that the floor structure magnifies a specific frequency component f1 contained in the input vibration source. On the contrary, in case wherein the floor is provided with a vibration restraining apparatus, the peak splits into to peaks and the height of the peaks is far lower than the distinct peak in the first case. As a result the area of the spectrum is smaller in the second case than in the first case. The results coincides with a characteristic observed in the time histories, that is, when the floor is provided with the apparatus, large response displacement in a form of a simple harmonic oscillation observed in the first case is reduced in the second case and as a result, amplitude of the response is much smaller in the second case than in the first case.