CA2391683A1 - Simple pendulum with variable restoring force - Google Patents

Description

Stml~te Pendulum with Variabte Restoring Force The frequency of a simple pendulum is controlled by the length of the pendulum, in conjunction with the force due to gravity acting on the mass of the pendulum. The gravitational force (restaring force) causesa displaced pendulum to naturally return to zero displacement (ar the point at lowest height of the pendulum mass). The magnitude of the restoring force for a given displacement of the mass is only related to the pendulum length. The higher the magnitude of the restoring force at a given displacement, the higher the frequency of that pendulum system, implying that the pendulum length has been decreased.
If a variable restoring farce, in-the form of a connected inverted pendulum, is applied to a simple pendulum, a frequency other than that controlled by the pendulum length is produced. The frequency of such a pendulum can be adjusted by varying the mass ratio between the primary and secondary masses and by varying the lengths of the primary mass's suspension cables (ar Linkages) or by varying the length of the secondary mass's supporting members). The attached sample calculation demonstrates how the relationship between mass ratio and pendulum length ratio can be used to affect the frequency of operation of this device.
An example of how this invention is used is the following application:
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 frequency is almost equal to that of the primary 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 frequency of the TMD system can be tuned to a desired level.
The application of this invention is outlined as follows:
A primary mass ml is supported from above (by means of cables or linkages) and a secondary mass m2 is supported from below {by means of articulating columns).
The secondary mass m2 is connected to the primary mass ml so that they can translate laterally together, but the masses are free to translate vertically relative to each other.
This use of the invention in this application is innovative since the extended frequency range of this TMD allows it to be used in situations where the vertical clear space available precludes the possibility of using a typical simple pendulum or multi-stage pendulum TMD {to achieve a Kong period of motion). Furthermore, and more importantly, by varying any combination of support member length ratio {1/i2) and mass ratio (ml/m2); a much wider range of frequencies can be attained than for a "typical" TMD.
The device can be configured to operate at a single frequency by using the same mass ratio and support member length ratio relationship in two simultaneous directions (see attached linearized calculation for cc~ and f). Furthermore; it can be configured to operate at different frequencies in two perpendicular directions simultaneously (total of two frequencies): This is accomplished by providing a different mass ratio and length 2fl ratio relationship in two perpendicular directions for the same system.
Figures IA and iB illustrate a coal guration appropriate to Example 1 described below.
Figures 2A and 28 illustrate a configuration appropriate to Example 2 described below.
Figures 3A and 3B illustrate a configuration appropriate to Example 3 described below.
Examples:
Examples 1 and 2 {see Figures 1A, 18, 2A and 2B) show that the application of this invention can be configured to operate at a single frequency (Example 1) or two

2 frequencies in two perpendicular directions (Example 2~. These canfiguratians consist of two masses. TPte primary mass (rni) is suspended from cables or other suspension linkages, while the secondary mass ~mz) is supported on articulating columns.
These two masses are jained such that they can move relative to each other in a lateral direction, while also allowing relative vertical displacement.
For Example L, the singular frequency of the system can be: varied by adjusting the relative mass ratio and/or presetting the length ratios between the primary and secondary systems.
For Example 2, to attain a different frequency in two different perpendicular directions, the length ratio of the support cables can be adjusted .(during or after installation) to .different effective values for etch direction. In this example, the mass ratio is nat used to attain two different frequencies.
Another example (see Figures 3A and 3B) is also given whereby the system can be configured to operate at two different frequencies in two perpendicular directions.
1~ Far this example, the effective mass ratio and/or length ratio can be adjusted simultaneously to affect the operating frequency in two perpendicular directions. This system configuration can provide for a uvider attainable frequency range (compared to the configuration described in the first two examples).

Claims