The composition of our world is in constant fluctuation, a phenomenon beautifully articulated by Heraclites in his reference to Panta Rhei, which translates to ‘everything flows’. Applying a modern twist to this ancient Greek wisdom, one might declare ‘everything oscillates’.
This oscillation, or vibration, permeates every aspect of reality. From the subatomic particles that make up our world to celestial bodies at the edges of the cosmos, there is a persistent tendency towards oscillation. This fundamental attribute of the universe deeply influences the design of complex machinery such as aircraft wings, motor engines, and optical systems. Additionally, it’s being illustrated in natural instances such as tides driven by the lunar cycle, atmospheric seasonal changes, and even the stability of the solar system which relies on orbital resonances – proportional relationships of the planet’s orbital periods.
Common mechanical systems, like pendulums and springs, exemplify this oscillatory behaviour, usually fluctuating around an equilibrium state which gets continuously powered against an opposing force. This mirrors how the balance wheel in a wristwatch ingeniously flips back and forth, driven by a spring, or how, in a quartz timepiece, a crystal vibrates, kept in motion by regular bursts of electricity.
Every system exhibits specific oscillation patterns, which are its normal modes. If incited by a skillfully matched force, these oscillations can achieve high amplitudes. Visible examples include a child on a swing or a wine glass which upon a light hit, emits a unique ringing sound but could break if exposed to a high-amplitude sound of the same pitch. This phenomenon of exaggerated response to an external force is referred to as resonance.
Controlled resonance can be quite beneficial. In fact, it is crucial for the successful operation of several musical instruments, essential for radio communication, laser physics and numerous engineering fields. However, it can also be devastating if not appropriately contained. A prime example of this peril is the structural failure and subsequent collapse of the Tacoma Narrows Suspension Bridge in 1940.
Dublin’s O’Connell Street boasts the Spire of Light, towering 120 metres high. Although it’s visually simple, the Spire’s creation in 2003 required sophisticated engineering. The structure’s potential for destructive wind-induced oscillations needed to be carefully managed. Like many mechanical constructs, the Spire has its normal modes of vibration. If powerful winds oscillate at a frequency that matches a distinctive mode, it could lead to catastrophic amplitudes.
“Pendulums Providing Stability
During the initial planning phase, meticulous mathematical modelling and theoretical analysis confirmed that the primary resonating period of the Spire oscillates roughly every 3.6 seconds, with a secondary mode resonating near 1.2 seconds. Inside the Spire, there are two pre-calibrated mass dampers, weighing roughly a tonne each, designed to mitigate these vibrations. Comparatively, they function like enormous pendulums, with resonating periods matching the first two primary modes. These dampers utilize the vibration energy and then dissipate it, functioning similarly to a car’s shock absorbers. So far, they have proven to be very effective.
Aesthetically, the simplicity of the Spire belies its ingeniously complicated structural design.
Recently, Taipei 101 – Taiwan’s loftiest building successfully weathered a 7.4 earthquake. The building’s design had been crafted to endure typhoons with wind speeds reaching 200km/h and earthquakes projected within a 2000 year timeframe.
The architecture incorporates a colossal pre-calibrated mass damper, akin to the one found in the Spire, although on a vastly larger scale. This damper has the capability to suppress vibrations by 50% or greater, thereby preventing catastrophic structural failure. This enormous pendulum bob, a hefty steel sphere weighing in at 660 tonnes, hangs nearly 300 metres above the ground and surpasses the weight of the dampers in the Spire by several orders of magnitude.
Peter Lynch, a professor emeritus from the University College Dublin’s School of Mathematics & Statistics, shares his thoughts and insights on his blog – thatsmaths.com.”