WO2004003306A1

WO2004003306A1 - Simple pendulum with variable restoring force

Info

Publication number: WO2004003306A1
Application number: PCT/CA2003/000956
Authority: WO
Inventors: Scott Lee Gamble; Jan Kottelenberg; Trevor Haskett; Francois Rouviere; Brian Breukelman
Original assignee: Motioneering Inc.
Priority date: 2002-06-26
Filing date: 2003-06-26
Publication date: 2004-01-08
Also published as: AU2003243869A1; CA2391683A1

Abstract

A vibration absorption system for large structures such as high-rise buildings utilizes a primary mass suspended by tension means below a fixed support of the structure and a secondary mass supported above a support surface of the structure by compression means. The masses are adjacent each other and linkage means interconnects the masses for similar lateral and vertical displacements. By adjusting the ratio of the masses and/or the ratio of the lengths of the tension and compression supporting elements it is possible to tune the eigenfrequency of the system to a desired level in accordance with anticipated vibration levels. The system allows an effective installation within a restricted volume at the top of a high-rise building where sufficient vertical adjustment of a simple pendulum type of vibration damper would not otherwise be available.

Description

Simple Pendulum with Variable Restoring Force

Background of the Invention

There are many structures that vibrate under the influence of external forces and it is very desirable to minimize the effects of such vibrations in order to maintain the integrity of such structures. Large (tall) buildings can be subjected to considerable forces due to prevailing winds, turbulencein which can set up vibrations within the building structure. Buildings in certain geographical areas can be subjected to ground-based displacement forces such as earthquakes and tremors, which can result in considerable damage, or even destruction if the induced vibrations are excessive. In the past it has been known to counteract vibrations in buildings by the use of suspended masses, in the form of a simple pendulum, which move in opposition to the induced vibrations and help to dampen those vibrations and thus help to keep the building more stable and less prone to damage. The same principle can be used to dampen vibrations in other large structures, including but not restricted to bridges and construction and production machinery.

Increasingly, high-rise buildings are being built with more aggressive sienderness ratios (the ratio of building height to width). While the structure may be strong from a design load perspective, it may also be quite flexible. In moderate to strong wind events, occupants of the uppermost floors will be subjected to vibrations that can range from annoying to worrisome or even dangerous. Suspended mass vibration absorbers or dampers are most effective if located at the very top of the structure. However, it is the real estate at the top of such a high-rise building that has the greatest commercial or retail value, and therefore the space given over to such a vibration absorber or damper comes at a great price. Additionally, for a vibration absorber or damper based on a pendulum configuration the required pendulum length may be difficult to contend with. Fundamental building periods are commonly in the range of 5 to 8 seconds, and therefore the pendulum length can approach 16m, a length which is much too great for common use. A Tuned Mass Damper (TMD) is a machine or system that removes vibrational energy from a structure to which it is attached. The structure can be a building, bridge or another machine. A TMD can be configured as but is not limited to, a mass suspended on cables or other linkages. Usually, an energy dissipation device is attached to the mass to provide damping. Tuning of the TMD is required so that its eigenfrequency is almost equal to that of the structural system to which it is applied. On a TMD that is configured as a simple pendulum the length of the cables or suspension linkages is the means by which the frequency of the TMD is determined. By changing the effective length of the cables or suspension linkages, the eigenfrequency of the TMD system can be tuned to a desired level.

Within a given available vertical space it is easy to increase the eigenfrequency of a pendulum by shortening its length. This has the effect of increasing the rate at which the restoring force (due to gravity) is generated per unit of lateral displacement. An alternate means of augmenting the rate of increase of the restoring force includes attaching a spring to the pendulum. On the other hand, within a fixed vertical space, noting that space is a premium at the top of a high-rise building, it is not possible to achieve a lower eigenfrequency without some type of additional works (e.g. an inclined gate pendulum) since a lengthening of the pendulum is generally not an viable option.

Summary of the Invention

The present invention provides a system for allowing an extension of the period of a pendulum beyond that that can be achieved solely through adjusting the length of a simple pendulum.

If a negative restoring force, in the form of a connected inverted pendulum, is applied to a simple pendulum, an eigenfrequency other (lower) than that controlled by the primary pendulum length is produced. The eigenfrequency of such a combination of pendulums can be adjusted by varying the mass ratio between the primary and secondary masses and/or by varying the ratio of the lengths of the primary mass's suspension cables (or linkages) to the length of the secondary mass's supporting member(s). The present invention is based on the above principles and permits the creation of a compact dynamic vibration absorption system that is easily adapted to existing and/or new building construction and which improves on prior art damping systems. The present invention may be characterized as a "Tuned Mass Damper" (TMD), a machine or system that removes or reduces vibrational energy from a structure, such as a building, a bridge or a machine, to which it is mounted.

The principles of the present invention are, in fact, applicable to other structures, appliances or devices which utilize a pendulum and in which available vertical space may be a design constraint. Notwithstanding that the invention flowed from investigations into improving the vibration damping within high-rise buildings and the like, the use of an inverted pendulum supported from below in conjunction with a simple pendulum supported from above can find application in simpler consumer goods such as metronomes and grandfather clocks, for example.

Generally speaking and in summary, the present invention may be considered as providing a pendulum arrangement with adjustable restoring force comprising: a first mass (m^); a second mass (m₂) positioned adjacent the first mass; tension means suspending the first mass below a fixed support as a simple pendulum having a length (/j); compression means supporting the second mass above a lower support surface as an inverted pendulum having a length (/₂); and linkage means interconnecting the masses and constraining the masses to similar lateral displacements and velocities; wherein the eigenfrequency of vibration of the system is tunable to a desired eigenfrequency by altering the ratio of said masses m_t and m₂ and/or the ratio of said lengths l_t and l₂.

The present invention may also be considered as providing a dynamic vibration absorption system for protecting a structure against excessive vibrations comprising: a first mass

a second mass (m₂) positioned adjacent the first mass; tension means suspending the first mass below a fixed support of the structure as a simple pendulum having a length (/ ; compression means supporting the second mass above a support surface of the structure as an inverted pendulum having a length (/₂); and linkage means interconnecting the masses and constraining the masses to similar lateral displacements and velocities; wherein the eigenfrequency of vibration of the system is tunable to a desired eigenfrequency by altering the ratio of said masses ^ and m₂ and/or the ratio of said lengths l and

Brief Description of the Drawings

Figure 1 illustrates a schematic representation of the present invention showing the relationship of the masses and the pendulum lengths.

Figure 1A is a top plan view of the schematic representation of Figure 1A, configured to operate at a single eigenfrequency.

Figure 2A is a top plan view of a schematic representation of the invention configured to operate at two eigenfrequencies in orthogonal directions.

Figure 2B is a partial elevational cross-section of the embodiment of Figure 2A.

Figure 3A is a top plan view of a schematic representation of the invention configured to operate at two different eigenfrequencies in two orthogonal directions.

Figure 3B is an elevational view of the schematic representation of Figure 3A.

Figure 4 is a perspective view of a possible installation of the present invention within a designated space of a structure to which the invention can be applied.

Description of the Preferred Embodiment

The principles of the present invention can be ascertained from the showing of Figures 1 and 1A. Therein it is seen that a first or primary mass 12 having mass ni_t is suspended from a support within a structure by one or more tension means such as cables 14. The mass preferably is generally rectangular with a central opening 16, although other configurations could be utilized. The cables or suspension means 14 can be varied in length in accordance with standard practice, the length of each cable being indicated by the variable l_v Located within the opening 16 is a second or secondary mass 18 with its mass being designated m₂. This mass is supported above a support surface of the structure by compression means such as one or more articulating columns 20. The columns 20 can be varied in length in accordance with standard practice, the length of each column being indicated by the variable /₂. The eigenfrequency (/) of the system is determined by the equations:

δ) =

(mjiriz + 1) x j

and f = αV(2.ττ)

It will be clear from the above equation that the eigenfrequency can be altered by changing the ratio m m₂ and/or the ratio A /₂.

In addition to the masses 12, 18, the tension means 14 and the support columns 20 an installation of the present invention may include an energy dissipation unit 22 anchored to a side of the installation area and connected to the primary mass 12. This unit will help to dissipate kinetic energy within the primary mass 12 during vibration of the structure, and can be mechanical, pneumatic or hydraulic in nature. The two masses 12 and 18 are preferably joined by interconnecting means 24 located between the masses, which means allow the masses to move relative to each other in a lateral direction, while also allowing relative vertical displacement therebetween.

In the embodiment of Figure 1A, the singular eigenfrequency of the system can be varied by adjusting the relative mass ratio and/or by changing the length ratios between the primary and secondary systems, as by altering the relative lengths of the support elements 14, 20.

The elements of the second embodiment as illustrated in Figure 2A are the same as those for the first embodiment shown in Figure 1A. However, in Figure 2B, crossed members 26 extend between pairs of tension members 14 and are used to tune or adjust the length ratio of the support cables to different effective values for each of two perpendicular directions. In this example, differing mass ratios are not used to attain two different eigenfrequencies. In the embodiment of Figures 3A and 3B, the system can be configured to operate at two different eigenfrequencies in two perpendicular directions. In this case a single primary or first mass 28 is suspended by one or more tension means or cables 30, a first pair of secondary masses 32 is provided on opposite sides of the primary mass adjacent thereto and a second pair of secondary masses 34 is provided on the other opposite sides of the primary mass adjacent thereto. The secondary masses 32, 34 are supported by suitable compression means 36, 38 respectively and an energy dissipation unit 40 is positioned between one of the secondary masses and an adjacent wall of the installation area. Means 42 between the primary and secondary masses interconnect the masses, allowing for relative lateral and vertical movement as in the other embodiments. In this embodiment the effective mass ratio and/or the length ratio can be adjusted simultaneously to affect the operating frequency in two perpendicular directions. This system configuration can provide for a wider attainable frequency range in comparison to the other embodiments described herein.

Figure 4 illustrates schematically a practical installation of the vibration absorbing system of the present invention, as for example in an isolated compartment 50 at the top of a high-rise building. The compartment 50 includes side walls 52 (only two of the four walls are shown) and a floor 54. The walls 52 carry suspension beams 56 which cross each other and are secured at the crossing points as by welding and/or rivetting. A first or primary mass 58 is suspended in the middle of the compartment from the support beams 56 by a series of symmetrically positioned tension cables 60 which can be adjusted in length. A second or secondary mass 62 is located within an inner cavity 64 of the primary mass 58 and is supported above the floor 54 by a plurality of symmetrically positioned articulated compression columns 66. Energy dissipation units 68 are centrally located adjacent each side of the primary mass 58 and anchoring means 70 are connected at each end of each side of the primary mass 58 to corner blocks 72 secured to the floor of the compartment. The anchoring means 70 do not restrict lateral or vertical movement of the primary mass, but only serve to reduce any rotation during movement thereof. This particular installation is compact, especially vertically, and it can be tuned to approximately match the fundamental frequency of the building by altering the mass ratio and/or the length ratio of the cables 60 and the columns 66.

The foregoing has described the present invention and a practical application of the principles thereof. It is understood that a skilled practitioner in the art would be able to extend the invention to other applications and could effect modifications to the invention without departing from the spirit thereof. Furthermore, as indicated previously the principles of the present invention are not restricted to vibration dampers for large scale structures, but are equally applicable to relatively small items that use a pendulum, such as clocks and metronomes. Accordingly the protection to be afforded this invention is to be determined from the scope of the claims appended hereto.

Claims

CLAIMS:

1. A dynamic vibration absorption system for protecting a structure against excessive vibrations comprising: a first mass (mj); a second mass (m₂) positioned adjacent said first mass; tension means suspending said first mass below a fixed support of said structure as a simple pendulum having a length (/j); compression means supporting said second mass above a support surface of said structure as an inverted pendulum having a length (/₂); and means interconnecting said masses and constraining said masses to similar lateral displacements and velocities; wherein the eigenfrequency of vibration of said system is tunable to a desired eigenfrequency by altering the ratio of said masses m_x and m₂ and/or the ratio of said lengths l_t and l₂.

2. The system of claim 1 wherein the tunable eigenfrequency of vibration (r) is determined by the ratio of said masses (m_ /77₂) and the ratio of said lengths (/ /₂) in accordance with the expression:

U) = inhln .j ) x q

(m.,/m₂ + 1) x ι_t

and f = u)/(2.π)

3. The system of claim 1 or claim 2 wherein said second mass m₂ and said compression means exert a force in opposition to the gravity restoring force of said first mass m_t in its simple pendulum configuration, thereby allowing the eigenfrequency of the system to be tuned to any frequency between 0 Hz and the natural frequency of a pendulum with length A,.

4. The system of any one of claims 1 to 3 including brace means to effectively shorten the length of said tension means and/or said compression means in only one direction, to thereby effect a different ratio (V7₂) in each of two orthogonal directions and thus achieve different eigenfrequencies in each orthogonal direction.

5. The system of any one of claims 1 to 4 including damping means connecting said first mass and/or said second mass to said structure to control the amplitude of oscillatory motion or to dissipate vibrational energy of said structure as heat.

6. The system of claim 5 wherein said damping means comprises a viscous damping device.

7. The system of any one of claims 1 to 6 wherein said tension means comprises one or more elongated cables connected at one end thereof to said fixed support and connected at the other end thereof to said first mass.

8. The system of any one of claims 1 to 7 wherein said compression means comprises one or more articulated columns connected at one end thereof to said support surface and connected at the other end thereof to said second mass.

9. A pendulum arrangement with adjustable restoring force comprising: a first mass (m_,); a second mass (m₂) positioned adjacent said first mass; tension means suspending said first mass below a fixed support as a simple pendulum having a length (/_Λ); compression means supporting said second mass above a lower support surface as an inverted pendulum having a length (/₂); and means interconnecting said masses and constraining said masses to similar lateral displacements and velocities; wherein the eigenfrequency of vibration of said system is tunable to a desired eigenfrequency by altering the ratio of said masses m^ and m₂ and/or the ratio of said lengths l_t and l₂.