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.
In large, high-population communities, it can be difficult to build new housing away from busy transport systems such as motorways, under- and over- ground railway systems and tram lines. In some cases, the more easily identifiable impact of the noise output of these systems may be less of an issue than the vibrations which cause the sound in the first place. If a house is exposed to vibration, it presents two main issues; a) structural damage caused by the wall moving in and out of its at-rest position.
The effect of vibration on a building is best demonstrated by constructing a simple mathematical model of the system. In its simplest form, the building can best be modelled as a mass-spring damper system as seen below.
Input signals from heavy traffic or construction travel through the ground to the building. The foundations of the house, and the ground surrounding them, act as a series of springs and dampers, mitigating transmission of vibration at some frequencies, and increasing it at others. The frequencies of vibration transmitted in this way tend to be most important below around 300Hz.
Modelling the spring and damping effects of the foundations and the surrounding soil is extremely tricky and, due to the inhomogeneous nature of such things, an exact solution is almost impossible to find! However, modelling the behaviour of the building to an input vibration is somewhat simple, and can be facilitated by taking measurements of the vibration of walls and floors. The vibration of the building itself can be modelled as a series of plates connected by a spring-damper arrangement, as seen above.
Building vibration occurs most prominently around lower frequencies (typically below 300Hz), which this is because of the nature of the transmissibility of the soil and foundations of the building, as well as typical vibration input characteristics from construction, traffic and rail networks. This presents a particular problem, as panel resonances for walls and slab flooring tend to be around 10-30Hz for vertical vibration, and 5-10Hz for horizontal vibration, so these panel resonances can be easily excited. Panel resonances in buildings can cause damage to facades and roofing, as well as contributing to feelings of nausea and a lack of faith in the construction of the building. Factors which influence the enjoyment of the property are more likely to occur than those affecting the structural integrity of the building, as the magnitudes associated with human effects are more easily achieved than those associated with structural damage.
On especially tall buildings such as skyscrapers, where height is significantly greater than width or breadth of the building, the effect of wind on the structure is an important source of building vibration. In TV towers, Radio antennae and chimneys, the effect of wind can be structurally devastating if not properly accounted for – This effect is best demonstrated on a different type of structure, the infamous Tacoma Narrows bridge which, as a result of wind induced vibration effects shook and twisted itself to destruction in the 1940’s.
Buildings can be classified into two categories with regards to wind-induced vibration; Vibration Sensitive (flexible) and Vibration Insensitive (Rigid). Classification of buildings into these two types is governed by the relationship between height width and stiffness – generally, however, most buildings above 50m in height are deemed to be vibration sensitive.
Aeroelastic phenomena are very complex to model, but their effects can be described quite simply. The following is a list of effects likely to be found in regards to tall buildings.
Wind excitation can cause vibration through several different mechanisms:
- Gust actions in the wind direction
The pseudo-periodic nature of gusting wind can cause turbulence at the bluff face of a structure. This in turn causes vibration of the building.
- Buffeting in wind direction
A high-frequency instability caused by airflow separation around a building. A random forced vibration capable of causing stress fractures on building facades and, in extreme cases, damage to internal supporting structures.
- Vortex Shedding
When a bluff face is presented to a flow of moving fluid, it causes flow separation and reconnection about the body. This leads to periodic generation of vortices behind the object, which cause the structure to vibrate at the frequency of vortex shedding.
A phenomenon which occurs when a positive feedback loop is set up between the natural frequency of a building and the aerodynamic forces acting upon it.
It is generally found that wind-induced vibration is unlikely to damage the structure of the building, but is more likely to damage facades and roofs. It can however induce feelings of nausea and a lack of trust in the safety of the building, which can cause a distinct loss of enjoyment of the property for the occupants.
Such effects as these can be mitigated to some extent by the inclusion of mass-tuned dampers. These are masses attached to springs that can be placed on top of a building, the natural frequency of which is tuned so as to match the natural frequency of the building. This then causes the mass-tuned damper to vibrate instead of the building when natural frequency is reached, damping the vibration of the building at this important frequency. One of the largest mass-tuned-dampers is attached to the Taipei 101 tower, the world’s tallest skyscraper, in order to cope with wind and seismic activity.
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;
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.
The method used for measurement of vibration depends somewhat on which application is being evaluated (Human response, building, machine etc.) and which standard is being employed. For most general purposes vibration can be measured with an accelerometer, but some applications require a Geophone, which measures velocity instead. Outlined below are some typical measurement scenarios and recommended measurements solutions.
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.