OSCILLATIONS AND ENGINEERING

When designing new products, designers need to consider unwanted oscillations in the product, whether that be a new vacuum cleaner, a new bridge, a new electric toothbrush or a new aircraft.
Figure 18.1 shows the Millennium Bridge over the river Thames in London. The bridge was revolutionary: a suspension bridge without the large supporting towers that are generally integral to the design of suspension bridges. It was built to celebrate the new millennium and it opened on 10 June 2000; the first new crossing built over the Thames for over 100 years.
Unfortunately, it had to be closed two days later when engineers detected that, when there were a lot of people walking across the bridge, it started to sway and twist. The effect was made worse because people automatically adjusted their walking so that each pace coincided with the movements of the bridge.

It took nearly two years before the engineers were able to fix the problem and for the bridge to be reopened – at a cost of nearly five million pounds!
Why do you think a designer, designing a new electric toothbrush, should be aware of the effects of oscillations?
It is not only large oscillations that are dangerous; very small, repeated vibrations will cause cracks to form in metals. You will be aware that if you bend a thin sheet of metal back and forth a few times it becomes easier to bend – a few more times and it will break. This is an extreme example of metal fatigue. Much smaller vibrations repeated often enough will cause microscopic cracks to form at points of high stress. These microscopic cracks will widen and, eventually, the structure will fail.
The first passenger jet airliner, the de Haviland Comet, suffered from this problem and after two of the aircraft disintegrated in mid-air, all Comets were grounded. After meticulous investigation, engineers concluded that the most likely cause of the accidents was metal fatigue at the high stress points near the corners of the ‘almost’, square windows. You may have noticed that the windows in more modern airliners are more oval in shape that avoids the high stress points found at the corners of a square shape.

Oscillations and vibrations are everywhere. A bird in flight flaps its wings up and down. An aircraft’s wings also vibrate up and down, but this is not how it flies. The wings are long and thin, and they vibrate slightly because they are not perfectly rigid. Many other structures vibrate – bridges when traffic flows across, buildings in high winds.
A more specific term than vibration is oscillation. An object oscillates when it moves back and forth repeatedly, on either side of some equilibrium position. If we stop the object from oscillating, it returns to the equilibrium position.
We make use of oscillations in many different ways – for pleasure (a child on a swing), for music (the vibrations of a guitar string), for timing (the movement of a pendulum or the vibrations of a quartz crystal). Whenever we make a sound, the molecules of the air oscillate, passing the sound energy along.
The atoms of a solid vibrate more and more as the temperature rises.
These examples of oscillations and vibrations may seem very different from one another. In this chapter, we will look at the characteristics that are shared by many oscillations.

Free or forced?

Free

The easiest oscillations to understand are free oscillations. If you pluck a guitar string, it continues to vibrate for some time after you have released it. The guitar string vibrates at a particular frequency (the number of vibrations per unit time). This is called its natural frequency of vibration, and it gives rise to the particular note that you hear. Change the length of the string, and you change the natural frequency.
Every oscillator has a natural frequency of vibration, the frequency with which it vibrates freely after an initial disturbance.

Forced

Many objects can be forced to vibrate. If you sit on a bus, you may notice that the vibrations from the engine are transmitted to your body, causing you to vibrate with the same frequency. These are not free vibrations of your body; they are forced vibrations. Their frequency is not the natural frequency of vibration of your body, but the forcing frequency of the bus.
In the same way, you can force a metre ruler to oscillate by waving it up and down; however, its natural frequency of vibration will be much greater than this, as you will discover if you hold one end down on the bench and then quickly push down and let go of the other end (Figure 18.2).