# Introduction to vibrations

## Introduction

Vibrations (or oscillations) occur primarily in solid objects (or assemblies of objects) as a result of forces acting upon the objects from outside, or from forces originating inside the objects.

### Example

An example of an outside force is wind acting upon a building or bridge. An example of an internal force is the cylinders in a gasoline car engine.

## Damping vibrations

Soft materials tend to damp out vibrations quickly while harder materials maintain vibrations longer. An object submerged in a dense fluid (liquid or gas) will also have any vibrations quickly dampened by the fluid.

### Examples

A rubber band (an "elastic" in the UK) will quickly stop vibrating, after being plucked, since the energy is rapidly dissipated as heat and sound. Glass, however, being quite hard, may be shattered by sounds at the resonant frequency, as the glass is incapable of rapidly damping the sound energy. Thus, the acoustic energy increases until fracture occurs.

### Home experiment

Strike a bell, then submerge the bell in water. The bell's vibrations and sound should end almost immediately, due to the damping effect of the water. You may observe waves generated in the water as the vibrations pass from the bell to the water.

## Frequency and wavelength

Every vibration has both a frequency (number of vibrations per time period) and a wavelength (time, or sometimes distance, between vibrations). These two values are inversely proportional to one another.

## Natural frequency and resonance

Every object "wants" to vibrate at a certain frequency, called the natural or resonance frequency. This frequency is dependent on the object's material, mass, and configuration. Some objects will also resonate at integer multiples of the natural frequency (twice, three times, etc.).

### Example

Each bell has a specific frequency at which it will vibrate, and thus gives off a certain note when struck.

### Home experiment

Try striking an empty wine glass with your fingernail. You should hear an audio vibration at a certain pitch. This pitch is the resonant frequency of the glass. Now partially fill the glass with water and repeat the experiment. The resonant frequency will have changed for the new configuration.

## Cancelling vibrations

Vibrations may be thought of as a wave phenomenon, meaning that each vibration wave has an associated crest and trough. If two vibrations of the same wavelength/frequency are superimposed (combined), they will either add to each other, if they are in phase (the crests and troughs match), or they will tend to cancel each other, if out of phase (the crests from one wave match the troughs from another). In fact, it is theoretically possible to completely cancel all vibrations by using two waves of identical magnitude and frequency/wavelength.

### Examples

Noise canceling headphones are available which electronically shift sounds half a wavelength behind the input sounds and thus cancel the noise. Some mufflers employ a mechanical system to accomplish the same result. Car engines almost always have an even number of cylinders, so that half the cylinders are up when the other half is down, in order to minimize vibration.

## Speed of propagation of vibrations

Many vibrations propagate (spread) at, or near, the speed of sound in the given material (the speed of sound, unlike the speed of light, is not constant). Some vibrations propagate several times faster however, via shock waves, and other vibrations propagate much more slowly.

### Example

The Earth undergoes a very slow oscillation, known as precession, which causes it to "wobble" about the poles every 25,800 years. The most noticeable effect is that the North Star changes over tens of thousands of years. This extremely slow vibration is caused by tidal forces exerted by the Moon and Sun.

## Uses for vibrations

• Diagnosing mechanical systems: Each type of wear, failure, or loss of lubrication in a mechanical system changes it's configuration and/or acoustic damping properties and thus it's resonant frequency. Experienced operators can recognize differences in sounds made by a machine and know that those differences indicate that specific maintenance operations must be performed on the machine.
• Acoustic lubrication: Since vibrating objects are only in contact with each other part of the time, they exhibit reduced friction between them. For optimal effect, the frequency of the vibration must match the resonant frequency of the objects.

## Dangers of vibrations

• Vibrations may lead to the failure of a component or entire mechanical system. During an earthquake, for example, vibrations may lead to structural failure of buildings, causing loss of life. Wind may also induce vibrations in improperly designed buildings, such as the Tacoma Narrows Bridge, which collapsed due to resonant frequency vibrations in only moderate winds.