architecture - acoustic notes - school of architecture and interior design

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1 Acoustical Design for Architects Mike Wilson Low Energy Architecture Research Unit School of Architecture and Interior Design University of North London Spring House 6-40 Holloway Rd. London N7 8JL U.K. Tel: +44 171 753 7006 Fax: +44 171 753 5780 Introduction For good room acoustics the following conditions need to be satisfied 1) There needs to be good sound distribution in the room. This may be effected by various acoustic ‘faults’ such as concentrations and shadows, ringing and colouration, or echoes. 2) The background level needs to be an optimum for the acoustic activity in the space. Often this optimum will be the minimum sensibly obtainable but may not if masking noise is required such as in open plan offices. 3) The reverberation or rate of decay of the sound should be an optimum for the acoustic activity. Sound Behaviour within Rooms Sound within rooms can be analysed using different techniques. These can usefully be divided into the following categories: 1) Geometric methods. By using the basic law of angle of incidence equals angle of reflection the sound field may be described. The drawback of this method is that it takes no account of the wave nature of sound where typical wavelengths can be of the same order of magnitude as the reflecting or obstructing objects. One simple example of this is the acoustic barrier. The sound behind the barrier is not simply reduced equally over the whole noise spectrum but the tonal character is changed. The longer the wavelength or the lower the frequency the more the sound wave diffracts or bends round the barrier reducing the attenuation. With sound reflectors the lower frequencies may not ‘see’ the barrier at all, the middle frequencies may suffer diffuse reflection while only the higher frequencies undergo specular or mirror-like reflection. 2) Statistical methods. The rate of decay of sound in the room depends on the mean free path of the sound wave between reflections and the absorption of surfaces,

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Page 1: Architecture - Acoustic Notes - School Of Architecture And Interior Design

1

Acoustical Design for Architects

Mike WilsonLow Energy Architecture Research UnitSchool of Architecture and Interior DesignUniversity of North LondonSpring House6-40 Holloway Rd.London N7 8JLU.K.

Tel: +44 171 753 7006Fax: +44 171 753 5780

Introduction

For good room acoustics the following conditions need to be satisfied

1) There needs to be good sound distribution in the room. This may be effected byvarious acoustic ‘faults’ such as concentrations and shadows, ringing and colouration,or echoes.

2) The background level needs to be an optimum for the acoustic activity in the space.Often this optimum will be the minimum sensibly obtainable but may not if maskingnoise is required such as in open plan offices.

3) The reverberation or rate of decay of the sound should be an optimum for theacoustic activity.

Sound Behaviour within Rooms

Sound within rooms can be analysed using different techniques. These can usefullybe divided into the following categories:

1) Geometric methods. By using the basic law of angle of incidence equals angle ofreflection the sound field may be described. The drawback of this method is that ittakes no account of the wave nature of sound where typical wavelengths can be ofthe same order of magnitude as the reflecting or obstructing objects. One simpleexample of this is the acoustic barrier. The sound behind the barrier is not simplyreduced equally over the whole noise spectrum but the tonal character is changed.The longer the wavelength or the lower the frequency the more the sound wavediffracts or bends round the barrier reducing the attenuation. With sound reflectors thelower frequencies may not ‘see’ the barrier at all, the middle frequencies may sufferdiffuse reflection while only the higher frequencies undergo specular or mirror-likereflection.

2) Statistical methods. The rate of decay of sound in the room depends on the meanfree path of the sound wave between reflections and the absorption of surfaces,

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objects and air.

3) Wave Theory. A full description of the sound field in a room depends on solving thewave equations in that room. This is difficult without immense computing power andis normally limited to simple geometry. It is essential however in predicting standingwaves ( otherwise known as room modes or eigen functions) , and particularlyimportant in small room (studio) acoustics.

Analysis of Room Shape

Most acousticians would try to avoid concave focusing shapes. If unavoidable they canbe treated with absorber but this will often lead to loss of loudness. Concave shapesare often associated with echoes. Within approx 50 ms of the direct sound arriving atthe listener the following reflections are integrated by the ear. Thus strong earlyreflections are very important in ensuring a sound is perceived sufficiently loudly.Where neither wall nor ceiling exist to provide these reflections the area of the floorin front of the source provides an important reflecting surface. This is important inamphitheatres where the apron provides such a facility. Rays can be drawn to ensurethe audience can hear the reflected sound and this determines the raking. Note thatglazing rays over the heads of an audience are heavily absorbed. A reflection arriving80 ms after the direct sound will be perceived as part of the general reverberation ofthe room or if it is sufficiently strong as an echo. Concave shapes concentrate soundand therefore increase the likelihood of an echo. An important consideration is therelationship between the radius of curvature of the concave surface and the roomdimensions. In the following diagram for a room with a dome or vault the radius shouldbe less than half the source - max ceiling height to ensure the reflected sound is nomore concentrated than that from a flat surface. Note that the sound reflected from aflat surface would be concentrated in distance d while the concave surface covers adistance d’.Fig 1 ( Source Ref1)

A similar methodcan be applied toalert designers tothe potential of anecho in anauditorium .Assuming asimple rectangularshape for an echoto occur twoconditions need tobe satisfied:

1) The pathd i f f e r e n c ebetween reflectedand direct sound should be at least 17m. This is the distance covered by a sound

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wave in 50 ms travelling at 340 m/s.

2) The reflected sound should have sound energy at least 10% of the direct sound.

The following diagram shows the critical dimensions

Fig 2 ( Source Ref 1, p. 120.) CR = Critical Region, r, x - axis, source-receiverdistance, h, y-axis, effective ceiling height

Ray tracing is a very common technique for investigating the behaviour of reflectorsand an example is shown below

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Fig 3 ( Source ref1, p 125) Ceilingprofile for theGerman Opera inBerlin. Top:proposal based onray construction.Bottom: ceiling asbuilt ( architect,B o r n e m a n n :a c o u s t i cc o n s u l t a n t s ,Cremer andGabler)

Elliptical shapesneed very specialconsideration. It isvitally importantthat no source ofsound is locatednear either of the foci as these will be focussed at the other focus. They are bestavoided but are a common architectural form.

In general the areas that need attention for echoes in theatres and concert halls arethe rear wall, particularly the intersection of ceiling and rear wall and balcony fronts.This may be achieved by the use of absorber or correct orientation of the surfaces.

Reflectors are often used in theatres and concert halls either to increase earlyreflections to parts of the seating area which are some distance from the source ormore particularly in concert halls to increase diffusion. Care must be paid to the sizeof the reflector as small reflectors will not reflect low frequency sound ( due todiffraction effects) and the reflection does not become fully specular until thedimensions of the reflector are several times larger than the wavelength of the sound.

Ringing and colouration are a phenomenon in small rooms that are caused by flutterechoes and standing waves. Some acousticians will argue that these are essentiallythe same phenomena but it is easier to treat them separately.A flutter echo is caused by repeated echo between two hard parallel surfaces and ismost clearly noticeable when the surfaces in the other dimensions are absorbing.Where the dimension of the space is small these appear as a ring but with largerdimensions can appear like (subdued) rapid machine gun fire. They can be cured bytreating one of the surfaces with absorber or where this could cause an unacceptableloss in reverberation such as in a recording studio by building the walls out of parallel-an early acoustic version of deconstructivism.

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Sound as a wave

To understand standing waves it is necessary to understand a little about sound asa wave.Sound in air is a longitudinal wave, that is the pressure fluctuations which are thesound wave take place in the direction of travel of the wave. A pure tone is a sinewave where the wavelength is the distance between two successive compressions orrarefractions and the frequency is the number of waves that pass a point in spaceevery second.

Fig 4

The range of audible sound stretches from a frequency of 20 Hz to 20000 Hz ( Hz= Hertz = waves per second). As we grow older our hearing at the high frequenciesfalls off (presbycusis) . Additionally hearing loss caused by excessive noise during alifetime ( the permanent threshold shift as opposed to the temporary threshold shiftwhich is experienced when coming out of a noisy space such as a disco) occurs athigh frequencies around 4 kHz.

Standing waves are caused by the incident and reflected wave at a surface interferingwith each other. The result is a series of nodes and antinodes in space, the formerbeing places where there is no change in the relevant property ( e.g. sound pressure)with time and the latter where the property fluctuates at a maximum. A pressurefluctuation maximum (antinode) is produced against the wall whereas the air particlescan barely move against the hard wall and give rise to a particle velocity node. Apartial standing wave is formed against any surface but a full standing wave will notbe set up unless the nodes and antinodes from another partial standing wave formedagainst an opposite parallel surface coincide. The room dimension under which thiswill occur is related to the wavelength by the expression:

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Page 32: Architecture - Acoustic Notes - School Of Architecture And Interior Design

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ÒaÒSøeR_øúýiøeR�:}û È 3#d65úò� È ¾Iâß���ÁéÎIâ"Ô¦Ûkâe×�áÓ¾IÙk×�ÛÝÐ,ÑÝØ�ËðÕ\×�Ûà¶O×Ièaâ�Ð,ÑÝ×aØð˨×aÏ�Õ¨Ô�¼�ÑÝ×�Ûkâ�ÏÖâ¦ÑÝ×�Þ�au¼oÕ�ÞåË�ÞiÏÎ�Ûkâ"Ë�Þ�ÑkÌ¡×Iâ�×IË æ ÎIâÔ¦Ûkâe×�áaÞ¨û¾aÊIËf˨×�Õ�¹3âÔÖÞ�ÑÝ×SûSÀ+Õ�Ï�º�ê ¾aÎIÔÔ"âèIÕ\×SûS´�Ô¦Õ\×^@�Ë�ÛaákËkûSÀ_ÊIâ"Ôâ�ÒfbÜÑÝ×IË�Þ¨ûSÁ�ÎIâÔ¦Ûkâe×�áà½�ÞåËà¾aÏÎ�Ûkâ"Ë�Þ!ÂOÏ�Û È û�3#d65eRø È »_âeËÜÔ"Û�ÞÉÏeÎIÛ�â�Ë�Þ�ÑÝÌ.Ï�ÊùË\Ð�ØðÕ\ÔußfÑfØíÌ5ÑfÐAÏ�â~×�Ò�Õ�Þ�ÞåâèaË�Þ�ÑkÔÖÕ\Ð æ ÎIâ"Ô¦Ûkâe×�áaÞ¨ûS¸5Æ ÇìÐ<â"Ì5Ì5âeÏÊ�Þ¨ûO¾IËfß�ÑÝ×�Ûà¶OÎaÐ,ÑÝÒIË�Õ�×¼�Ñf×aÌ�Ë\Ð9Ë\×ùß¨Ë Ñä×g¾aßÜâeË\×ùߨË�Õå×IÛÅ¿OËÜß�Êk×IÑ�Ô"ÑkáÝÙ)ÕåÏ+ÏeÊùËža˨Ð<èaâ"ßfË�ÑkÌ ´!Ð<ߨÊIâeϦËfßÜÏÎaÐ<ËkûSÀuÕ\ÐÉâ¦Þ[3#d�dkó_û_ÒaÒgd�daý#3�ó��� È ¼�¸5Á�¾I¶�Ç�ÎIâ¦ÛkËí´Åû�3#d65h:ò È Á�¾E5e�_øaø�ai3#d65eR: È Ã�Õ)�aâe×�áãÎ�ÞåË�ÑkÌ�ÏÊIËkû_Ï"ÊI˨Ð5Ø)ÕÜÔ�ØãÕfÞ�Þ�ÑkÌoÏ"ÊIË æ ÎIâ"Ô¦Ûkâ�×�á�Î�Þåâ�×�áÏÊIËÜÐ5Ø)Õ¨Ô"ÔÙgÑÝÒIËÜ×gßfËfâ"Ôâ�×�áaÞ¨û/@�à Á�Ð5Î�áaákËÜØ)ÕÝûS¶O×I˨Ð,ákÙ_ûSÃ�ÑkâÖÞiÏÎaÐ<ËðÕ\×�Û¼�ÔâeØ)Õ\ÏÖËÅâ�×�ÁéÎIâ"Ô¦Ûkâe×�áaÞ£¾IÙkØÅÒ�ÑaÞåâ�ÎaØ�ûO¾I˨ÒaÏ¦Ë¨Ø æ ˨Ðj3#d�dkó_ûSµ ÑÝÏ"Ϧ˨Ð,ÛaÕÜâ�× ÈR È ´�ß�ÑÝÎ�ÞiÏÖâßíÀtÐÉâèIÕ¨ßfÙ�â�×ñÑkÌ5Ì9âßfË�Þ�ýoµ�Ë�Õ¨Ô�Õ\×�Ûà¸AØãÕfákâ�×IËäÛ}ûSÀk@´�Ô"Ô¦ÑkÚ�Õ¨Ù_ûSÀ_Ð,Ñkߟ<º�´ÅûS·�ÑkÔ�ÎaØðË[5aûSÀuÕ\Ð5Ïl3Åÿ73#d65h:��iû_ÒaÒöøhdaý���� È5 È ´�ß�ÑÝÎ�ÞiÏÖâßíÀtÐÉâèIÕ¨ßfÙ æ ˨ϦÚ�Ëf˨×ñÑkÌ9Ì5âßfËäÞ¨ûSÀk@�´�Ô"Ô¦ÑkÚ�Õ¨Ù_ûSÀ_Ð,Ñkߟɺx´Åûÿ73#d65hd��iû_ÒaÒf�Iòaý���d Èd È ¿OÊIËÅÌ5â"ËfÔ¦ÛãÒIËÜÐ<Ì<ÑÝÐ5ØãÕ\×IßfË�ÑkÌ�Ò�Õ\Ð5ÏÖâ¦Õ¨Ô"ÔÙgÑÝÒI˨×ÓÛÝÎ�Õ¨Ô�ákÔÖÕ¨ëfâe×�á}ûuÇ÷�˨Ð5Ð<ÙgÕ�×�ÛൡÆ�»+ÑÝÐiÛ}ûS´!ÒaÒIÔâ"Ë�Ûà´�ß�ÑÝÎ�ÞiÏÖâß�Þ�ÿ�R��iû�3#d�R��_û_ÒaÒ^�m3føúý�����R È3�ó È Á�µ�¶Q¸�×IÌ<ÑÝÐ5Ø)Õ�Ϧâ¦ÑÝ×�À+Õ�ÒI˨Ðj37�eB�5hd}ûS¿�ÊIËíâ�×�ÞiÎIÔ¦Õ�Ϧâ¦ÑÝ×ÓÑkÌ�ÛkÚ�ËfÔÔ"â�×�áaÞÕfáaÕ¨âe×�ÞiÏ�ËÜïaϦ˨Ð5×�ÕÜÔ�×�ÑkâÖÞåË È3�3 È ¿OÊIË�Þ�ÑÝÎa×�ÛBÕ\Ï"Ϧ˨×aÎ�Õ�Ϧâ¦ÑÝ×ÓÑkÌoÒ�ÕfÞ�Þåâ"èaËÅèa˨×aÏÖâÔ¦Õ�Ï�ÑÝÐ,Þ¨ûO¾^bÜÕ\Ð9Ð,Ñ}ûÀ_Ð,Ñkߟɺx´Åû�3#d�dkó_û�37�ñÿ�ò��éÒaÒ^�m3Üýn��R3�� È ¾IÑÝÔ"ÕåÐ Õ Ð9ß�Êaâ�Ï"˨ß�ÏeÎkÐ9Ë�Õ¨Þ�Õå×)â�×IâeϦâÖÕ\Ï�ÑÝÐìÌ<ÑÝÐ�Îa×Iß�ÑÝ×IèaËÜ×aϦâ¦ÑÝ×�ÕÜÔ�ÒIÔÖÕ\×a×Iâ�×�áBÕ�×�ÛBÛaÕ¨ÙaÔâÖáÝÊaϦâe×�áãϦËfßÜÊa×Iâ¦çkÎIË�Þ¨ûN Æ!ËäÕ\×SûSà ¹3â"Ô¦Þ�ÑÝ×Sû/b�¹üÕÜÔM�a˨Ð�ûO¾IËfßäÑÝ×�Ûà¶�ÎaÐiÑÝÒIË�Õ\×ñ¼�ÑÝ×IÌ5˨ÐÉ˨×IßfË�ÑÝ×ö¾}ß�â˨×IßfËðÕ\×�Ûà¿.ËfߨÊa×�ÑkÔÖÑaákÙgÕ\ÏÏÊIË)¾I˨Ð<èaâß�Ë�ÑkÌ�´�Ð<ߨÊIâ�ÏÖËfߨÏ"ÎaÐ<ËkûSÀuÕ\Ð<âÖÞ[3#d65hdãÒaÒ����Iý���:3fø È Æ�Ë�Þåâ¦áÝ×ñÑkÌìÕ ×�Õ\Ï"ÎaÐ,Õ¨Ô"ÔÙBèa˨×aÏÖâÔÖÕ\ϦË�Û)Ô¦Õ æ ÑÝÐ,Õ�Ï�ÑÝÐ<Ù æ ÎIâ"Ô¦Ûkâe×�áàâ�×Â.ËfâßfËäÞiϦ˨Ð�ûS¶O×�ákÔ¦Õ�×�Û}ûSÁ¡»+ÑÝÐiÛBÕ\×�Ûà´ ¾ZÊ�ÑÝÐ9Ï5ûSÀSÂ1¶.´o3#d�3fûO¾IËfèaâ"ÔÔ"Ë3#d�d�3fû_ÒaÒ%ø/3#daýiøe���37� È ÀuÕfÞ�ÞåâèaËðÕ\×�Û[@�Ù æ Ð<â¦Ûg¾_ÑkÔÖÕ\Ð�¼�ÑÝØíØ�˨Ð<ß�â¦Õ¨Ô.Á�ÎIâÔ¦Ûkâe×�áaÞ¨ûS¸5¶.´ ¿�ÕfÞ��Ç�Ð,ÑÝÎaÒ^]�¸åûS´�ÛkèIÕ\×IßfËäÛB¼�ÕfÞåËà¾aÏÎ�Ûkâ"Ë�Þ£¾I˨Øðâ�×�Õ\Ð�ûS´�ÒaÐ<âÔp3#d�d�3ª¬«­«L®�¯g°�±² q

THE NATURE OF VIBRATION : BASIC CONCEPTS AND DESCRIPTORS

Introduction This Section begins with a consideration of the nature of vibration, and of the terms and

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parameters which may be used to describe and measure it, starting with the simplest, singlefrequency vibration and then continuing to more complex types.

Single frequency vibration A vibration is a type of motion in which there is a to and fro oscillation about a fixedposition. In the case of the simplest type of vibration the displacement, from the fixedposition varies sinusoidally with time, t, and described mathematically by :

x = X.sin t = X sin 2ft

where X is the vibration amplitude, and is the angular frequency, in radians per second, equalto 2f, where f is the frequency of the vibration, in cycles per second, or Hertz. Frequencyis the reciprocal of the period, T, of the vibration, which is the time taken for one completecycle of the motion to occur.

ie f= l/T

The Root Mean Square value, RMS, of a vibration is given by :

where x(t) denotes that displacement x is a function of time, t.

In the case of a sine wave vibration where x = Xsin2ft, evaluation of the above expressionshows that RMS = X/ ie that:

RMS = PEAK / = 0.7071 x PEAK

In this case also, the peak value is the same as the amplitude, and the peak to peak valueis twice the amplitude. A reduction by a factor of in terms of displacement corresponds to areduction by a factor of 2 in vibration energy (compare with the relationship: sound intensity(sound pressure) ) so that, for a sinusoidal vibration the RMS value is 3 dB below the peak2

value.

Displacement, Velocitv and Acceleration

Velocity is the rate of change of displacement, with respect to changes in time. During acomplete cycle of the vibration the velocity also changes, through a complete cycle, as wellas the displacement. Similarly acceleration is rate of change of velocity, and cyclic changesof acceleration will also occur during the vibration. These three cycles have the samefrequency, but different amplitudes: X (displacement), V (velocity), and A (Acceleration).

Displacement, velocity and acceleration therefore give three different ways in which avibration may be described and measured. The three are obviously related, and, for singlefrequency vibration, sinusoidal vibration only the relationships, between the three amplitudesare:

V= 2fX

and A= 2fV

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from which A = 4f X2

A similar set of equations relate the three RMS values.

Displacement, X may be measured in m., mm. or m. (microns). Velocity, V, may bemeasured in m.s , or mm.s .Acceleration, A, is measured in m.s .-1 -1 -2

Vibration Isolation

A vibration isolator is a spring or mount which reduces the transmission of the vibration tothe sturcture at freque ncies 2 x natural frequency of spring or mount. The transmissibiltiy1/2

(T) is given byT = 1/ (1 -[f/f ] )r

2

where f is the driving frequencyand f is the natural frequency of mount ( isolator)r

.

Springs and mounts may be simply sized by their static defection under load. The naturalfrequency of the loaded mount is given by:

f = 15.8/d where d is the static deflection in mm and f the natural frequecy of the loadedr r1/2

mount.

More Complex Vibrations, and Vibration Spectra. More complex vibrations may be thoughtof as being built from a combination of simple sinusoidal vibrations, and represented by afrequency spectrum. The frequency spectrum of a single frequency vibration with a sinusoidalwaveform is a single line. Vibrations with a harmonic waveform, ie one which repeats itselfexactly, have a line spectrum, in which the frequency components are integer multiples of thefundamental frequency defined by the period of the waveform. Such a series of lines is oftencalled a Fourier series, after the French mathematician J.B.Fourier (1768-1830) who showedthat any repetative function can be broken down (ie analysed into) a series of sinusoidalfunctions. The waveform of a random vibration never repeats itself and has a continuous

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frequency spectrum, ie one in which the lines have moved infinitesimally close together. Thiscontinuous spectrum may be analysed into octave or one-third octave bands, exactly as forsound signals.The spectrum of a single transient vibration is also a continous spectrum, with,usually, higher levels at the lower frequencies and with the levels reducing at higherfrequencies. Repeated transients produce a line spectrum in which the line spacing isdetermined by the repetition rate, but where the shape of the spectrum is determined by thewaveform of the transient. Examples include the vibration produced by rotating machines suchas fans, pumps and motors, and reciprocating machines such as engines.

THE EFFECTS OF VIBRATION ON PEOPLE

Depending upon the level, and a variety of other factors, vibration may affect people’scomfort and well-being, impair their efficiency at performing a variety of tasks. or even atvery high levels become a hazard to their health and safety. The best known example of theharmful effects of vibration is the White Finger syndrome (also known as Reynaud’s disease)in which prolonged use of hand-held equipment, such as chain saws, in very cold conditions.produces loss of sensation in the fingers. The vibration produced by the various forms oftransportation (e.g. road traffic, trains and aircraft) is of great interest for a variety of reasons.First of all. there is concern about the safety and efficiency of the driver or operator subjectedto vibration; secondly, there is the effect of vibration levels on the comfort of passengers; andthirdly, there is often great concern amongst members of the public about vibration producedin buildings. including domestic dwellings adjacent to roads or railway lines or near to airroutes. A great variety of industrial machinery produces vibration which is experienced bypeople at work. Particular sources which can cause vibration to be experienced by theoccupants of nearby buildings and thus often give rise to concern amongst members of thepublic include heavy-duty air compressors, forge hammers, pile driving and quarry blastingoperations.

FACTORS INVOLVED IN HUMAN RESPONSE TO VIBRATION

The assessment of human response to vibrati on is made difficult by the fact that there are alarge number of factors involved, and because of the great differences between individuals.The main physical factors determining the response to a vibration are the amplitude (orintensity) and frequency, and also the duration (exposure time), point of application anddirection of the vibration. Amongst the configurations which are of interest are thetransmission of vibration from the floor through the feet of the standing person and from theseat via the buttocks and possibly the head (through the headrest) of the seated person. Inthese cases the vibration may be transmitted and felt throughout all parts of the body, and itis the whole body response which will be required. In other cases the vibration may beapplied and sensed at a particular part of the body - the vibration produced in the fingers andhands by power tools being a good example. In this particular case it is the response of thehand-arm system which is important.

As far as vibration transmission is concerned. the human body may be thought of as acomplex mass-spring system. It therefore has a complicated frequency response whichincludes resonances associated with either the whole body or various parts of the body suchas the head or the shoulder girdle. These frequencies may vary greatly for different people.Different parts of the body are therefore most sensitive to different frequencies of vibration.Therefore there is not only a difference in individual sensitivity to vibration, but also a

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difference in individual transmissibility as well. Even the response of any one individual canvary with posture and body tension. The situation may be further complicated by the effectsof seats, headrest. gloves, etc., unless great care is taken to measure the vibration level at theexact point of application of the vibration to the body. One more difficulty in the assessmentof human response to vibration is in separating it from the response to the high noise levelswhich are often associated with vibration-causing processes.

EARLY RESEARCH INTO HUMAN RESPONSE : THE REIHER-MEISTER AND THEDIECKMANN SCALES FOR ViBRATION ASSESSMENT

Many schemes have been developed for the assessment of human response to vibration. Oneof the earliest. published by Reiher and Meister in 1931, covers the frequency range 1-100Hz and vibration amplitudes, specified as displacements in the range 1-100 m.Using theReiher-Meister scale it is possible to rate the vibration as belonging to one of six categoriesranging from imperceptible to painful. Separate scales are used for vibrations in the verticaland horizontal directions. The threshold of perception corresponds to a velocity amplitude of0.3 mm/s and the annoyance threshold to 2.5 mm/s.

Dieckmann, in 1955, proposed a similar scheme but extending to lower frequencies (downto 0.1 Hz) and higher amplitudes than Reiher and Meister. The vibration level is quantifiedin terms of K-values, ranging from 0.1 to 100, which are related to the intensity. The effectof a vibration can be assessed from its K-value:

K = 0 1 - lower limit of perceptionK = 1 -allowable in industry for any period of timeK = 10 - allowable only for a short timeK =100 - upper limit of strain allowable for the average man

The K-values may be read off charts of frequency against amplitude, similar to theReiher-Meister scales, or they may be calculated in terms of displacement amplitude A andfrequency f.

BRITISH AND INTERNATIONAL STANDARDS ON HUMAN REPONSE TOVIBRATION

ISO 2631 Evaluation of human exposure to whole-body vibration

The Introduction to the standard states that : "Various methods rating the severity of exposureand defining limits of exposure based on laboratory or field data have been developed in thepast for specific applications. None of these methods can be considered applicable in allsituations and consequently none has been universally accepted.

In view of the complex factors determining the human response vibrations, and in view ofthe shortage of consistent quantitative data concerning man’s perception of vibration and hisreactions to it, this International Standard has been prepared first, to facilitate the evaluationand comparison of data gained from continuing research in the field; and, second, to giveprovisional guidance as to acceptable human exposure to whole body vibration."

Part 1 1985 : General requirements

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This Part of the standard takes into account frequency (in the range 1-80 Hz), vibrationamplitude (acceleration), duration (from 1 minute to 24 hours exposure) and the direction ofthe vibration relative to the human body. Three different criteria are proposed; workingeffficiency, health and safety, and comfort. These three criteria give rise to three boundariesor limits; the fatiguedecreased proficiency boundary, the exposure limit (for health andsafety),. and the reduced comfort boundary. Fig. shows the limits for the fatiguedecreasedproficiency boundary in terms of the amplitude, frequency and duration for a vertical vibration(along the toe-to-head axis). Exposure limits are 6 dB above and reduced comfort values 10dB below these values, the shape of the contours remaining the same. The human subject ismost sensitive to vertical vibrations in the frequency range 4-8 Hz. Above 8 Hz the responsecontours correspond to constant velocity amplitudes. The ISO standard also allows the effectof broad-band vibrations (i.e. containing many frequencies) to be evaluated .

Parts 2,3 and 4 of ISO 2631 are concerned with the vibration of humans in buildings, at lowfrequencies, and on board ships.

Part 2 1989 : Human exposure to continuous and shock-induced vibration in buildings (l to80 Hz).

Part 3 1985 : Evaluation of exposure to whole-body z-axis vertical vibration in the frequencyrange 0.1 to 0.63 Hz.

Part 4 : Evaluation of crew exposure to vibration on board sea-going ships (1 to 80 Hz}. Thispart of the standard is at present at the stage of draft.

The subject matter of parts 1,2 and 3 of IS0 2631 are also cover by BS6841 and BS6472.Although there are some similarities there are also some very significant differences betweenthe British and International Standards. One of these is the introduction of the concept ofVibration Dose Value into the British Standards, in order to take into account the effects ofimpulsive and intermittent vibration.

THE EFFECT OF VIBRATION ON BUILDINGS

It is almost inevitable that high noise and vibration levels experienced by the occupants ofa building should give rise to concern about the possible effects that these may have on thebuilding. However, cases in which even minor damage to a building can he attributed directlyto the effects of vibration alone are very rare. Usually many other factors are involved aswell, such as ground settlement or movement caused by changes of moisture content. It isgenerally accepted that the vibration levels in a building would become absolutely intolerableto the human occupants long before they reached a level at which there was danger ofdamage to the building. In cases where minor damage does occur, and in which vibration isalleged to play a part, the most common occurrences are: damage to unsound plaster, crackingof glass, loosening of roof tiles and cracks to masonry. However, it is very likely that existingminor damage may he noticed for the first time by an occupant whose attention and concernhas been aroused hy the disturbance caused by a new source of vibration.

Heavy vibrating machinery located at high levels in a building can produce intense vibrationsin the horizontal direction, and these are more likely to be damaging than vertical vibration.

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Bells situated in church towers can also produce high levels in the building structure.Sustained sources of vibration may produce resonances in buildings or parts of buildings.However, this is less likely to cause problems if the vibrations are transient. The naturalfrequency of a building will depend mainly on its height and base dimensions, typical valuesranging from 10 Hz for a low building to 0.1 Hz for a very tall building. The naturalfrequency is of interest since this type of vibration may be excited by wind loading of thebuilding. Floors, ceilings and windows also have their own natural frequencies. Typical valuesfor floors are in the range 10-30 Hz depending on size and type of construction. People inbuildings are more aware of vibrations transmitted via the floor than from any other part ofthe structure. It is important therefore that the natural frequency of the floor does not coincidewith the range of maximum sensitivity (4-8 Hz) for vertical vibrations of the human body atwhich whole-body resonance occurs. The maximum amplitude usually occurs in the centreof the floor. Modern long-span floors are likely to cause an increase in floor vibrationamplitudes. Natural frequencies of windows range from 10 to 100 Hz depending on the sizeand thickness of the glass, and for plaster ceilings typical values range from 10 to 20 Hz.

Many investigations have been carried out in an attempt to define threshold limits for theoccurrence of vibration induced damage to buildings. The evidence from these investigationhas been fully reported and discussed in a Building Research Establishment Report by R.Steffens entitled ’Structural Vibration and Damage’, first published in 1974, and recentlyre-issued. In one investigation on the effects of blasting on buildings it was shown thatbuildings can withstand peak amplitudes of about 400 m. In contrast, typical levels producedin buildings by nearby road traffic often lie in the range 5-25 m. (10-30 Hz). It is often foundthat internal sources of vibration in a building, such as footsteps, door slamming, furnituremoving, washing machines and vacuum cleaners, will produce levels comparable with or evengreater than the external source which is the subject of complaint (road traffic, compressor,pile driver, etc.) Typical vibration levels produced by footsteps and by door slamming can bein the region of 50-150 m.

Other investigations have suggested that limits for damage are best expressed in terms of peakvibration velocity, and various values have been suggested ranging from 50 to 230 mm.s-1

depending on the type of building and the degree of damage. For comparison it is interestingto note that a level of 75 mm.s corresponds to a Dieckmann K-value of 60, which would be-1

extremely unpleasant, and is well into the painful zone of the Reiher-Meister scale (assumingfrequencies in the range 5-40 Hz)

Yet another method for rating vibration, based on energy considerations and developed byZeller in Germany, has been used for assessing possihle damage to buildings. This involvesthe acceleration and the frequency of the vibration, the Zeller power being given by theacceleration squared divided by the frequency, and measured in mm /Hz .2 3

BS7385 Evaluation and Measurement for Vibration in Buildinqs Part 1. Guide formeasurement of vibrations and evaluation of their effects on buildings

This standard, which is identical to IS0 4866 :1990, discusses some of the principles involvedin the measurement and evaluation of building vibration, and gives guidance on informationto be recorded.The following factors are considered :

-the characteristics of vibration (type of signal, range of magnitudes and frequencies)

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produced by different types of source, such as traffic, blasting, pile driving, and machinery

-type of building. Buildings are grouped into fourteen different classes, taking into accountthe different types of construction, types soil and foundations, and a political importancefactor.

-selection of measurement parameters, equipment, transducers, measurement positions, datacollection and analysis.

Most ground-borne vibration entering buildings from man-made sources is in the frequencyrange from 1Hz to 150 Hz. Natural sources such wind, and earthquakes produce significantamounts of vibrational energy lower frequencies, down to 0.1Hz. Vibration induced damageto buildings is classified into categories : cosmetic, minor and major.

Part 2 : 1993 Guide to damage levels from ground-borne vibration

The preferred method of measurement is to simultaneously record unfiltered time-histories ofthe three different orthogonal components (eg x, y, and z) of particle velocity. The (total)particle velocity may then be found, by taking the root mean square value of the threecomponents, andd its peak value obtained. The peak values of the individual componentsshould also be measured, since it is this type of data which has usually been presented in thevarious case histories used to develop the limits in the standard.

The case history data suggests that the probability of damage tends towards zero at levelsbelow 12.5 mm.s peak component particle velocity. The limit for cosmetic damage varies-1

from 15 mm.s at 4 Hz to 50 mm.s at 40Hz and above, for measurements taken at the base-1 -1

of the building. Different low frequency limits (below 40 Hz) are given for two differenttypes of buildings. The limits for cosmetic damage should be doubled for minor damage, anddoubled again for major damage.

BRE Digest 353, 1990 Damage to structures from ground-borne vibration

This Digest reviews various methods for measuring and assessing building damage caused byvibration, including German, Swiss and Swedish standards. The German standard, DIN 4150Part 3 1986, which has been widely used, adopts a similar approach to B57385 Part 2.Guideline values of peak component particle velocity, in mm.s , are given for three different-1

types of building structure. Different limits are given for the frequency ranges : less than 10Hz, 10 to 50 Hz, and 50 to 100 Hz.

SOURCES OF VIBRATION IN BUILDINGS

Road Traffic.

It is the variability of the interaction between tyres and the road which is the main source ofvibration produced by traffic. ’Out of balance’ forces produced by the operation of the vehiclealso cause vibration, but with modern vehicles these are of less importance than the effectsof variability in the road surface caused either by random surface roughness or by

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imperfections such as bumps or potholes. A perfectly balanced engine driving a vehicle alonga perfectly smooth road would not produce any vibration.

The main parameters determining the magnitude and frequency of traffic vibration are : roadsurface profile, vehicle mass and road speed, and the characteristics of the vehicle suspensionsystem, and in particular its natural frequency.

Vibration from trains.

The vibration producing mechanisms are not fully understood, but it is believed that the mainsource of ground vibration from trains is the variability in the interaction between wheels andrails, arising from imperfections, irregularities and roughnesses in the surfaces of both.Irregularities in the track system supporting the rails may also cause vibration. The importantparameters are rail and wheel profiles, vehicle mass, speed and suspension characteristics.

Wind induced vibration

Variability in the wind loading forces on buildings cause vibration, and this is particularlyimportant for tall buildings. Steffens states that serious vibration in tall buildings is likely ifthe natural frequency of the building is less than the frequency of vortex shedding at themaximum wind velocity, and gives a method for calculating both quantities.

Other sources

Other sources of vibration in buidings include earthquake s, blasting operations, pile-driving,acoustic excitation eg from blasting, road and rail traffic and aircraft, machinery of variouskinds, and human activities such as walking and door slamming. BS7385 Part 1 indicates thecharacteristics of vibration produced in buildings by various sources.

Steffens gives a fascinating and comprehensive account of vibration produced by a wide rangeof sources, including bell ringing, church organs, industrial knitting machines and doorslamming, as well as all the sources mentioned above.

Vibration from pile-driving

There are many different methods of pile-driving, and these may result in vibration whichis either continuous, or intermittent, or impulsive in nature.

BS5228 Part 4 (Appendix A) gives a detailed account of the characteristics of vibrationassociated with various types of pile-driving operations and a wide range of case study data.

Vibration from machinery

The motion associated with the operation of reciprocating machi nes (eg internal combustionengines) inevitably causes vibration.Rotating machinery (such as pumps, motors, fans) alsocauses vibration because there will always be some ’out of balance’ forces associated withthe rotary motion, although in principle the perfectly balanced rotating machine would notproduce any vibration.

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Vibration is also produced as a by-product of the ’working forces’ associated with varioustypes of machine including , for example : cutting, pressing, pumping, abrading and polishing,electrical forces in rotating machinery, combustion forces, aerodynamic and hydrodynamicforces in fans and pumps, forces in bearings, gear meshing forces, and impact forces.

Vibration is also produced by the imperfect operation of machinery caused by wear, loosenessand mis-alignment of parts, and imperfect balancing. It is for this reason that goodmaintenance procedures are so important in minimising vibrationand noise from machines.

Since most machinery operates on a cyclic basis of either rotational or reciprocal movementthe frequency spectrum of machine vibration usually consists of a series of pure tonecomponents (fundamentals and harmonics) associated with the repetition rates of the variouscycles, (and with frequencies therefore dependent on machine speed), superimposed upon abroad band spectrum of raNDOM VIBRATION caused by impacts, wear, and irregularitiesin the machine motion. The narrow band component of the spectrum, or ’vibration signature’as it is sometimes known, can be used to diagnose the source of a particular noise or vibrationfrequency, eg to identify a particular set of gears, or fan or bearing. For a particular machinethe spectrum can also be used to identify the vibration producing mechanism, such as ’outof balance’ or ’misalignment’ and this knowledge forms the basis of vibration monitoring ofmachinery in order to give early warning of malfunction.

THE TRANSMISSION OF VIBRATION

THE PROPAGATION OF VIBRATION IN UNIFORM MEDIA

There are two sorts of elastic waves which can travel in an infinite, ie unboundedhomogeneous solid elastic medium : longitudinal compressional waves, often called P waves,and transverse shear waves, often called S waves. Only the P waves can be propagated in afluid such as air or water. In bounded solids, such as plates, beams, rods and bars (such asin the elements of a building) there are in addition a number of other types of waves, suchas flexural and torsional waves, which are combinations of the two main types. Also inbounded solids and fluids surface waves are transmitted, but, as the name suggests, only onand at limited depths below the surface. Surface waves in solids are also known as Rayleighwaves.

NB Homogeneous means having the same properties throughout the medium, ie ’being thesame everywhere’. Isotropic means having the same properties in every direction

Propagation of ground-borne Vibration

Ground-borne vibration is, then, transmitted by P, S, and, near the surface, by Rayleighwaves. The velocity of shear waves in soils ranges from approximately, 30 m.s to 300 m.s-1 -1

, and for rock it is about 1000 m.s . The velocities of compressional waves is about 2.5 to-1

4 times higher than for the shear waves, and the Rayleigh waves travel at speeds slightlylower than shear waves. The amplitude of surface waves reduces rapidly with depth belowthe surface, so that they are confined within a wavelength or so of the ground. Because of thisRayleigh waves are subject to less spreading loss than P or S waves, and especially in lightlydamped soils or rock, they can travel greater distances with less attenatuion.

Page 43: Architecture - Acoustic Notes - School Of Architecture And Interior Design

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The propagation of vibration in the idealised situation of an infinite, homogeneous, isotropicmedium is well understood, and can be predicted from theory. The propagation of vibrationin the ground is much more complex. Soils are not homogeneous, but are granular, with thevoids between grains sometimes being filled with water. The medium is also usuallynon-isotropic,consisting of a number of strata or layers, each with different elastic properties.Additional types of waves arise from interactions at the boundaries between layers, andbetween waves propagating in the solid soil grains and the water surrounding them. There isusually inadequate or incomplete information about the thicknesses and extent of the variouslayers, and about the relevant elastic properties of each soil or rock type ie elastic moduli,density, wave speeds and damping constant.

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