JP3185692B2 - Method of adjusting spring characteristics of tuned mass damper and mechanism for adjusting spring characteristics - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a tunable mass damper having a spring characteristic of a tunable mass damper which can reduce the amplitude of a specific natural frequency in a building as closely as possible to an ideal linear characteristic. Adjustment method and its adjustment
The present invention relates to a spring characteristic adjusting mechanism .

[0002]

2. Description of the Related Art Generally, a TMD (tunable mass damper) for reducing the amplitude of a specific natural frequency is known as a vibration isolator for a building. This tuned mass damper reduces the amplitude of the natural frequency by providing an additional mass that resonates in synchronization with the natural frequency of the building, and effectively reduces the amplitude of the natural frequency from a small amplitude to a large amplitude. In order to exhibit the vibration reduction effect, it is necessary to use an elastic body having a linear spring characteristic with a constant spring constant regardless of the magnitude of the displacement.

[0003]

However, even if the elastic body is formed uniformly over its entire length to give a linear spring characteristic, a qualitative tendency is that as the displacement increases, the spring constant decreases. It is difficult to design and manufacture an elastic body exhibiting a truly linear spring characteristic by compensating for this, and the development and manufacturing costs rise.

[0004] The problem is particularly remarkable in the case of a rubber elastic body that is frequently used as an elastic body of a tunable mass damper in a building.

SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and has as its object to simply provide a spring characteristic of a tunable mass damper interposed between a building and an additional mass to absorb their relative displacement. It is another object of the present invention to provide a tunable mass damper spring characteristic adjustment method and a spring characteristic adjustment mechanism that can approximate the ideal linear spring characteristic as much as possible at low cost.

[0006]

In order to achieve the above object, a method of adjusting the spring characteristic of a tunable mass damper according to the present invention comprises attaching an additional mass to a building via an elastic body to reduce the amplitude of a specific natural frequency. The spring characteristic Q = f (x) of the tunable mass damper to be reduced is the ideal linear spring characteristic R = g.
(X) does not match, and when the canceling spring characteristic S =-(RQ) for canceling the difference (RQ) between the spring characteristics exhibits nonlinearity, the difference between the building and the additional mass In order to approximate the composite spring characteristic of the composite spring as a whole to the linear spring characteristic R, the auxiliary spring is attached to the building in addition to the building. When no relative displacement is generated between the building and the additional mass, an initial amount of strain δ ₀ is given between the building and the additional mass so that the elastic restoring force acts at right angles to the relative displacement direction. The spring constant ks, the initial compression strain δ ₀ , and the mounting width H are set based on the following conditions (1) and (2).

(1) The auxiliary spring has a spring characteristic Q = F
(X) and the linear spring characteristic R = g (x) and is known both said object to displacement point x ₁ equal to a natural length the length L when it is parallel to relative displacement.

L = (x ₁ ² + H ² ) ^1/2 (2) The extreme value of the component force P _{x in} the relative displacement direction of the elastic restoring force P = −ks · δ of the auxiliary spring and its displacement point are A known extreme value of a canceling spring characteristic S =-(RQ) which cancels a difference between the spring characteristic Q = f (x) and the linear spring characteristic R = g (x) and a displacement point x ₂ (0 < x ₂ <x ₁ ).

P _x = −P · {x / (x ² + H ² ) ^1/2 }

The spring characteristic Q of the elastic body of the tunable mass damper is Q =
If f (x) does not match the ideal linear spring characteristic R = g (x), the spring characteristic Q and the linear spring characteristic R
By attaching an auxiliary spring that can cancel out the difference (R-Q) as much as possible between the building and the additional mass, and combining it with an elastic body,
The composite spring characteristic in the composite state can be made as close as possible to the ideal linear spring characteristic R. At this time, if the canceling spring characteristic S =-(RQ) that cancels the difference (RQ) exhibits nonlinearity, it cannot be directly canceled by a linear spring having a constant spring constant. Therefore, an auxiliary spring having linear spring characteristics is arranged between the building and the additional mass by giving an initial strain amount δ ₀ in a direction orthogonal to the relative displacement direction, and the auxiliary spring is inclined according to the relative displacement x. Then, the above-mentioned spring characteristic difference (R-Q) is canceled by the component force in the relative displacement direction of the elastic restoring force of the auxiliary spring.

[0011] That is, the force component P _x of the relative displacement direction of the auxiliary spring acting as the offset force giving nonlinearity was sin curve based min relative displacement direction of the offset force when not displaced relative A displacement point x at which these forces intersect is obtained from the known spring characteristic Q = f (x) of the elastic body and the ideal linear spring characteristic R = g (x).
To calculate the _1, auxiliary spring in the displacement point x ₁ is to determine its length so that the natural length, the relative displacement direction of the component force in the displacement point x ₁ to 0. Further, based on the known spring characteristic Q = f (x) and the ideal linear spring characteristic R = g (x), a canceling spring characteristic S that cancels a difference (R−Q) therebetween is obtained.
= − (RQ) and its displacement point x ₂ (0 <x ₂ <x
₁ ), the extreme value and the displacement point x ₂ are made to match the extreme value of the component force P _x in the relative displacement direction with the displacement point, and the initial strain amount δ ₀ , mounting width H, spring constant ks is calculated in reverse, and the composite spring characteristic in a state where the elastic body and the auxiliary spring are combined is approximated to the ideal linear spring characteristic R as much as possible.

Therefore, as described above, in the method of adjusting the spring characteristic of the tunable mass damper of the present invention, the spring characteristic of the elastic body interposed between the building and the additional mass and absorbing the relative displacement between them is determined by the linear spring characteristic. By using an auxiliary spring having the following, it is possible to approximate the ideal linear spring characteristic R as easily and at low cost as possible. Also, said tuning
Characteristic adjustment suitable for the spring characteristic adjustment method of the mass damper
The mechanism is specified by attaching an additional mass to the building via an elastic body
Of a tunable mass damper to reduce the amplitude of the natural frequency of
The characteristic Q = f (x) shows an upwardly convex non-linearity,
Does not match the linear spring characteristic R = g (x).
When the difference (R−Q) in the characteristic exhibits nonlinearity,
A linear characteristic with a constant spring constant ks between the object and the additional mass
The auxiliary spring presented is arranged and combined, and the entire composite spring is
Approximate the composite spring characteristic to the linear spring characteristic R.
A spring characteristic adjusting mechanism for a tuned mass damper,
The auxiliary spring moves the relative displacement x in a state where the relative displacement x does not occur.
First so that the elastic restoring force acts at right angles to the
Of the building and the additional mass given the initial compression strain.
Coil bars mounted between each by pin connection
The additional mass of the coil spring corresponds to the building.
When the relative displacement x is obtained, the tilt is made in accordance with the relative displacement x.
The spring characteristic is determined by the component of the elastic restoring force in the relative displacement direction.
It is a configuration that cancels the gender difference (RQ). Further, the pin
The coil springs attached by coupling are aligned
Telescopic upper rod slidably fitted to each other
And upper rod integrally formed with the lower rod
Both upper and lower sides of the pulling seat and the lower spring seat
The ends are joined, and the upper and lower rod ends are pin-joined
Is desirably provided with a mounting hole for use.

[0013]

FIG. 1 shows a seismic isolation building provided with a TMD (tuned mass damper) whose spring characteristics have been adjusted by the spring characteristic adjusting method according to the present invention at the top of the building, and FIG. It is explanatory drawing which expands the principal part in FIG. 1, and shows the operation state in exaggeration.

As shown in FIGS. 1 and 2, TMD 1 is a building 6
And an additional mass 4 attached to the top of the device via a buffer spring device 2, a reaction force receiving member 3 also fixed to the top, and interposed between the reaction force receiving member 5 and the additional mass 4. And a damper 5 for damping vibration.

The cushioning spring device 2 is interposed between the additional mass 4 and the building 6 which move relatively in parallel to each other, and includes a main cushioning spring 8.
And the auxiliary spring 10 are combined. The main buffer spring 8 is an elastic body formed by sequentially laminating a rubber plate 8a and a steel plate 8b and uniformly forming it over its entire length, and is capable of supporting the load of the additional mass 4 and being horizontally displaceable. However, the vertical subsidence caused by the horizontal displacement hardly occurs and is negligible.

Here, assuming that the elastic restoring force of the main buffer spring 8 is Q and its spring characteristic can be expressed by Q = f (x), the main spring 8 is connected to the rubber plate over its entire length as described above. As shown in FIG. 3, the spring characteristic Q = f (x) shows an upwardly convex non-linearity because the steel plate and the steel plate are uniformly formed.
It is hard with small displacement and soft with large displacement.

However, as described above, the specific natural vibration of the building 6 can be satisfactorily applied to the TMD 1 from a small amplitude to a large amplitude.
In order to absorb the pressure, the spring characteristic of the buffer spring device 2 ideally has a linear spring characteristic R = g (x) in which the elastic restoring force changes linearly with respect to the displacement as shown in FIG. Need to be.

Therefore, in order to make the composite spring characteristic of the buffer spring device 2 composed of the main buffer spring 8 and the auxiliary spring 10 close to the ideal spring characteristic R, the spring characteristic Q of the main buffer spring 8 is adjusted by the auxiliary spring 10. And the difference (R−
It is necessary to compensate by offsetting Q). That is, if the auxiliary spring 10 can create a canceling spring characteristic S =-(RQ) exhibiting a downwardly convex non-linearity that can cancel the difference (RQ) of the spring characteristics, the buffer spring device 2 Composite spring characteristics T
To the ideal linear spring characteristic R.

Therefore, in the present embodiment, the auxiliary spring 10
Is set as follows and combined with the main buffer spring 8 to make the composite spring characteristic T in the combined horizontal direction as close as possible to the ideal linear spring characteristic R.

That is, a coil spring having a linear characteristic is used as the auxiliary spring 10, and a vertical displacement is applied between the building 6 and the additional mass 4 in a state where the additional mass 4 is not horizontally displaced. Arrange at right angles to the direction of displacement. At this time, the initial strain amount (length) δ ₀ is applied to the auxiliary spring 10.
When the additional mass 4 is horizontally displaced relative to the building 6 by a universal joint or the like, the elastic restoring force of the auxiliary spring 10 is provided. Horizontal component force P of P
_{Let x} act on the additional mass 4. Here, since the spring characteristic Q of the main buffer spring 8 is higher than the ideal linear spring characteristic R, the horizontal component force P _x of the auxiliary spring 10 is the elastic restoring force Q of the main buffer spring 8. Must be acted in the opposite direction so as to cancel out. Therefore, the initial strain amount δ ₀ of the auxiliary spring 10 is given as a compression amount.

That is, if the angle from the vertical direction of the auxiliary spring 10 that is inclined according to the horizontal displacement amount x of the additional mass 4 is θ, the building 4 has the horizontal direction of the auxiliary spring 10 shown in the following equation (1). force component P _x is controlled so as to act as a canceling force of the elastic restoring force Q of the main buffer spring 8, the spring characteristics of the canceling force has a convex nonlinear characteristic under which the sin curve based.

P _x = −P sin θ = −ks · δ · sin θ (1) The amount of distortion δ can be expressed as δ = δ ₀ + H− (x ² + H ² ) ^1/2 (2) Therefore, the elastic restoring force P = ks · δ of the auxiliary spring becomes P = −ks · {δ ₀ + H− (x ² + H ² ) ^1/2 } (3), and sin θ becomes sin θ = x / (X ² + H ² ) ^1/2 (4) Therefore, the component force P _x in the relative displacement direction acting as the canceling force is P _x = −ks · ｛δ ₀ + H− (x ² + H) ² ) ^1/2 ｝ · {x / (x ² + H ² ) ^1/2 } (5) can be expressed as a functional expression (5) of relative displacement x, and the expression (5) is It is sufficient to set ks, δ ₀ , and H so as to be as close as possible to the canceling spring characteristic S = − (Q−R).

[0023] Here, the spring characteristic Q = F (x) and the ideal spring characteristic R = g (x) is a relative displacement direction of the component force of the displacement point x ₁ in the auxiliary spring 10 matches 0, i.e. [delta] = 0 since it is necessary to, when [delta] = 0 at x = x ₁ in the equation _{(2), δ 0 = (} x 1 2 + H 2) 1/2 -H ......... (6) is obtained, the auxiliary spring The amount of initial distortion (length) of is obtained. When shown by substituting the equation (6) into equation _{(5), P x = -ks} · {(x 1 2 + H 2) 1/2 - (x 2 + H 2) 1/2} · {x / (X ² + H ² ) ^1/2 ｝ (7) Here, based on the condition that both extreme values (in this case, minimum values) of the relative moving direction component force P _x and the canceling spring characteristic S = − (Q−R) match, a known value S is used.
= − (Q−R) to its extreme value (S _min ) and its displacement point x
₂ is obtained and the displacement point x ₂ is substituted into the partial differential equation (the following equation (8)) of the above equation (7). Since the value is 0, H is expressed by the following equation (9). It is determined as follows.

[0024]

(Equation 1)

(Equation 2) Further, if the equation (8) is modified, the spring constant ks becomes the following equation (1)
0), the spring constant ks can be obtained by substituting the already obtained extreme values (S _min ) of x ₂ , H, and S.

[0025]

[Equation 3] As described above, various settings of the auxiliary spring 10 can be determined. The auxiliary spring 10 is specifically configured as shown in FIG. 4, for example. That is, an upper spring seat 16 and a lower spring seat 18 are integrally formed on an extensible upper rod 12 and a lower rod 14, which are fitted with each other so as to be slidable with their axes aligned, and these springs are formed integrally. Upper and lower ends are integrally connected to the seats 16 and 18 to provide a coil spring 20 having excellent linear characteristics. At the ends of the upper and lower rods 12 and 14, mounting holes 22 and 24 for pin connection are provided, and the coil spring 20 has a natural length and the span L of the upper and lower mounting holes 22 and 24 is calculated as H + δ ₀ as described above. The dimensions of each member are designed so that The spring constant of the coil spring 20 used is naturally set to ks. The auxiliary spring 10 is vertically attached to the additional mass 4 and the building 6 in a state where they are not displaced in the horizontal direction. At this time, the additional mass 4
The span of the engaging pin for attaching the auxiliary spring provided on the side of the building 6 and the side of the building 6 is set to H, and the coil spring 20 of the auxiliary spring 10 with the auxiliary spring 10 attached has the initial compressive strain. (Length) δ ₀ .

Therefore, as described above, according to the method of adjusting the spring characteristic of the tuned mass damper 1, the spring characteristic Q of the main damping spring 8 interposed between the additional mass 4 and the building 6 which are relatively displaced horizontally. Is the ideal linear spring characteristic R
When the auxiliary spring 10 exhibits a linear spring characteristic in which the spring constant is constant irrespective of the displacement, the auxiliary spring 10 is moved between the additional mass 4 and the building 6 without any horizontal displacement. The linear spring characteristic R is a simple configuration in which the main spring 8 and the auxiliary spring 10 are combined and the composite spring characteristic T is a desired ideal.
Can be approximated as much as possible.

If the auxiliary spring 10 is manufactured using a coil spring which can be easily designed and manufactured to a predetermined spring constant and has excellent linearity, the spring characteristics can be adjusted at low cost and with high accuracy.

In the illustrated example, the case where an elastic body made of laminated rubber is used as the main buffer spring 8 of the TMD is exemplified. However, the present invention is not limited to this, and the main buffer spring 8 is an elastic body such as an air spring. You may.

[0029]

As described above in detail in the embodiments,
According to the present invention, the spring characteristic Q of the tunable mass damper for reducing the amplitude of a specific natural frequency by attaching an additional mass to a building via an elastic body matches the ideal linear spring characteristic R. When there is no displacement, use an auxiliary spring that exhibits a linear spring characteristic in which the spring constant is constant regardless of the displacement, and apply this to the relative displacement direction with no horizontal displacement occurring between the building and the additional mass. With a simple configuration in which the elastic body and the auxiliary spring are combined at a right angle, the combined spring characteristic in a state where the elastic body and the auxiliary spring are combined can be made as close as possible to the desired ideal linear spring characteristic R.

Further, if an auxiliary spring is manufactured using a coil spring which can be easily designed and manufactured to have a predetermined spring constant and has excellent linear spring characteristics, the spring characteristics can be adjusted at low cost and with high accuracy. .

[Brief description of the drawings]

FIG. 1 is a diagram showing a schematic configuration of a base-isolated building provided with a tunable mass damper adjusted by a spring characteristic adjusting method according to the present invention.

FIG. 2 is an explanatory diagram showing an enlarged state of a main part in FIG. 1 and exaggerating its operation state.

FIG. 3 is a graph conceptually showing a relationship between a spring characteristic Q of a buffer spring, an ideal linear spring characteristic R, and a canceling spring characteristic S for canceling a difference therebetween.

FIG. 4 is a sectional view showing a specific configuration example of an auxiliary spring.

[Explanation of symbols]

 2 buffer spring device 4 additional mass 6 building 8 main buffer spring (elastic body) 10 auxiliary spring 12 upper rod 14 lower rod 16 upper spring seat 18 lower spring seat 20 coil spring 22 mounting hole

Claims (3)

(57) [Claims] 1. The spring characteristic Q = f (x) of a tunable mass damper for reducing the amplitude of a specific natural frequency by attaching an additional mass to a building via an elastic body has an ideal linear spring characteristic R = g. (X), and the difference (R−
Q) canceling spring characteristic for canceling S =-(RQ)
Presents a non-linear characteristic, an auxiliary spring having a constant linear characteristic with a constant spring constant ks is arranged between the building and the additional mass to be composited, and the composite spring characteristic of the composite spring as a whole is determined by the linear spring. A method of adjusting a spring characteristic of a tunable mass damper that approximates a characteristic R, wherein the auxiliary spring has an elastic restoring force perpendicular to the relative displacement direction in a state where no relative displacement occurs between the building and the additional mass. The initial compression strain δ ₀ is given between the building and the additional mass so as to act on the mounting mass H, and the spring constant ks, the initial strain δ ₀ , the mounting width H Is a method for adjusting a spring characteristic of a tunable mass damper, which is set based on the following conditions (1) and (2). (1) the auxiliary spring, when the spring characteristic Q = F (x) and the linear spring characteristic R = g (x) and is known both said object to displacement point x ₁ equal is parallel to relative displacement Length L
Is the natural length. L = (x ₁ ² + H ² ) ^1/2 (2) The extreme value of the component force P _{x in} the relative displacement direction of the elastic restoring force P = −ks · δ of the auxiliary spring and the displacement point are determined by the spring characteristic Q = F (x) and the linear spring characteristic R = g (x)
Offsetting spring characteristics to offset the difference between the S = - known extreme and its displacement point _x 2 of the _{(R-Q) (0 <} x 2 <x 1)
To match. P _x = −P · {x / (x ² + H ² ) ^1/2 } 2. An additional mass is attached to a building via an elastic body.
Tunable mass damper to reduce the amplitude of a specific natural frequency
The spring characteristic Q = f (x) of the PA shows an upwardly convex nonlinearity.
And does not match the ideal linear spring characteristic R = g (x),
When the difference (R-Q) between the spring characteristics exhibits nonlinearity
And a line where the spring constant ks is constant between the building and the additional mass.
An auxiliary spring having a shape characteristic is arranged and combined, and the composite
The composite spring characteristic as a whole is close to the linear spring characteristic R.
This is the spring characteristic adjustment mechanism of the tuned mass damper
hand, When the relative displacement x is not generated, the auxiliary spring is
The elastic restoring force acts at right angles to the relative displacement x direction.
While the initial compression strain is given to the building,
Between the weight and the
Made of il spring, In the coil spring, the added mass changes relative to the building.
When the position x is reached, it is inclined according to the relative displacement x,
The spring characteristic difference (R−
Q) A mass mass damper that cancels out
F characteristic adjustment mechanism. 3. The carp attached by the pin connection
The springs are slidably fitted to each other with their axes aligned.
One for each of the retractable upper and lower rods
Body-formed upper spring seat and lower spring
The upper and lower ends are joined to the
The end of the pad has a mounting hole for pin connection.
3. A tunable mass damper according to claim 2, wherein
F characteristic adjustment mechanism.