Damping device for tower-like structure

A damping device for a tower-like structure, includes a liquid column tube having an arbitrary shape and a pair of opposite upstanding end portions thereof where liquid levels are formed, and an orifice provided at an intermediate portion within the liquid column tube, the liquid column tube being mounted upon the tower-like structure. The damping property of the damping device can be quantitatively defined by employing the orifice. Furthermore, as the intermediate portion of the liquid column tube defined between the opposite upstanding end portions can be appropriately configured, the installation space for the damping device is optimized.

FIELD OF THE INVENTION 
The present invention relates to a damping device for suppressing vibration 
of a tower-like structure due to the wind or earthquake. 
BACKGROUND OF THE INVENTION 
Recently, in connection with techniques for suppressing vibrations of a 
tower-like structure such as, for example, a high-rise building or a tower 
of a suspension bridge or a cable-stayed bridge due to the wind or an 
earthquake, there has been proposed various damping devices based upon the 
principle of a dynamic vibration damper. 
Generally, the principle of the dynamic vibration damper is to absorb the 
vibrational energy of the structure by providing a natural frequency tuned 
to a natural frequency of the structure and also by providing a suitable 
damping mechanism. The principle has been realized in various forms. 
A typical form employs the combination of a mass, a spring and a damper. 
However, such a dynamic damper has the following problems: 
(1) It is hard to adjust the natural frequency. 
(2) Maintenance is required for aged deterioration of the spring, the 
damper or the like. 
(3) The structural composition and the mechanism are complicated. 
(4) Space for accommodating the damping device is limited. 
Recently, as one means for solving the above problems, there has been 
proposed in Japanese Patent Laid-open Publication Nos. 62-101764, 
62-292943 and 63-172092 a dynamic vibration damper which utilizes a liquid 
free surface wave motion (sloshing) within a liquid-filled tank. In 
accordance with this dynamic vibration damper, the natural frequency of 
the sloshing is tuned to that of the structure, and the damping mechanism 
is formed by disposing a porous member or the like within the liquid as an 
obstacle against the motion of the liquid. However, such a dynamic 
vibration damper likewise has the following problems: 
(1) The sloshing action in response to the vibration having a large 
amplitude is very complex, and it is therefore hard to calculate the 
damping effect from the natural frequency and the damping properties. 
(2) The damping properties of the porous member or the like is indefinite, 
and the calculation thereof is difficult. 
(3) The space for installing the damping device is limited due to the size 
or the like of the liquid-filled tank. 
OBJECT OF THE INVENTION 
It is an object of the present invention to provide a damping device which 
may precisely exhibit the desired damping function and which may increase 
the degrees of freedom by means of which the damping device may be 
installed within the mounting space defined within the structure. 
SUMMARY OF THE INVENTION 
According to the present invention, there is provided a damping device for 
a tower-like structure, comprising a liquid column tube having an 
arbitrary shape and a pair of opposite upstanding end portions thereof 
where liquid levels are formed, and an orifice provided at an intermediate 
portion of the liquid column tube, the liquid column tube being mounted 
upon the tower-like structure. 
When the tower-like structure is vibrated, the liquid within the liquid 
column tube is oscillated in the longitudinal direction of the tube so as 
to cause vertical vibration of the liquid levels. At this time, the 
oscillation of the liquid is suitably damped by means of the orifice so as 
to thereby suppress the vibration of the structure. As the motion of the 
liquid is one-dimensional, the damping factor can be easily controlled.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
There will now be described some preferred embodiments of the present 
invention with reference to the drawings. 
Referring to FIG. 1 which shows a preferred embodiment of the present 
invention, reference numeral A designates a damping device for a 
tower-like structure (not shown), which will be hereinafter referred to as 
a structure. The damping device A is comprised of a liquid column tube 1 
to be located at a position of the structure where displacement due to 
vibrations are large, a liquid 2 contained within the liquid column tube 
1, and an orifice 3 fixedly provided within the liquid column tube 1. A 
pair of liquid levels 2a of the liquid 2 are present at opposite 
upstanding end portions of the liquid column tube 1. The cross sectional 
shape of the liquid column tube 1 may be optional such as, for example 
circular or rectangular (square, oblong, or the like). Furthermore, the 
liquid column tube 1 may be optionally curved in the longitudinal 
direction thereof. 
When the structure is vibrated in either one of the directions designated 
by means of the double-headed arrow S shown in FIG. 1, the liquid levels 
2a are oscillated in the vertical directions of the double-headed arrows 
B. While the vertical motion of the liquid is damped by means of the 
damping ability of the liquid 2 itself, it is primarily damped by means of 
the orifice 3. 
Vibrational energy of the structure is absorbed by means of the oscillating 
motion of the liquid 2 within the liquid column tube 1 so as to damp the 
vibration of the structure. Suitable setting of the damping factor of the 
orifice contributes to enhanced efficiency of absorption of the 
vibrational energy. A plurality of orifices 3 may be provided. 
Such a damping device will be hereinafter referred to as TLCD (Tuned Liquid 
Column Damper). 
Letting S and B denote the displacements of the structure and the liquid 
levels 2a, respectively, an equation of motion of the liquid 2 within the 
liquid column tube constituting the damping device is expressed as 
follows: 
EQU .rho.ALB+(1/2).rho.AK.vertline.B.vertline.B+2.rho.AgB=-.rho.ACS 
where .rho. is the density of the liquid; g is the gravitational 
acceleration; A is the sectional area of the liquid column tube 1; L is 
the length between both liquid levels 2a along the liquid column tube 1; C 
is the horizontal distance between both liquid levels 2a; and K is a 
coefficient (pressure loss coefficient) depending upon the opening ratio 
of the orifice 3. Furthermore, B is the first derivative of B with respect 
to time, and B and S are the second derivatives of B and S with respect to 
time, respectively. 
In the above equation, the right-hand side of the equation represents a 
term for vibrating the liquid 2 which term can also function as a reaction 
for suppressing the vibration of the tower-like structure. The first and 
third terms on the left-hand side of the equation represent a mass effect 
and a spring effect, respectively. From both terms, a natural period T of 
the vibration of the liquid column can be obtained as follows: 
EQU T=2.pi..sqroot.L/2g 
The second term on the left-hand side of the equation represents a damping 
property of the vibrating of the liquid 2 as determined by means of the 
orifice 3 provided within the liquid column tube 1. The damping property 
plays an important role in connection with the damping operation for the 
vibration of the structure. That is, in order to exhibit a sufficient 
damping effect by means of the vibration of the liquid column and thereby 
dampen the vibration of the structure, the damping property must be 
quantitatively defined at an optimum value. In the prior art damping 
device including a porous member of the like, the damping property could 
not be easily quantitatively defined. To the contrary, in view of the fact 
that the damping device of the present invention employs an orifice, and 
the pressure loss coefficient K is given as a known constant, the 
quantitative definition of the damping property can be easily and reliably 
determined. Thus, according to the present invention, the calculation of 
the damping effect and the design of the TLCD can be easily and reliably 
achieved by providing the orifice within the liquid column tube. 
FIG. 2 illustrates an example of the calculation of a response curve which 
indicates that the vibration of the tower-like structure can be damped by 
means of the provision of the TLCD. In this graph, the ordinate axis 
denotes the response magnification of the tower-like structure, while the 
abscissa axis denotes an input to natural frequency ratio which is defined 
by means of the relationship frequency of an external force)/(natural 
frequency of the tower-like structure). 
In this manner, the equation of motion can be simply an reliably 
quantitatively defined. Therefore, the TLCD serving as the damping device 
can be simply designed as shown by charts in the following manner. 
A simple designing method for the TLCD will now be described. The natural 
period T of the vibration of the liquid column tube is obtained as 
mentioned above. On the other hand, the natural frequency of the structure 
can be obtained according to data used in designing the structure. 
Accordingly, the length L is decided in such a manner that the ratio 
between the natural frequency of the structure and the natural frequency 
of the TLCD or the liquid column tube, that is, the tuning ratio is 
approximately to 1. 
FIG. 3 is a graph showing the relationship between a response value R.sub.D 
(shown by means of the ordinate axis) indicative of a displacement of the 
liquid column due to the vibration of the structure and a damping factor 
h.sub.D of the damping device (shown by means of the abscissa axis). The 
relationship varies with a change in the opening ratio .alpha. of the 
orifice. As shown in the graph, the opening ratio .alpha..sub.1 is larger 
than the opening ratio .alpha..sub.2, and the opening ratio .alpha..sub.2 
is larger than the opening ratio .alpha..sub.3. As is apparent from the 
graph, R.sub.D is substantially proportional to h.sub.D, and the smaller 
the opening ratio .alpha., the smaller the gradient of the straight line 
(which is inclined with respect to the abscissa axis), that is, the larger 
the damping factor. 
FIG. 4a is a graph showing the relationship between a response value 
R.sub.S of the structure and the damping factor h.sub.D of the damping 
device. In this graph, .mu. (.mu..sub.1 &lt;.mu..sub.2 &lt;.mu..sub.3) 
represents the ratio of (effective mass of the damping 
device)/(generalized mass of the structure). As is apparent from the 
graph, the response value R.sub.S decreases with an increase in the 
damping factor h.sub.D up to a predetermined value, and increases with a 
further increase in the damping factor h.sub.D from the predetermined 
value. R.sub.SL designates a permissible limit of the amplitude of the 
structure, and a dotted line extending along the permissible limit 
R.sub.SL and extending parallel to the abscissa axes intersects some of 
the curved lines. According to the value of .mu. in this case, the 
effective mass of the damping device, that is, the size of the damping 
device can be determined. In the case of .mu.=.mu..sub.2, the dotted line 
intersects the curved line of .mu..sub.2 at two points h.sub.DA and 
h.sub.DB. Accordingly, if the damping factor h.sub.D falls within the 
range defined between h.sub.DA and h.sub.DB, the value of the response 
structure must not be greater than the permissible limit R.sub.SL. An 
optimum value of the damping factor h.sub.D is represented by means of the 
value h.sub.Dopt present at an intermediate point between h.sub.DA and 
h.sub.DB. 
FIG. 4bis a graph showing the relationship between the response value 
R.sub.D (shown by the ordinate axis) of the damping device due to the 
vibration and the damping factor h.sub.D (shown by means of the abscissa 
axis) of the damping device. As is apparent from the graph, the 
relationship varies with a change in the value of .mu.. It is appreciated 
that the larger the damping factor h.sub.D, the smaller the response value 
R.sub.D, and that the smaller the damping factor h.sub.D, the larger the 
response value R.sub.D. R.sub.DL designates a permissible limit for the 
response value of the liquid column, and it depends upon the movable range 
of the liquid levels 2a which range also depends upon the clearance of the 
damping device. R.sub.DO designates the response value of the liquid 
column at the optimum damping factor h.sub.Dopt in the case of .mu..sub.2, 
and it is set so as to be smaller than the permissible limit R.sub.DL. 
FIG. 4c is a graph showing the relationship between the response value 
R.sub.D (shown by means of the ordinate axis) of the damping device due to 
the vibration and the damping factor h.sub.D (shown by means of the 
abscissa axis) of the damping device, wherein the damping factor h.sub.D 
varies with a change in the opening ratio .alpha. of the orifice. It is 
appreciated that the intersection between a horizontal dotted line 
corresponding to the optimum response value R.sub.DO and a vertical dotted 
line corresponding to the optimum damping factor h.sub.Dopt obtained in 
FIG. 4a lies upon the straight line .alpha..sub.2. 
Thus, the optimum damping factor h.sub.Dopt and the other characteristic 
values of the damping device are determined. 
Each of the graphs shown in FIGS. 3 and 4 can be obtained by means of 
calculations regarding the liquid column tube and the orifice, and they 
are clearly quantitatively defined. In the prior art damping device 
utilizing sloshing, such a quantitative definition of the damping factor 
was difficult to obtain because of the complexity of the sloshing motion 
and the damping property by means of the porous member. According to the 
present invention, the quantitative definition of the damping factor can 
be easily carried out by utilizing the orifice within the liquid column 
tube so as to improve the performance of the damping device and render the 
manufacture thereof easy. 
FIG. 5 is a schematic side elevation of a preferred embodiment of the 
present invention in the case of a primary vibration mode, wherein the 
damping device A is normally located within the vicinity of the top of a 
tower-like structure 4 where the greatest effect can be exhibited. On the 
other hand, in the case of a secondary vibration mode, the damping device 
may be located within the vicinity of an intermediate portion of the 
structure since the amplitude may become maximized at this location. 
Particularly in the case that the structure is a tower of a suspension 
bridge having a base at its lower end which is fixed at its upper end by 
means of wires, the damping device is located at the intermediate portion 
of the tower where the displacement amplitude becomes a maximum. 
FIG. 6 is a perspective view showing the alignment of the liquid column 
tube 1 in the case that an obstacle 5 is present upon the tower-like 
structure 4 at a position where the damping device A is to be located. In 
the prior art, if such an obstacle 5 is present, the damping device could 
not be located upon the structure because the obstacle 5 is in the way. In 
other words, it was necessary to assure a space for the exclusive use by 
means of the damping device. According to the present invention, it is 
only necessary to provide the liquid column tube 1 with a predetermined 
length. The shape of the tube 1 except at the opposite ends thereof is 
configured at the planner's discretion. For example, even when the 
alignment is bypassed as shown, the natural frequency of the liquid column 
tube 1 is not affected. Accordingly, it is unnecessary to assure a space 
for the exclusive use by means of the damping device. Additionally, since 
water is normally used for the liquid 2, it can also serve various other 
purposes such as, for example, fire-fighting or the like. 
FIGS. 7a and 7b show an embodiment wherein a pair of damping devices A are 
mounted upon a spherical tower-like structure such as, for example, an 
elevated tank. The damping devices A of the TLCD are provided so as to 
extend from the bottom of the tank toward the top thereof and along the 
peripheral contour in such a manner as to be crossed at right angles with 
respect to each other as shown in FIG. 7b . In this embodiment, the 
vibration of the tank in all directions upon the mounting surface of the 
tank can be damped. 
FIG. 8 shows an embodiment wherein a plurality of damping devices A are 
mounted upon the spherical tank 6. This embodiment is effective in the 
case that the natural period of the vibration of the overall structure is 
short as compared with that of the embodiment of FIGS. 7a and 7b. 
FIG. 9 shows an embodiment wherein a pair of damping devices A comprising a 
TLCD are located at positions upon the structure 4 under construction 
where the vibration tends to occur. Since the tower-like structure 4 
suffers vibration due to the wind or an earthquake not only after the 
completion of construction but also during construction, it is preferable 
to mount the damping device upon the structure 4 while the same is under 
construction. Reference numeral 7 designates a crane for constructing the 
tower-like structure. 
FIG. 10 shows an embodiment wherein the damping device A is located within 
a crane 8 for constructing the tower-like structure 4 under construction. 
In the embodiment shown in FIG. 9, it is necessary to change the position 
of the damping device in accordance with the increased elevation of the 
structure 4. To the contrary, in the embodiment shown in FIG. 10, the 
crane 8 is a creeper crane or a similar crane which can be lifted in 
accordance with the increased elevation of the tower-like structure 4. 
Accordingly, the damping device A located within the crane 8 is maintained 
at the top portion of the tower-like structure 4 at all times until 
completion of construction. That is, it is unnecessary to independently 
move the damping device per se. 
FIG. 11 shows an embodiment wherein a plurality of damping devices A are 
mounted upon an observatory which is another example of the tower-like 
structure 4. The damping devices A are located upon window frames of the 
observatory in such a manner as to surround the same and by taking into 
consideration the natural period of vibration, limited space and 
esthetics. With this arrangement, the vibration of the observatory in 
every horizontal direction can be damped. 
FIGS. 12a and 12b show an embodiment wherein a variable orifice 11 
adjustable in its opening ratio is used, with the orifice aperture being 
shown at 9a. The variable orifice 11 is composed of a pair of fixed 
members 10 and a pair of movable members 9. The fixed members 10 are fixed 
on opposite sides within the liquid column tube 1 having a rectangular 
cross-section. The movable members 9 are slidably engaged between the 
fixed members 10 in such a manner as to be movable in the directions of 
the double-headed arrows shown in FIGS. 12a and 12b. The movable members 9 
are inserted through the opposite walls of the liquid column tube 1, and 
are sealed by a known watertight structure. A driving means (not shown) is 
connected to one or both of the movable members 9, and an operating handle 
(not shown) is connected to the driving means so as to move one or both of 
the movable members 9 into and out of the liquid column tube 1. In 
operation, when the handle is operated so as to move one or both of the 
movable members 9 in order to change the aperture 9a defined between the 
movable members 9, the opening ratio of the variable orifice 11 is 
adjusted to a desired value. 
FIGS. 13a and 13b show another embodiment of the variable orifice 11, 
wherein the fixed member 10 and the lower movable member 9 shown in FIGS. 
12a and 12b are omitted. That is, the upper movable member 9 alone is 
slidably inserted through the wall of the liquid column tube 1. 
FIG. 14 shows a further embodiment of the variable orifice 11, wherein the 
movable member 9 is rotatably supported upon a shaft 9b within the liquid 
column tube 1. The movable member 9 has a size large enough to close the 
cross-section of the liquid column tube 1. 
FIG. 15 shows a further embodiment of the variable orifice 11, wherein a 
pair of movable members 9 each having a segmental cross-section are 
rotatably provided within the liquid column tube 1 in opposed relationship 
with respect to each other. The liquid column tube 1 is formed with a pair 
of arcuate recesses 1c for receiving the segmental movable members 9. The 
movable members 9 are connected with each other outside the liquid column 
tube, and are supported upon a rotating shaft (not shown). 
Thus, the use of the variable orifice 11 provides an easy change in the 
damping factor h.sub.D of the damping device. Furthermore, when the amount 
of the liquid to be charged into the liquid column tube 1 is adjusted so 
as to change the length L of the liquid column between the opposite liquid 
levels 2a along the liquid column tube 1 in addition to the change in the 
damping factor h.sub.D, the characteristics of the damping device can 
easily follow any change in conditions of the structure such as, for 
example, a change in the natural frequency even in the case that the 
damping device is applied to the structure under construction. 
FIGS. 16a and 16b show different embodiments wherein two liquid column 
tubes 1 and 1' constituting the damping device of the present invention 
are combined so as to be arranged in a perpendicular relationship with 
respect to each other. Such perpendicular arrangement is intended to meet 
the requirement such that any vibration in two or more directions as well 
as in one direction will be absorbed. In the embodiment shown in FIG. 16a, 
the two liquid column tubes 1 and 1' are arranged in a T-shaped 
configuration. Reference characters B and B' denote distances between the 
opposite upstanding portions of the liquid column tubes 1 and 1', 
respectively (which distances will be hereinafter referred to as 
upstanding distances), and reference characters W and W' denote the widths 
of the liquid column tubes 1 and 1', respectively. Accordingly, it is 
necessary to provide an installation space of B'.times.(B+W'), and it is 
also necessary to charge the liquid 2 in an amount corresponding to the 
sum of the volumes of the liquid column tubes 1 and 1'. If the structure 
is large, not only the lengths of the liquid column tubes 1 and 1' but 
also the widths thereof become several meters, resulting in enlargement of 
the installation space and the amount of the liquid required. 
In the embodiment shown in FIG. 16b, the two liquid column tubes 1 and 1' 
are arranged in a crossed configuration so as to form a central 
intersecting conduit portion 1a as a common conduit portion of both the 
tubes 1 and 1'. A desired number of the orifices 3 are provided within the 
liquid column tubes 1 and 1'. In this embodiment, it is necessary to 
define an installation space of B.times.B'. Accordingly, the installation 
space can be reduced as compared with that of the embodiment shown in FIG. 
16a. Furthermore, the amount of the liquid 2 can be reduced by the volume 
of the intersecting conduit portion 1a. The intersecting conduit portion 
1a may also be formed at end portions of the liquid column tubes 1 and 1'. 
FIG. 17 shows an embodiment wherein the opposite upstanding portions of the 
liquid column tube are connected to each other so as to form a closed-loop 
type liquid column tube 1. The closed liquid column tube 1 is formed with 
a filler opening to be closed by means of a lid 12 for charging the liquid 
2 or an inert gas to be hereinafter described, into the tube 1. In the 
embodiment shown in FIG. 1, the opposite upstanding portions of the liquid 
column tube 1 are open at their upper ends. Accordingly, the liquid in the 
tube 1 vaporizes after a long period of time so as to cause a reduction of 
the damping effect. Furthermore, if an unexpected vibration having a large 
amplitude is induced within the liquid column tube 1, the liquid can 
overflow. Moreover, rust and corrosion tend to be generated upon the inner 
wall of the liquid column tube 1 in the vicinity of the liquid levels 2a. 
To the contrary, the closed liquid column tube 1 as shown in FIG. 17 can 
prevent the vaporization of the liquid 2 and the overflowing of the liquid 
2 upon generation of a large vibrational amplitude. Furthermore, the 
generation of rust or the like upon the inner wall of the tube 1 within 
the vicinity of the liquid levels 2a can be prevented by charging an inert 
gas into the tube 1. 
The vibration characteristics of the tower-like structure under 
construction change with each step of construction. Such a change in the 
vibration characteristics can be followed to some extent by changing the 
amount of the liquid within the liquid column tube as mentioned 
previously. However, there are many cases where the change in the 
characteristics cannot be compensated for or accommodated merely by 
changing the amount of liquid within the column tube. In these cases, it 
is necessary to replace the liquid column tube 1 with a longer or shorter 
one. Such replacement is troublesome and uneconomical. 
FIG. 18 shows an embodiment which eliminates the above disadvantages, 
wherein the length of a horizontal portion of the liquid column tube 1 is 
adjustable. That is, the horizontal portion is provided with a slidable 
portion 1b which is sealed in a watertight manner by means of a packing 
13. With this arrangement, the distance B defined between external 
sidewalls of the liquid column tube 1 is changed by sliding the slidable 
portion 1b, thereby changing the length L defined between the liquid 
levels 2a along the liquid column tube 1. 
Accordingly, the vibration characteristic can be made optimal in accordance 
with each step of construction by changing the length of the damping 
device as well as the amount of the liquid within the damping device. Even 
when the tower-like structure is under construction, the vibration 
characteristics can be easily changed with the damping function maintained 
constant. 
The liquid to be used with the damping device is normally water. However, 
if the water is frozen in a cold environment, the damping function cannot 
be exhibited or achieved. Accordingly, it is necessary to prevent the 
freezing of the water by continuously supplying heat from a heat source, 
causing an increase in the maintenance cost of the damping device. 
Such a disadvantage can be eliminated by mixing an antifreezing fluid such 
as, for example, ethylene glycol with the water. 
As described above, the following effects can be exhibited according to the 
damping device of the present invention. 
(1) As the orifice has a predetermined definite mechanism which is used, 
within the liquid column tube, the characteristic values can be easily 
quantitatively defined so as to thereby obtain a high-performance damping 
device. 
(2) As a change in the natural frequency of the structure in concert with 
the proceeding of the construction thereof can be followed by changing the 
length of the liquid column tube and the amount of the liquid to be 
charged into the liquid column tube, the damping device can be easily 
adapted to the structure while under construction. 
(3) As the shape of an intermediate portion of the liquid column tube can 
be appropriately selected with the length L of the tube fixed, a degree of 
freedom with respect to the installation space within the structure can be 
increased. 
(4) As a damper or the like which is susceptible to aging is not used, the 
maintenance of the damping device is easy. 
(5) In the case of using a variable orifice, a change in conditions of the 
structure can be easily compensated for or accommodated. 
(6) By combining two liquid column tubes and intersecting the conduits of 
the tubes so as to form a common intersecting conduit portion, the 
installation space for the damping device and the amount of the liquid to 
be charged into the damping device can be reduced, and the vibration in 
all directions can be damped by means of the damping device. 
(7) By forming the liquid column tube into a closed-loop type 
configuration, the vaporization of the liquid within the liquid column 
tube and the generation of rust or the like upon the inner wall of the 
liquid column tube can be prevented. 
(8) By mixing an antifreezing fluid with water as the liquid to be charged 
into the damping device, the freezing of the water within a cold 
environment can be prevented without the necessity of the provision of a 
heat source or the like, thereby facilitating the maintenance work and 
reducing the operative costs thereof. Obviously, many modifications and 
variations of the present invention are possible in light of the above 
teachings. It is therefore to be understood that within the scope of the 
appended claims, the present invention may be practiced otherwise than as 
specifically described herein.