November_1970 — Page 34

Vibrations in buidings

DEVELOPMENTS in machinery and transport tend to increase vibration and noise to an extent that may be not only objectionable to people but may interfere with laboratory work and some trade processes. Fears are also expressed that buildings may be damaged by vibration.

During the past 25 years, the Build. ing Research Station in Britain has carried out a considerable number of investigations of ground and structural vibrations from sources which includ- ed forge hammers, compressors, machinery, blasting, pile-driving, road traffic and aircraft, church bell ringing and domestic activities. In no instance was any observed damage found to be directly attributable to the effects of vibration alone.

The risk of damage to normal buildings is extremely small, even when the level of vibration is consider ed objectionable or intolerable by the occupants of the building.

The control of noise is not a pri- mary concern of this article. But the frequencies of vibrations encountered in buildings lie mostly within the range 5-50 Hz and when the frequency ex- ceeds about 20-30 Hz it passes into the audible range. If its energy is suffi- cient, i.e. above the threshold of audi- bility of sound in air, the vibration will then be perceived by the ear as sound. Furthermore, even sub-audio frequen- cies generated in a structure may in- duce higher (audio) frequencies in some parts of the structure; this possi- bility is an important reason for isolat- ing vibrating sources so as to reduce the energy transmitted to the struc- ture.

Terms used in vibration studies

Vibration is repeated movement about a position of rest and many vibrations, particularly those produced by machinery, are of periodic (simple harmonic) nature, like that of a vibrat- ing string. Specific terms are used to describe the extent of the movement, the number of times it is repeated in unit time and the nature of the vibra- tion whether it is free or forced. Cycle: a completed sequence of re- peated events.

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frequency (Hz)

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Part 1 An explanation of some of the terms used in vibration studies and their relationships; human sensibility to vibration the Reiher-Meister and Dieckmann scales; vibration and damage to build- ings.

Period (T): the time taken, usually a fraction of a second, for one complete cycle of movement.

Frequency (f): the inverse of period; the number of times the cycle is re- peated in unit time, usually one second in which case it is expressed in hertz (1 Hz=1 c/s). Amplitude of displacement (A): the maximum displacement from the mean position (position of rest), or half the total, peak-to-peak displace- ment. A convenient unit is the micron, μ; 1μ-10 m. In this article, the simpler term amplitude is used to de- note amplitude of displacement. Velocity: the rate of change of dis- placement. For a vibration of sinu- soidal form, the peak velocity for maximum amplitude A and frequency f is given as 2-4.f. The peak velocity for an amplitude of 400μ and fre- quency 20 Hz would thus be appro- ximately 50 mm/sec. Acceleration: the rate of change of velocity. The maximum acceleration in a vibration of sinusoidal form is given as 42 A.f2. It is sometimes con- venient to express acceleration in venient to express acceleration in

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terms of the gravitational value g; a maximum acceleration of 0.01 g is given, for example, by a sinusoidal vibration of maximum amplitude 25μ and frequency 10 Hz.

Free vibration takes place when an elastic body or system is disturbed from its position of rest by a force or impulse that then ceases to act on it; for example, when a weight resting on a spring is displaced and then released. The frequency of the free vibration is called the 'natural frequency' and its particular value depends on factors such as the elasticity, or stiffness, and the weight or load. The amplitude of free vibration will diminish with time, at a rate dependent on the amount of damping present in the system.

There is a relationship between the theoretical natural frequency of vibra- tion of a system and its deflection under static, point, loading; this is given as fn=15.8/y, where fn is the natural frequency in Hz and y is the static deflection in millimetres. The re- lationship is useful in selecting suitable types of antivibration mountings for machinery, apparatus and structures.

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painful

imperceptible

just perceptible

clearly perceptible

annoying

unpleasant

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amplitude (μ)

Fig. 1. Human sensitivity: Reiher-Meister

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Far East BUILDER, November 1970