In order to understand the concept of the vibration measurements, some basic vibration physics is presented.

In any natural simple vibration (simple harmonic motion), the following applies. It is noted that vibrations are complex, however, each oscillation can be broken down into simple harmonic motion.
 

A sinusoidal displacement,

Displacement = a* sin (wt) holds the following relationships.
Velocity = aw * cosine (wt) and,
Acceleration = -aw² * sin (wt) therefore,
Velocity = Displacement * w and,
Acceleration = - Displacement * w²
Fig-1
Where,

The natural frequency of a building or an element in a building is, to a large extent, governed by its size and, to a lesser extent, by its fixity.

The natural frequency of a tall building can be approximated by:
 

This simple formula has been shown to give results, which are as accurate as sophisticated and complex calculation procedures.

Damping values are more difficult to evaluate; generally in the absence of measurement, specialist advice should be sought.

Should the structure or nature of use be sensitive the specialist advice on stiffness, the magnitude of forces and the interception of buildings with the medium transmitting the forces should be sought. Some information can be found in reference literature.

The natural frequencies of elements of buildings, such as floors are largely governed by their physical dimensions.

Dynamic forces induced by people (when dancing for instance) may become unacceptably large if those people regularly jump up and down.

Cases where vibration has caused damage to buildings and its contents have been extremely rare and the generalisation can be made that vibration must become unpleasant or painful to the occupier long before there is any possibility of damage to the building itself.

Nevertheless, complaints are often perceived that minor damage, such as the cracking of plaster ceilings, brickwork and window glass, as well as the loosening of roofing tiles, have been caused by some particular source of vibration. Such complaints are common which may be due to the extreme sensitivity of the human body. When a new source of heavy vibration arises and is such as to disturb the occupier of a building, he may become concerned about the structural effects of such vibration. He may then assume that cracks, which have escaped notice for some time, have been caused by vibration. There are many causes of cracking in buildings and crack should not be attributed to the effects of vibration until other causes have been eliminated.

Work in USA in connection with blasting vibration included tests on floors and ceilings where deliberate attempts were made to cause damage by excessive blasting or by mechanical agitation, even under sustained resonant conditions. Sustained amplitudes of vibration of the order 2500 microns (2.5mm) were required to produce severe cracking of plaster and these are far in excess of the amplitudes produced by traffic, factory machinery, compressors, or other common sources of vibration.

Door slamming or walking about heavily is likely to produce greater vibration and shock than most external sources of vibration.

The actual perception of motion may not, in itself, be annoying. An individual's perception of what is "normal" or "abnormal" may depend on previous experience and expectations. For example, someone who lives, as well as works, in a multi-storey building may be less affected by building motion than someone who only works in such a building.

Recent British Research Establishment (BRE) tests, under controlled conditions in three tall buildings, showed that even when levels of vibration caused feelings of nausea in a number of subjects, the safety of the building was not prejudiced.

Under certain conditions the human body can detect amplitudes as small as one micron; amplitudes of the order of 0.50 micron can be detected with the fingertips (all displacements are peak amplitude). The basic data concerning "whole-body" sensitivity to vibration are provided by the Reiher-Mesiter scale. Although this was developed over sixty years ago, its validity is still accepted for steady-state vibrations, but for transient vibrations, e.g. floor vibration produced by people walking, there is evidence that amplitudes much greater than those given by the scale are necessary to produce sensation at a given frequency.

In the Reiher-Mesiter investigation it was noted that vertical vibration was most readily detected when people were standing, and horizontal vibration was more noticeable when laying down. The sensation produced depends on frequency and amplitude. An amplitude of 100 micron constitutes an annoying vibration if the frequency exceeds 5 Hz and a painful vibration if the frequency exceeds 20 Hz. An amplitude of 10 micron is just perceptible at 5 Hz, but would be annoying at 50 Hz.

Expressed in terms of peak velocity, the threshold of perception corresponds to a velocity of 0.3 mm/sec and a vibration is annoying if the velocity exceeds 2.5 mm/sec. This is half of our expected limit for the switchyard.

The problem concerned with human perception of random motion is covered in the DIN 4150 Standard (Table 1). In the standard, values for the degree of perception (K) are derived from :

It is likely that the majority of problems concerned with vibration will be in the area of human tolerance to its effects. Major sources of vibration energy are road and rail traffic and the wind. Human tolerance is dictated not only by scientific but also psychological factors, and as such a rigid definition of what constitutes a nuisance may not be possible.