Tuned mass damper and method for adjusting natural period of tuned mass damper

Abstract

To provide a tuned mass damper with a simplified structure for cost reduction, and a method for adjusting the natural period of the tuned mass damper.SOLUTION: A tuned mass damper includes a spherical sliding bearing (10) and a weight (20) mounted on the spherical sliding bearing (10).SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a tuned mass damper and a method for adjusting the natural period of a tuned mass damper. [Background technology]

[0002] In buildings, vibration control devices are sometimes installed to suppress vibrations caused by earthquakes, etc. For example, Patent Document 1 discloses a vibration control device (tuned mass damper) in which a weight is placed on the top of a vibration control mechanism consisting of upper and lower clamping members with arcuate surfaces and a cylindrical roller member interposed therebetween, and in which a flywheel is attached to the cylindrical roller member. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 4-161678 Summary of the Invention [Problem to be solved by the invention]

[0004] There is a demand for simplified construction and reduced cost in tuned mass dampers.

[0005] The present invention has been made in consideration of the above-mentioned circumstances, and an object of the present invention is to provide a tuned mass damper having a simple structure and reduced costs, and a method for adjusting the natural period of a tuned mass damper. [Means for solving the problem]

[0006] <1> A tuned mass damper according to a first aspect of the present invention is characterized by comprising a spherical sliding bearing and a weight placed on the spherical sliding bearing.

[0007] According to this invention, a weight is provided that is placed on the spherical sliding bearing. This allows the tuned mass damper to be configured with a simple structure, thereby reducing the cost of the tuned mass damper.

[0008] <2> A tuned mass damper according to a second aspect of the present invention is characterized in that, in the tuned mass damper according to the first aspect, the spherical sliding bearing includes a shoe, the shoe includes a concave spherical surface facing upward or downward, and the natural period of the tuned mass damper is determined by the magnitude of the radius of curvature of the concave spherical surface.

[0009] According to the present invention, the natural period of the tuned mass damper is determined by the magnitude of the radius of curvature of the concave spherical surface of the shoe, which makes it possible to reliably determine the natural period of the tuned mass damper, for example.

[0010] <3> A tuned mass damper according to a third aspect of the present invention is the tuned mass damper according to the second aspect, further comprising an elastic member, and the natural period is determined by the magnitude of the radius of curvature of the concave spherical surface and the magnitude of elasticity of the elastic member.

[0011] The natural period of the structure in which the tuned mass damper is installed may differ between the predicted value during design review and the actual measured value. For this reason, it may be necessary to adjust the natural period of the tuned mass damper after construction, based on the radius of curvature of the spherical sliding bearing determined during design review. The natural period of the tuned mass damper is determined by the radius of curvature of the concave spherical surface of the shoe and the elasticity of the elastic member. As a result, for example, if it is necessary to further adjust the natural period of the tuned mass damper after adjusting the natural period of the tuned mass damper by changing the radius of curvature of the concave spherical surface of the shoe, it is possible to adjust the natural period of the tuned mass damper without additionally changing the radius of curvature of the concave spherical surface of the shoe. This can improve the efficiency of the design of tuned mass dampers, for example.

[0012] <4> A tuned mass damper according to a fourth aspect of the present invention is the tuned mass damper according to the third aspect, characterized in that the elastic member is capable of preventing the shoe from tipping over.

[0013] According to this invention, the elastic member can prevent the shoe from tipping over. The elastic member can adjust the natural period of the tuned mass damper and prevent the weight from tipping over, making it unnecessary to provide a separate structure for preventing the weight from tipping over. Therefore, for example, the structure of the tuned mass damper can be made simpler. Therefore, for example, the cost of the tuned mass damper can be reduced.

[0014] <5> A tuned mass damper according to a fifth aspect of the present invention is the tuned mass damper according to the third or fourth aspect, characterized in that the elastic member is connected to the shoe.

[0015] According to this invention, the elastic member is connected to the shoe. This allows the shoe to function as a connecting member for the elastic member. Therefore, for example, the structure of the tuned mass damper can be made simpler. Therefore, for example, the cost of the tuned mass damper can be reduced.

[0016] <6> A tuned mass damper according to a sixth aspect of the present invention is the tuned mass damper according to any one of the third to fifth aspects, characterized in that the elastic member is connected to the weight.

[0017] Here, depending on the diameter of the elastic member and the vertical dimension of the spherical sliding bearing, the elastic member may interfere with the floor surface when connected to the shoe. The elastic member is connected to the weight. This makes it possible to, for example, prevent interference between the elastic member and a floor surface, thereby increasing the degree of freedom in the attachment position of the elastic member.

[0018] <7> A tuned mass damper according to a seventh aspect of the present invention is a tuned mass damper according to any one of the second to sixth aspects, characterized in that the shoe includes an upper shoe, and the upper shoe functions as a base on which the weight is placed.

[0019] According to this invention, the upper shoe functions as a base on which the weight is placed. This allows the upper shoe to function as both the natural period adjustment means and the base for the weight. This makes it possible to simplify the configuration of the tuned mass damper, for example. This makes it possible to reduce the cost of the tuned mass damper, for example.

[0020] <8> A tuned mass damper according to an eighth aspect of the present invention is the tuned mass damper according to any one of the first to seventh aspects, characterized in that it includes a plurality of the spherical sliding bearings.

[0021] According to this invention, a plurality of spherical sliding bearings are provided under the weight. By supporting the weight with a plurality of spherical sliding bearings, for example, it is possible to prevent the weight from tipping over on the spherical sliding bearings. Therefore, it is possible to support the weight more stably.

[0022] <9> A method for adjusting the natural period of a tuned mass damper according to aspect 9 of the present invention is a method for adjusting the natural period of a tuned mass damper comprising a spherical sliding bearing, a weight placed on the spherical sliding bearing, and an elastic member, characterized in that the natural period is adjusted by the magnitude of elasticity of the elastic member.

[0023] Here, after installation of the tuned mass damper, it may become necessary to further adjust the natural period of the tuned mass damper. The natural period of the tuned mass damper is adjusted by the magnitude of elasticity of the elastic member. This makes it possible to adjust the natural period of the tuned mass damper without changing, for example, the shape of the spherical sliding bearing. This makes it possible to improve, for example, the efficiency of the design of the tuned mass damper. Effect of the Invention

[0024] According to the present invention, it is possible to provide a tuned mass damper having a simple structure and reduced costs, and a method for adjusting the natural period of a tuned mass damper. [Brief description of the drawings]

[0025] [Figure 1] 1 is a first example of a perspective view of a tuned mass damper. [Diagram 2] FIG. 2 is a second example of a perspective view of a tuned mass damper. [Diagram 3] This is the first example of a front view of a tuned mass damper. [Figure 4] This is a second example of a front view of a tuned mass damper. [Diagram 5] This is the third example of a front view of a tuned mass damper. [Figure 6] This is the fourth example of a front view of a tuned mass damper. [Figure 7] This is the fifth example of a front view of a tuned mass damper. [Figure 8] This is the first example of how to attach a weight to a spherical sliding bearing in a tuned mass damper. [Figure 9] This is the second example of mounting the weight and spherical sliding bearing in a tuned mass damper. [Figure 10] This is the first example of the arrangement of elastic members in a tuned mass damper. [Figure 11] This is the second example of the arrangement of elastic members in a tuned mass damper. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026] Hereinafter, a tuned mass damper 100 according to an embodiment of the present invention will be described with reference to the drawings. The tuned mass damper 100 is disposed, for example, in the upper part of a building. Examples of the building include a high-rise building, a wind turbine tower, a wind turbine jacket structure, a wind turbine monopile, a bridge girder, a bridge main tower, and an oil drilling jacket. That is, the tuned mass damper 100 is disposed, for example, in the upper part of a high-rise building, a wind turbine tower, a bridge, a jacket structure, or the like. The tuned mass damper 100 may be disposed, for example, in the upper part of the aforementioned wind turbine jacket structure or wind turbine monopile. The tuned mass damper 100 is used, for example, to suppress vibrations of a building by damping vibrations of the upper part of the building when an earthquake, strong wind, or the like occurs. As shown in FIG. 1, the tuned mass damper 100 includes a spherical sliding bearing 10, a weight 20, and an elastic member 30.

[0027] The spherical sliding bearing 10 has a known structure, for example, as shown in Fig. 3 or 4. The spherical sliding bearing 10 includes a shoe 11 and a slider portion 12. The shoe 11 includes an upper shoe 11U and a lower shoe 11L. The shoe 11 includes a concave spherical surface facing upward or downward. That is, for example, the upper shoe 11U includes an upper shoe concave spherical surface 11Ud facing downward. The lower shoe 11L includes a lower shoe concave spherical surface 11Ld facing upward. The slider portion 12 is disposed between the upper shoe 11U and the lower shoe 11L. The slider portion 12 includes an upper convex spherical surface 12PU that faces upward and slides against the upper shoe concave spherical surface 11Ud, and a lower convex spherical surface 12PL that faces downward and slides against the lower shoe concave spherical surface 11Ld. In the spherical sliding bearing 10, the radius of curvature of the upper shoe concave spherical surface 11Ud is the same as the radius of curvature of the upper convex spherical surface 12PU. The radius of curvature of the lower shoe concave spherical surface 11Ld is the same as the radius of curvature of the lower convex spherical surface 12PL, for example. The radius of curvature of the upper shoe concave spherical surface 11Ud and the radius of curvature of the lower shoe concave spherical surface 11Ld may not be the same. In that case, for example, as shown in Fig. 5, it is preferable to provide a hinge portion 12H on the slider portion 12 to divide the vibration region to be controlled into two. That is, the radius of curvature of the upper shoe concave spherical surface 11Ud and the radius of curvature of the lower shoe concave spherical surface 11Ld may be made different, and the shape of the slider portion 12 may be made to match each of the upper shoe concave spherical surface 11Ud and the lower shoe concave spherical surface 11Ld, so that the slider portion 12 rotates between the upper shoe 11U and the lower shoe 11L.

[0028] In the spherical sliding bearing 10, the lower shoe 11L is fixed to, for example, the floor of a building. The upper shoe 11U is placed on the lower shoe 11L via the slider portion 12. In this way, in the spherical sliding bearing 10 having the above configuration, the upper shoe 11U and the lower shoe 11L are displaced relatively in the horizontal direction. At this time, the slider portion 12 slides on the upper shoe 11U and the lower shoe 11L, respectively, smoothing the relative movement between the upper shoe 11U and the lower shoe 11L. In this embodiment, for example, the following two examples of the spherical sliding bearing 10 are preferably used.

[0029] (First example of spherical sliding bearing 10) The spherical sliding bearing 10 according to the first example is of the double pendulum type shown in FIG. 3. That is, the upper shoe 11U and the slider portion 12 are displaced in the horizontal direction. Specifically, the slider portion 12 is displaced relative to the lower shoe 11L in the horizontal direction. Furthermore, the upper shoe 11U moves relative to the slider portion 12 in the horizontal direction. The plate thickness or planar dimensions of the upper shoe 11U, the slider portion 12, and the lower shoe 11L are preferably determined appropriately according to, for example, the weight and size of the weight 20 placed on the upper shoe 11U. The curvature radius and friction coefficient of the upper shoe 11U, the slider portion 12, and the lower shoe 11L, and the weight of the weight 20 are preferably determined appropriately according to, for example, the natural period, effective mass, target damping, and the like of the building in which the tuned mass damper 100 is arranged.

[0030] (Second example of spherical sliding bearing 10) The spherical sliding bearing 10 according to the first example is of the single pendulum type shown in FIG. 4. That is, the upper shoe 11U displaces in the horizontal direction, but the slider portion 12 does not move in the horizontal direction. Specifically, the slider portion 12 displaces only so as to rotate inside the lower shoe concave spherical surface 11Ld of the lower shoe 11L. In other words, the slider portion 12 does not displace relative to the lower shoe 11L in the horizontal direction. The upper shoe 11U moves relative to the slider portion 12 in the horizontal direction. When the spherical sliding bearing 10 is of the single pendulum type, it is preferable to make the movement amount of the upper shoe 11U larger than that of the upper shoe 11U of the double pendulum type, for example, in order to ensure the movement amount of the upper shoe 11U. Specifically, for example, in order to make a single pendulum type spherical sliding bearing 10 have the same performance as a double pendulum type spherical sliding bearing 10, the size of the upper shoe 11U is made twice that of the double pendulum type, and the radius of curvature of the upper shoe concave spherical surface 11Ud is made twice that of the double pendulum type.

[0031] In the tuned mass damper 100 according to this embodiment, for example, one spherical sliding bearing 10 is provided as shown in Figures 2 and 3. However, the present invention is not limited to this, and for example, as shown in Figure 6, the tuned mass damper 100 may be provided with a plurality of spherical sliding bearings 10. In this case, it is preferable that three or more spherical sliding bearings 10 are provided along a circle centered on the center of gravity of the weight 20 in a plan view. This preferably prevents the weight 20 from tipping over on the spherical sliding bearing 10.

[0032] The weight 20 is placed on the spherical sliding bearing 10. That is, the weight 20 is connected to the upper shoe 11U of the spherical sliding bearing 10. In other words, in the tuned mass damper 100, the upper shoe 11U functions as a base on which the weight 20 is placed. With this, when the upper shoe 11U of the spherical sliding bearing 10 moves relative to the lower shoe 11L, the weight 20 also moves along with the upper shoe 11U. At this time, the weight 20 suppresses vibration of the building by inertia due to its mass (details will be described later). In this embodiment, the weight 20 is preferably one having a weight of, for example, about 0.5% to 1.0% of the weight of the building in which the tuned mass damper 100 is provided.

[0033] The weight 20 is connected to the upper shoe 11U, for example, as follows: That is, the weight 20 and the upper shoe 11U are fixed together by a bolt B, for example, as shown in FIG. Alternatively, for example, as shown in FIG. 9, the fixing member F is first arranged around the weight 20 to connect them. Specifically, the fixing member F is arranged so that both ends of the fixing member F are located on the side surfaces of the upper shoe 11U and the portion of the fixing member F other than both ends is in contact with the weight 20. Then, both ends of the fixing member F are fixed to the side surfaces of the upper shoe 11U by, for example, bolts B. The fixing member F is, for example, a belt-like member that can be wrapped around the weight 20. Alternatively, the fixing member F may be, for example, a cloth-like or plate-like member that can cover the weight 20. The weight 20 is connected to the upper shoe 11U by any of the above methods.

[0034] The elastic member 30, for example, controls the amount of relative displacement of the upper shoe 11U with respect to the lower shoe 11L. For example, a spring or highly elastic rubber is preferably used for the elastic member 30. The elastic member 30 is arranged, for example, on all four sides of the spherical sliding bearing 10 and the weight 20. This makes it possible to respond to any movement of the upper shoe 11U in any horizontal direction. The elastic member 30 is arranged, for example, as in the following two examples.

[0035] (First example of arrangement of elastic member 30) In the first example, the elastic member 30 is connected to the shoe 11 as shown in Fig. 1. Specifically, the elastic member 30 is provided so as to be connected to the upper shoe 11U as shown in Fig. 10. In this way, for example, it is preferable that the upper shoe 11U ensures the function of the elastic member 30 in the tuned mass damper 100 as a connecting member.

[0036] (Second Example of Arrangement of Elastic Member 30) In the second example, the elastic member 30 is provided so as to be connected to the weight 20 as shown in Fig. 11. Here, when the elastic member 30 is a spring, depending on the diameter of the elastic member 30 and the vertical dimension of the spherical sliding bearing 10, the elastic member 30 may interfere with the floor surface when connected to the upper shoe 11U. In such a case, it is preferable to connect the elastic member 30 to the weight 20 so as to prevent the elastic member 30 from interfering with the floor surface. When the elastic member 30 is connected to the weight 20, it is more preferable to, for example, prevent the shoe 11 from falling over by the elastic member 30.

[0037] (Vibration damping by Tuned Mass Damper 100) As described above, tuned mass damper 100 having the above configuration is installed in the upper part of a building, and suppresses vibrations in the building by damping vibrations in the upper part of the building when an earthquake, strong wind, etc. occurs. Specifically, when the building vibrates, weight 20 of tuned mass damper 100 is vibrated in the opposite phase to the building's natural period, thereby damping the building's vibrations. For this reason, when installing tuned mass damper 100 in a building, the natural period of tuned mass damper 100 is adjusted to match the natural period of the building.

[0038] When the equivalent period of the tuned mass damper 100 is Teff, the weight of the weight 20 is W, the friction coefficient of the spherical sliding bearing 10 is μ, the displacement of the spherical sliding bearing 10 is u, the radius of curvature of the concave spherical surface of the spherical sliding bearing 10 is R, the number of elastic members 30 (springs) is n, the spring constant of the elastic members 30 (springs) is k, and the acceleration of gravity is g, the following two equations are used to calculate the equivalent period of the single pendulum type spherical sliding bearing 10 shown in Figures 4, 7, 8, 9, 10, and 11. The following equation 2 is used to calculate the equivalent period of the double pendulum type spherical sliding bearing 10 shown in Figure 3. Note that equation 2 is used to calculate the equivalent period of the double pendulum type spherical sliding bearing 10, particularly when the radius of curvature of the upper shoe concave spherical surface 11Ud and the radius of curvature of the lower shoe concave spherical surface 11Ld are the same.

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[0039] (Determination of the natural period of the tuned mass damper 100 and adjustment method) In this embodiment, the natural period of tuned mass damper 100 is determined, for example, by the radius of curvature of the concave spherical surface of spherical sliding bearing 10. Specifically, the natural period of tuned mass damper 100 is determined by the length of the pendulum of spherical sliding bearing 10, which vibrates according to the pendulum principle. That is, for example, the radius of curvature of upper shoe concave spherical surface 11Ud and lower shoe concave spherical surface 11Ld is increased to lengthen the natural period of tuned mass damper 100. For example, the radius of curvature of upper shoe concave spherical surface 11Ud and lower shoe concave spherical surface 11Ld is decreased to shorten the natural period of tuned mass damper 100.

[0040] In this embodiment, the natural period of the tuned mass damper 100 may be determined or adjusted by the magnitude of the elasticity of the elastic member 30 in addition to the magnitude of the radius of curvature of the concave spherical surface. Here, the natural period of a building may differ between the predicted value at the time of design review and the actual measured value. For this reason, it may be necessary to adjust the natural period of the tuned mass damper 100 based on the magnitude of the radius of curvature of the spherical sliding bearing 10 determined at the time of design review after construction. In such a case, it is preferable to adjust the natural period of the tuned mass damper 100 by adjusting the magnitude of the elasticity of the elastic member 30. That is, it is preferable to adjust the natural period of the tuned mass damper 100 by, for example, increasing or decreasing the number of elastic members 30 installed or changing the spring constant of the elastic member 30.

[0041] As described above, the tuned mass damper 100 according to this embodiment includes the weight 20 placed on the spherical sliding bearing 10. This allows the tuned mass damper 100 to be configured with a simple structure. As a result, the cost of the tuned mass damper 100 can be reduced.

[0042] Furthermore, the natural period of tuned mass damper 100 is determined by the magnitude of the radius of curvature of the concave spherical surface of shoe 11. This makes it possible to reliably determine, for example, the natural period of tuned mass damper 100.

[0043] Here, the natural period of the structure in which tuned mass damper 100 is installed may differ between the value predicted during design review and the actual measured value. For this reason, it may be necessary to adjust the natural period of tuned mass damper 100, which is determined by the radius of curvature of spherical sliding bearing 10 during design review, after construction. The natural period of tuned mass damper 100 is determined by the radius of curvature of the concave spherical surface of shoe 11 and the elasticity of elastic member 30. As a result, for example, in cases where it is necessary to further adjust the natural period of tuned mass damper 100 after adjusting the natural period of tuned mass damper 100 by changing the radius of curvature of the concave spherical surface of shoe 11, it is possible to adjust the natural period of tuned mass damper 100 without additionally changing the radius of curvature of the concave spherical surface of shoe 11. This makes it possible, for example, to improve the efficiency of the design of tuned mass damper 100.

[0044] Furthermore, the elastic member 30 can prevent the shoe 11 from tipping over. The elastic member 30 can adjust the natural period of the tuned mass damper 100 and can prevent the weight 20 from tipping over, which eliminates the need to provide a separate configuration for preventing the weight 20 from tipping over. This makes it possible to simplify the configuration of the tuned mass damper 100, for example. This makes it possible to reduce the cost of the tuned mass damper 100, for example.

[0045] Furthermore, the elastic member 30 is connected to the shoe 11. This allows the shoe 11 to function as a connecting member for the elastic member 30. This makes it possible to further simplify the configuration of the tuned mass damper 100, for example. This allows the cost of the tuned mass damper 100 to be further reduced, for example.

[0046] Here, depending on the diameter of the elastic member 30 and the vertical dimension of the spherical sliding bearing 10, when the elastic member 30 is connected to the shoe 11, the elastic member 30 may interfere with the floor surface. The elastic member 30 is connected to the weight 20. This makes it possible to suppress interference between the elastic member 30 and a floor surface, for example. This allows for a high degree of freedom in the attachment position of the elastic member 30.

[0047] Furthermore, the upper shoe 11U functions as a base on which the weight 20 is placed. This allows the upper shoe 11U to function as both the natural period adjustment means and a base for the weight 20. This allows, for example, the configuration of the tuned mass damper 100 to be simplified. This allows, for example, the cost of the tuned mass damper 100 to be reduced.

[0048] In addition, a plurality of spherical sliding bearings 10 are provided under the weight 20. By supporting the weight 20 by a plurality of spherical sliding bearings 10, for example, it is possible to prevent the weight 20 from tipping over on the spherical sliding bearings 10. Therefore, the weight 20 can be supported more stably.

[0049] Here, after installation of tuned mass damper 100, it may become necessary to further adjust the natural period of tuned mass damper 100. The natural period of the tuned mass damper 100 is adjusted by the magnitude of elasticity of the elastic member 30. This makes it possible to adjust the natural period of the tuned mass damper 100 without changing, for example, the shape of the spherical sliding bearing 10. This makes it possible to improve, for example, the efficiency of the design of the tuned mass damper 100.

[0050] The technical scope of the present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the spirit of the present invention. For example, if the elastic member 30 is used to adjust the natural period of the tuned mass damper 100 and as a result the elastic member 30 is unable to prevent the weight 20 from tipping over, an anti-tip roller FR may be provided under the upper shoe 11U as shown in FIG. 7 in order to prevent the weight 20 from tipping over on the spherical sliding bearing 10. For example, when connecting the elastic member 30 to the upper shoe 11U, in order to suppress interference between the elastic member 30 and the floor surface, a convex portion may be provided on the floor surface on which the lower shoe 11L is placed, thereby providing a gap between the elastic member 30 and the floor surface other than the convex portion.

[0051] In addition, within the scope of the invention, the components in the above-described embodiments may be replaced with well-known components, and the above-described modified examples may be combined as appropriate. [Explanation of symbols]

[0052] 10 Spherical sliding bearing 11 Shoes 11L lower shoe 11Ld Lower shoe concave spherical surface 11U Kamikutsu 11Ud Upper shoe concave spherical surface 12 Slider section 12PL downward convex spherical surface 12PU upper convex spherical surface 20 weights 30 Elastic member 100 Tuned Mass Damper B Bolt F Fixing member FR Anti-tip roller

Claims

1. A spherical sliding bearing; A weight placed on the spherical sliding bearing; A tuned mass damper comprising:

2. The spherical sliding bearing includes a shoe, the shoe includes an upwardly or downwardly facing concave spherical surface; the natural period of the tuned mass damper is determined by the magnitude of the radius of curvature of the concave spherical surface.

2. The tuned mass damper of claim 1.

3. Elastic member, Further comprising: The natural period is determined by the magnitude of the radius of curvature of the concave spherical surface and the magnitude of elasticity of the elastic member.

3. The tuned mass damper of claim 2.

4. The elastic member can prevent the shoe from falling over.

4. The tuned mass damper of claim 3.

5. The elastic member is connected to the shoe.

5. The tuned mass damper of claim 4.

6. The elastic member is connected to the weight.

5. The tuned mass damper of claim 4.

7. The shoe includes an upper shoe, The upper shoe functions as a platform on which the weight is placed.

7. The tuned mass damper according to claim 2, wherein the first and second surfaces are arranged in a first direction.

8. The spherical sliding bearing is provided in plurality.

7. A tuned mass damper according to claim 1.

9. A spherical sliding bearing; A weight placed on the spherical sliding bearing; An elastic member; A method for adjusting a natural period of a tuned mass damper comprising: The natural period is adjusted by the magnitude of elasticity of the elastic member. A method for adjusting the natural period of a tuned mass damper.

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