What is vibration?
In 1940, the Tacoma Narrows Bridge collapsed. It did so because engineers did not take one thing into consideration: vibration. When wind pushed against the side of the bridge, the wind separated at the surface and met at the other side, forming vortices. The vortices would induce a periodic twisting force on the cords holding the bridge. The twisting then induced a periodic force on the bridge which matched the bridge’s natural frequency. What this means is that the force kept amplifying, eventually destroying the bridge. Previously, it was “normal” for one side to sink when cars drove over it while the other side was relatively unaffected. But when a sufficient wind came, the entire bridge started twisting back and forth.
Understanding vibration is one of the main reasons that bridge design has improved. Vibration is the back-and-forth (oscillatory) motion of an object. The object oscillates about an equilibrium point. The easiest way to visualize this is by using a spring. Imagine a spring hanging from the ceiling and something heavy is put on it. Once it stops moving, it is at the equilibrium position. Push it and it will move back and forth. It is seen that there is a high point and a low point at which the spring will be found. The high point is the peak while the low point is the trough. The distance between the equilibrium point and one of these points is the amplitude, which shows how strong the vibration is. A higher amplitude corresponds to a higher force that is exerted (in terms of vibration). The distance between two peaks or two troughs is the wavelength and the time it takes for one wavelength to pass a point is the period. The inverse of the period is the frequency and it is measured in cycles per second, or hertz (Hz).
Frequency is likely the most familiar characteristic of any wave phenomenon. On the atomic scale and smaller, energy is directly related to an object’s frequency. Atoms, for example, constantly vibrate with an extremely high frequency of 10 THz (10 trillion hertz). Every object has what is called a natural frequency. Natural frequency could be defined as the frequency at which something will oscillate when struck. Say you plucked a guitar string. The string would vibrate at its natural frequency until it settled down. The important thing to remember is that a natural frequency is seen when there is no repeated force applied to the object. The issue with the Tacoma Narrows Bridge was that the wind ultimately caused a force to be repeatedly applied that nearly matched the natural frequency of the bridge, amplifying the force more and more until the entire bridge fell apart.
What types of vibration are there?
There are three main types of vibration: free, forced, and flutter.
- Free vibration: This is seen when a force is exerted and the object is left to vibrate on its own. The object would naturally settle, but in most applications, this takes too long and can be dangerous. So objects like dashpots and shock absorbers are used to damp the system.
- Forced vibration: This happens when a periodic force is applied and produces a vibration. In steady state, when the time between forces is the same along with their magnitudes, the forced vibration frequency will be the same as the force’s frequency. I.e., vibration frequency equals force frequency.
- Flutter (self-excited vibration): Here, the applied force frequency is the same or close to the object’s natural frequency. Since the frequencies are the same, the amplitude will continuously get larger. When you whistle, the force of the air matches the natural frequency of your lips. The natural frequency is dependent on the tension of your lips. Another example would be if you take a bath and wait for the water to settle. Push against the water with your hand, and don’t push on it again until the wave comes back and reflects from behind you. In other words, push with the wave periodically and if you aren’t careful, water will slosh onto the floor!