Generally, when measuring vibration as a purely mechanical occurrence, we are concerned with its frequency and the magnitude of its acceleration when undergoing harmonic oscillation about an equilibrium position. We choose acceleration as the measurement of amplitude as this is the easiest quantity to measure and, by application of basic calculus, we can infer the velocity and displacement of the vibration. The simplest analogy for a vibration example is that of a mass suspended on the end of a spring:

The frequency of vibration is the number of times the equilibrium point is passed in a given period of time. Each period of vibration covers the motion from equilibrium (or some other marker point) to maximum displacement to minimum displacement, back to the equilibrium or marker point again.

This is an example of simple harmonic motion, a sin curve with the equation; y=sin x. It is easy to see the displacement as a measure of amplitude; here, it is simply ‘1’. This is the factor by which the sin curve is multiplied and as such it’s minimum and maximum will be equal to 1 and -1 respectively. We chose to measure acceleration rather than velocity or displacement, as it is easier to measure and often more accurate due to the nature of the sensors used.

This previous model neglects the important contribution of damping to almost all vibrating systems. Damping can be applied through the addition of constraining layers of material, or from devices like dashpots and mass-tuned-dampers, and serves to dissipate energy from the vibration. Without damping, a vibrating system would just oscillate between two points without stopping. In reality, the material in the vibrating system will provide some damping, as will the air surrounding the system and so this eternally oscillating system could never really occur.

Damping is often expressed as damping ratio, which is the damping in the system divided by the critical damping value for the system. Critical damping is the amount of damping required for the system to return to equilibrium after being displaced, with no overshoot. In the graph above, critical damping is expressed as the green line. An under-damped system is one which allows some degree of oscillation before the system returns to its equilibrium position (The blue line on the above figure), and an over-damped system is one in which the return to equilibrium is hampered by the effects of the damping force (the red line on the above figure).

Some typical examples of vibrating systems include:

• Airplane wings
  Due to the heavy loads placed on the wing of an aircraft, and the fluctuating nature of the aerodynamic forces applied to it (which induce phenomena like vortex shedding and flutter), airplane wings vibrate during flight. Thankfully, systems are in place to stop these vibrations from becoming too great and damaging the wing.
• Heavy machinery
  Machines like diggers and other earth-moving machinery which have large powerful engines and hydraulic parts are often major sources of vibration, both in terms of exposing the user to vibration and generating noise from vibrating panels etc..
• Sound propagation
  Sound is a travelling series of vibrations at different frequencies containing data that the human ear interprets as information about the surrounding environment. It is generally caused by some other nearby system or surface vibrating, such as the diaphragm of a stereo, vocal chords, and car panels being buffeted by wind.

People are subjected to vibration every day, and it is often simply not thought about. When a mobile phone is put into silent mode, its vibration alerts us to messages; when travelling in a car we use the vibration of the car as a form of feedback to monitor its performance; Every sound we hear is the result of something somewhere vibrating – and the sound itself is caused by the air making our eardrums vibrate! However, aside from these useful applications, vibration can be the cause of some serious problems with regards to health, structural damage and stability, and noise problems.

Have you ever stopped to think how many times a day are you subjected to vibration? It’s probably more than you think – every car ride, every train journey, and even every walk subjects you to vibration! But it doesn’t stop there; in some industrial settings, if not properly monitored, levels of subjection to vibration can be enough to cause physical discomfort, reduced performance, or even cause serious illness!

So, how do you know what is a safe level of vibration for you? The fact of the matter is that, until you start to feel the effects of it, you probably won’t realize. With this in mind control organizations such as the ISO and European Council have published guiding documents on safe and maximum levels of vibration, using some key measures of vibration exposure.

This type of exposure is typical of someone sat in a heavy-duty vehicle, such as steamrollers, dumper trucks, and earth-moving machinery. It is also what you would be exposed to, to a lesser extent, whilst driving a car or riding on the bus. Prolonged exposure to whole-body-vibration can cause lower back pain, and cause interference with task completion. For example, someone trying to press a button to activate a specific mechanism on their earth-moving machine will find it difficult to press this button when there is a large magnitude vibration in the vertical direction. It can also cause difficulties with vision, which could prove hazardous when driving on a busy motorway. It has been shown experimentally by using psychophysical scaling techniques that people are more sensitive to whole-body vibration at some frequencies than at others. One scale commonly used to show this is the Wk weighting network specified in document series ISO 2631. This curve states that people are most sensitive around 80Hz, though there is a little variation in perception from person to person.

Three distinct positions are specified for evaluation of whole-body vibration; Sitting, Standing and Recumbent. Sitting is the most commonly used evaluation position, as it is the most commonly used position in real life. For measurement purposes, this creates coordinate systems at the head, seat and the feet, allowing for a total of 9 axis of vibration to be considered in a WBV measurement.

Each of these 9 axes (and pitch, yaw, and roll about the center of mass of the subject) is assigned its own weighting scale which needs to be considered in evaluating its effect – Couple this with needing to take account of the frequency and magnitude of the vibration, and you can soon see; WBV is a complex problem to model!

Standards referring to Whole-Body Vibration:

• ISO 2631 Evaluation of human exposure to whole-body vibration- general requirements
• Part 1 General requirements
• Part 2 Vibration in buildings
• Part 4 Guidelines for the evaluation of vibration and rotational motion on passenger and crew comfort in fixed guide way transport system.
• EU Physical Agents Directive (Vibration) 2002/44/EC

Much like whole body vibration, hand-arm vibration is something you may not even be aware you are exposed to. Usually, this is because your exposure may be in the form of vibration travelling from a car steering wheel through to your hands – it is usually only a problem when subjects are exposed to long periods of higher-magnitude vibration, such as when operating hand-held power tools. According to current ISO standards, two main grip methods are supported as being properly indicative of vibration levels; “Handgrip” and “Flat palm”. It is more common to use the handgrip position for evaluation, as this is the more common method of utilizing vibratory tools, which are the leading exponent in causing hand-arm vibration. This presents a choice two co-ordinate systems for measurement; Basicentric and Biodynamic, the first being based on the object being held and the second using the back of the hand.

As with WBV, there exists in ISO standards a set of weighting networks which are used to evaluate the importance and contribution of each of the three axes towards total vibration exposure.

So, this gives the potential for 6 different measurement axes with several choices of weighting networks depending on your choice of standard, as well as duration direction and frequency of excitation – whilst not as complex as WBV, HAV can still be tricky to measure!

Standards referring to Hand-Arm Vibration:

• ISO 5349-1 Measurement and evaluation of human exposure to hand-transmitted vibration – general requirements
• ISO 5349-2 Measurement and evaluation of human exposure to hand-transmitted vibration – practical guidance for measurement at the workspace
• EU Physical Agents Directive (Vibration) 2002/44/EC

Hand-Arm Vibration Syndrome
The main effect associated with prolonged exposure to hand-arm vibration is the so-called Hand-Arm Vibration Syndrome (HAVS). Luckily, education regarding HAVS is such that we now know how to reduce the risk of exposure and how to identify working practices which could lead to increased risk.

HAVS is often mislabelled as Vibration White Finger – this is indeed one of the symptoms, but is only one of a series of stages in HAVS;

• “Buzzing”
  The first sign is a feeling of buzzing or vibrating within the exposed extremities after use of vibratory equipment. It can gradually progress such that this buzzing sensation can be felt even when not having just used
• Finger Blanching
  Triggered by exposure to cold, areas of the skin on the fingers become pale. This can be accompanied by numbness in the digits, and is also known as Raynauds phenomenon.
• Discolouring of Fingers
  The tips of the fingers start to take on a dusky cyanotic colour, indicative of extremely reduced blood flow to the fingers.
• Necrosis of the Skin
  The final stage is similar to gangrene – starved of blood, the flesh in the fingers starts to die and will begin to fall off.

These extreme symptoms seldom occur any more, thanks to legislation go make employers culpable for this disease when it occurs amongst their workers, and education about the effects of hand arm vibration. HAVS is currently one of the most claimed-for industrial diseases in the UK.

This is vibration in one axis only, as the fixed nature of body panel allows little to no vibration parallel to the plate, and vibrates mostly normal to itself. As this is known about the project, evaluation can be undertaken with a single accelerometer.

Vibration resulting from holding a vibrating power tool such as a chainsaw or vibratory hammer is generally measured at the man-machine interface and considers 3 axes. For this purpose, it would be easiest to use a single triaxial accelerometer attached to the handle of the vibrating machine.

In a piece of heavy machinery such as a digger or dumper truck, vibration is transmitted primarily through the chair to the user. As there are generally two points of contact for the user, it is necessary to measure vibration at the seat, and at the point of contact between the chair and the users back. This requires two sets of triaxial readings to be taken, either at the same time or one after the other, potentially requiring two triaxial accelerometers.

• ISO 8041 – Human response to vibration – Measuring instrumentation. This standard sets requirements to the measuring system and also defines the vibration weighting networks.
• ISO 5348 – Mechanical vibration and shock – mechanical mounting of accelerometers.

• ISO 2631 Evaluation of human exposure to whole-body vibration- general requirements.
  • Part 1 General requirements.
  • Part 2 Vibration in buildings.
  • Part 4 Guidelines for the evaluation of vibration and rotational motion on passenger and crew comfort in fixed guide way transport system.

• ISO 5349-1 Measurement and evaluation of human exposure to hand-transmitted vibration – general requirements.
• ISO 5349-2 Measurement and evaluation of human exposure to hand-transmitted vibration – practical guidance for measurement at the workspace.

The human body’s sensitivity to vibrations is at its most sensitive within 4-8Hz in the longitudinal direction and 1-2Hz in the transverse direction. Longitudinal direction will be the vertical direction for a standing person.

ISO 2631 requires the whole body to be measured in the frequency range 0,5 – 160 Hz. Maximum allowed limit is 1.15m/s2. Single action level is set to 0.5m/s2.

The measurements should be measured simultaneously in all three axes using a triaxial accelerometer mounted into a seat cushion for a sitting person or on a plate or the basement for a standing person.

Besides the whole body vibration there is also hand-arm vibration standards. The ISO 5349 defines measurements to be taken in the frequency range from 1 to 1000 Hz. Maximum allowed limit is 5m/s2. Single action level is set to 2.5m/s2.

The measurements should be measured simultaneously in all three axes using a triaxial accelerometer mounted onto the vibrating device while the person is operating the device under test.