- Email: [email protected]
Sound-Insulating Linings Modified Constructions of Technical Rooms
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 106 (2015) 296 – 302
Dynamics and Vibroacoustics of Machines (DVM2014)
Sound-insulating linings modified constructions of technical rooms Michael I. Fesina, Alexander V. Krasnov, Larisa N. Gorina * Togliatti State University, Belorusskaya Str., 14 , Togliatti, 445667, Russian Federation
Abstract The article presents the developed concepts of original noise reducing devices, made in the form of sound-insulating linings wall constructions of technical rooms where noise generation technical objects (the engine room of the sea craft, electric transformer substation closed type, compressor or diesel genera-tor station, etc.) are mounted. The technical result, achieved through the using of the developed noise reducing devices is to get rid of "expressed failures" in the frequency characteristics of typical sound-insulating linings constructions due to the resonant excitation of the lower (transversal, longitudinal) acoustic eigenmodes of air cavities formed by the front panels of sound-insulating linings with oppositely placed wall (ceiling) guards technical premises. For this purpose, the relevant quarter and half-wave design of acoustic resonators and/or sound-absorbing groups preformed separate modules, using crushed fragmented sound absorbers. These constructions are arranged at the appropriate spatial zones of air cavities of sound-insulating linings, where sound pressure antinodes of the lowest resonant acoustic eigenmodes are localized. This allows you to improve the technical, cost and environmental properties of used noise reducing devices. © by Elsevier Ltd. This an open access © 2015 2014Published The Authors. Published byisElsevier Ltd. article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014). Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014)
Keywords: Noise reducing devices; sound-insulating lining; technical room; quarter- and half-wave acoustic resonators; briquetted absorbing separate modules; acoustic eigenmodes
The sound insulation of enclosing walls constructions of a technical premise, in particular of a ship engine room, could be increased by using of sound-insulating linings, lightweight solid-state plate aluminum or plywood elements, referred to some of the distance d from the surface of the partition wall. Terminological definition of "soundinsulating linings'' and the features of its embodiment are shown, in particular, on p. 98...99 of the monograph [1]. The use of composite soundproofing constructions of this type, set on the propagation paths of sound waves, triggers two solid-state dense hedges, which provide appropriate acoustic impedance jumps, created by teir own partition
* Corresponding author. Tel.: +7-8482-53-92-36. E-mail address: [email protected], [email protected], [email protected]
1877-7058 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014)
doi:10.1016/j.proeng.2015.06.038
297
Michael I. Fesina et al. / Procedia Engineering 106 (2015) 296 – 302
wall premises or extra plate mounted solid-state element - sound insulating linings. At the same time, the presence of the air gap d, formed between the solid-state barriers, makes some influence on the physical process of acoustic energy transfer (transformation) through these barriers. These features are characterized not only by mechanically excited vibrational resonance of plate solid-state barriers mass, but also by emerging elastic air mass acoustic resonance centered in the solid state formed between the plate cavity barriers. In particular, these resonant acoustic phenomena are pronounced when the thickness of the air gap d fits the integer (fold) number of half of the sound waves length (λв/2), with corresponding formation of resonating transversal eigentones f md. The arising air acoustic resonances of such type cause a significant loss of sound insulating effect in the applied composite sound insulating construction, appearing at the frequencies of lower transversal eigentones (f md) of the formed the air cavity. As it follows from the work results [2], even the sound radiation enhancing effect appearance (of 1.7 ... 7.7 dB) in the high frequency region of the audio spectrum is possible. At the same time, there are not only the high frequency resonating transversal eigentones f md, but also longitudinal eigentones fmL, fmB, fmH, arising in locked air cavities of sound insulating linings. They are formed along the dimensions (length L, width B and height H) of wall and ceiling panels, formed by technical premise partition walls and sound insulating linings, and attachable end surfaces of bearing elements of floor, walls and ceiling of technical premises (see. Fig. 1). Due to a large size of produced deadlock acoustic waveguides, coinciding with the dimensions of technical premises, resonant longitudinal eigentones are located mainly in the low and medium frequency sound range. As it is known, efficient low-frequency acoustic resonance suppression, produced through monolithic layers of porous sound-absorbing material, in most cases is not sufficiently productive and / or requires the use of a sufficiently sophisticated, time-consuming and expensive techniques (use of thick layers of costly porous soundabsorbing substance, the increase of air gaps dimensions). Arising under the thin-walled sound insulating linings, transversal and longitudinal acoustic resonances of the air cavity at their lower eigentones make intensive strength structural influence on thin-walled plate sound insulating linings. This may be responsible for secondary reradiation of its own structural acoustic radiation, with negative "gaps", occurred in the frequency response of a used sound insulation construction. That is why a formed bulky deadlock acoustic waveguide, characterized by dimensions of sound insulating lining thin front panel and by an oppositely disposed at a distance d bearing element of a technical premise, requires proper design and technological upgrading. In general terms, the elastic fluctuating on its own frequencies air mass, placed in a closed three-dimensional cavity (which is defined by the dimensions of length L, width B, height H and is limited by hard sound-reflecting walls), is characterized by a spectrum of natural frequencies of vibrations (eigentones), whose discrete values are determined according to [3…8] the expression (1):
fm
c
L , mB ,mH
= ට( 2
mL 2 L
) +(
mB 2 B
) +(
mH 2 H
) , Hz
(1)
where c - the speed of sound in air m/s (c= 344.057 m/s at 20 ° C); mL, mB, mH = 1,2,3 ... (integers). Air space closed three-dimensional cavities (see. Fig. 1b), presented in the form of elastic vibrating at its own frequency of air masses and formed deadlock acoustic waveguides, defined by their dimensions, are characterized by the corresponding spectrum of the natural vibration frequencies of f md, fmL, fmB, fmH (eigentones), whose discrete values can be determined from the corresponding expression (2), (3), (4): x when mounting a sound insulating lining to the side walls (left and right) of technical premises
2
2
2
c m m m fmd,mB,mH = ටቀ d ቁ + ቀ Bቁ + ቀ H ቁ , Hz 2
d
B
H
(2)
298
Michael I. Fesina et al. / Procedia Engineering 106 (2015) 296 – 302
x
when installing sound insulating linings to the front and back wall of a technical room
2
2
2
c m m m fmL,md,mH = ටቀ L ቁ + ቀ d ቁ + ቀ H ቁ , Hz 2
x
L
d
(3)
H
when mounting a sound insulating lining to a ceiling of a technical room
2
2
2
c m m m fmL,mB,md = ටቀ Lቁ + ቀ B ቁ + ቀ d ቁ , Hz 2
L
B
(4)
d
1 1
1
1
2
(а) 1
4
B
4
3 4
d
3
d 1
3 4
1
5
H
4
L
1
5
(b) (б) Figure 1 - General view of the technical room with noise-generating technical object (a) and calculation scheme of the technical room with mounted elements of sound insulating linings (b) 1 - bearing elements - walls, ceiling, interior partitions; 2 - generating noise technical object; 3 - faceplate sound insulating linings; 4 - separate bricketed absorbing modules; 5 - sound insulating linings
Michael I. Fesina et al. / Procedia Engineering 106 (2015) 296 – 302
As technical devices of attenuation of acoustic energy resonant amplification process that occurs at discrete frequencies of eigentones of the air volume of the cavities, formed by the enclosing panel sound reflecting surfaces of bearing elements and oppositely placed soundproof front flat sheet and / or front nonflat soundproof panels of sound insulating linings; appropriate types of acoustic resonators R - quarter wave acoustic resonators R' and halfwave acoustic resonators R'', shown in the diagrams in Fig. 2 (a, b) are used.
d 1
1 6
6 6 3
1
6
6 B
5 L
(а)
B 1 dmin dmax
3
8 H
7
9
7 7
5
(б) (b) (b)
Figure 2 - Detail of the technical room cavity with sound insulating linings and set quarter-R' (a) half-wave and R'' (b) acoustic resonators 1 - bearing elements - walls, ceiling, interior partitions; 3 - sound insulating linings faceplate; 5 - sound insulating linings of bearing elements; 6 a quarter-acoustic resonator R'; 7 - half wave acoustic resonator R''; 8 - the throat portion of the acoustic resonator R' or R''; 9 - the tubular portion of the acoustic resonator R' or R''
299
300
Michael I. Fesina et al. / Procedia Engineering 106 (2015) 296 – 302
The geometric length of the tubular portion lrd of quarter acoustic resonators R', intended in particular for suppressing of the lowest resonant transversal eigentone with frequencies fd, is determined by expression (5):
d
4ST
2
π
l'rd= -(0,1…0,3)ට
,m
(5)
where ST is a flow area in m2 of the tubular portion of the quarter acoustic resonator R'. Design of quarter acoustic resonators R' (see. Fig. 3a) is represented by a hollow tubular element, limited by reflecting rigid walls - a tubular part, one of the ending parts of which is overlapped by a reflecting hard bottom, forming its bottom portion. Pref2 Ротр2
11
12
Рпад3 P
11 RmB' 9
l RmB'
inc3
l RmL'
10
9
отр2 PРref2
9 Рпад4
Pinc4
Pref4
12
10 RmH'
РPпад2 inc2
10
RmL' PР ref1 отр1
inc4 РPпад4
PРref4 отр4
l RmB'/2
Rmd'
inc2 РP пад2
8
8
l RmL'/4
l Rmd'/2 PРref3 отр3
РPпад1 inc1
l RmH'
13
8
l Rmd'
отр1 PРref1
inc3 РPпад3
Pref3 Ротр3
Pinc1 Рпад1 10
(а) 8
13
8
РPпадinc
Рпад Pinc 4
12
Rmd ''
12
11 RmH ''
11
9
4
l RmB ''/4
l RmL ''/4
l Rmd ''/2 l Rmd ''
lR311/4
11
l RmH ''
9
l RmL ''/2
9 l RmB ''
l RmB ''
RmL '' l RmL '' 9 11
(b) Figure 3 – Schemes of interlocked modular units, composed of four acoustic resonators R (a - quarter Rmd', RmL', RmB', RmH', b - half-wave Rmd'', RmL'', RmB'', RmH'') with set damping elements 8 - neck portion; 9 - tubular portion; 10 - the bottom part (sound reflecting rigid bottom); 11 – air-swept porous plugs; 12 – perforation holes; 13 footer layer of sound transparent material
301
Michael I. Fesina et al. / Procedia Engineering 106 (2015) 296 – 302
The open end area of the tubular portion with a visco connected thereto a part of an oscillating air column (located behind the plane of the tubular part open cut) forms a neck portion of the quarterwave acoustic resonator R'. Formation of the set values of physical and structural parameters of the quarter-wave acoustic resonators R' made by a choice of their own (resonant) frequency fR', the geometric length of the tubular portion - lr', dynamic length - lR', the given hydraulic diameter of the flow cross section of the tubular part – dfl, the wall perforation coefficient of the tubular part – Kper, the total cross sectional area nhl perforations - Fper made in the wall of the tubular portion. The use of damping porous air-swept plugs of a tubular part, the use of protective footer damping layers of material, mounted on the throat and / or the area of the perforated zone of the tubular portion wall, are also considered . Similar conditions and requirements for supplementing and / or the alternative use of acoustic resonators R constructions, apply to the half-wave acoustic resonator R''. In this case, the geometric length of the tubular portion lrd'' of half-wave acoustic resonators R'', intended to suppress the lowest resonant transversal eigentone with a frequency fd may be determined by the expression (6):
4ST
l''rd=d-(0,2…0,6)ට
π
,m
(6)
Supplementing, taken into account structural parameter of the implement of effective facilities of half-wave acoustic resonators R'' is the need to respect the maximum possible access of their neck portions to each other, according the constructive-technological reasons. It is carried out by appropriate choice of the U-shaped curved geometric shape, providing a selection of the shortest distance ɣ between contours of passage sections in a half-wave acoustic resonator R'' neck portion plane. This provides a common-mode ingress and subsequent terms of in-phase spreading of sound waves in both open neck portion of the tubular part towards each other in every individual sample of a half wave acoustic resonator R''. Their further effective antiphase compensation is carried out in the medial zone of the tubular portion with the opposite spreading of sound pressure impulse towards each other in both areas of their U-shaped tubular portion. The above is also true of other complementary and / or alternative modification upgrading of half-wave acoustic resonators R'' constructions, it was already mentioned above, concerning quarter-wave acoustic resonators R'. The condition of the resonant amplification suppression (removal) of radiation of sound energy, concentrated on air volume eigentones, formed through the thickness of the air gap d, length L, width B and height H of edges technical room 1 - fmd, fmL, fmB, fmH (where m = 1, 2, 3, ...), based on the frequency tuned combination of values of its own (resonant) frequency of sound vibrations of different types of acoustic resonators R - fRd, fRL, fRB, fRH with the specified frequency of eigentones of the sound insulating lining air cavity - fmd, fmL, fmB, fmH. This is achieved by the conditions of providing the multiplicity of dimensions of the air cavity through the thickness of the air gap d, length L, width B and height H with the corresponding values of ulcer-quarter length sound waves (λ/4), and half the length of the sound waves (λ/2), complying (multiple) the given overall dimensions of air cavities of the acoustic resonators R' and R'' tubular parts (dynamic lengths l' R and l''R). Suppression of natural acoustic resonances of the cavity air at the higher harmonic components of multiple (overtones) eigentones, when m> 1 (m= 2, 3, 4, 5, 6 ...) can be carried out through selecting of appropriate values of geometrical lengths lr'' and lr', this type of half- R'' and quarter R', acoustic resonators R (Rmd, RmL, RmB, RmH), which will be a multiple number shorter by 2, 3, 4, ..., according to their basic geometrical length lr'' and lr', defined for the case m = 1. As an alternative and / or complementary technological solution, used for attenuation the acoustic energy resonant amplification process, that occurs at discrete frequencies of eigentones of sound insulating lining air cavities in spatial localization zone of the eigentone sound pressure antinodes, separate briquetted sound absorbing modules, containing separate crushed fragmented sound absorbing elements (which are placed in the cavities of closed separate containers of bearing sound transparent covers (see. Fig. 1b)) can be installed. Features of structural and technological implement of briquetted sound absorbing modules are presented in the monograph [9]. Special limited localized spatial zones in the air cavities, in which separate briquetted absorbing modules are mounted,
302
Michael I. Fesina et al. / Procedia Engineering 106 (2015) 296 – 302
mainly located in the peripheral angle and / or in the ending parts, and / or in the central spatial zones of air cavities, formed under a sound insulating lining. Conclusion Proposed modifications of structural and technological implement of sound insulating linings of wall (ceiling) enclosing constructions of noisy technical premises can eliminate the acoustic resonance impulse of air cavities, formed under sound insulating linings. As a consequence, it allows to increase the sound insulation capacity of enclosing elements of technical premises. Nomenclature 1 2 3 4 5 6 7 8 9 10 11 12 13
bearing elements - walls, ceiling, interior partitions generating noise technical object faceplate sound insulating linings separate bricketed absorbing modules sound insulating linings a quarter-acoustic resonator R' half wave acoustic resonator R'' the throat portion of the acoustic resonator R' or R'' the tubular portion of the acoustic resonator R' or R'' the bottom part (sound reflecting rigid bottom) air-swept porous plugs perforation holes footer layer of sound transparent material
References [1] Nikiforov А.S. (1990) Akusticheskoe proektirovanie sudovyh konstrukcij: Spravochnik. [Acoustic design of ship structures: Directory]. – L.: Sudostroenie. – 200 p. (in Russian) [2] Nurova E.N., Fesina M.I. (2013) K voprosu opredelenija potencialov uvelichenija zvukoizoljacii ograzhdajushhih peregorodok mashinnogo otdelenija plavuchego zemlesosnogo snarjada. [On the determination of the potential increase in soundproofing walls enclosing the engine room of the floating dredge]. Vektor nauki Tol'jattinskogo gosudarstvennogo Universiteta [Vector science Togliatti State University], №2 (24). – pp. 183-186. (in Russian) [3] Tupov V.B. (2005) Snizhenie shuma ot jenergeticheskogo oborudovanija: uchebnoe posobie dlja vuzov po napravleniju «Teplojenergetika» [Reduction of noise from power equipment: a textbook for high schools in the direction of "Thermal Engineering"], М.: Izdatel'stvo Moskovskogo jenergeticheskogo instituta [Publishing House of Moscow Power Engineering Institute]. – 232 p. (in Russian) [4] Helmut V.Fuchs. Shallabsorber und Shalldampfer. Springer-Verlag Berlin Heidelberrg. – 2007. – 546 p.. [5] Cummings A. The effect of a resonator array on the sound field in a cavity. J. Sound Vib. 154, H.1, 1992, S. 25-44. [6] Fücker P. Reflexionsschalldämpfung mittels Reihenresonator. In:Schirmer W (Hrsg) Lärmbekämpfung, Kap. 13. Tribune, Berlin. – 1979. [7] Galaitsis A.G., Ver I.L. Passive Silencers and Lined Ducts. In: L. L. Beranek and I. L. Ver, Eds., Noise and Vibration Control Engineering: Principles and Application, Wiley Interscience, New York. – 1992. [8] Spannheimer H., Freymann R., Fastf H. Aktiver Helmholtz-Resonator zur Daempfung von Hohlraumeigenschwingungen. Fortschritte der Akustik - DAGA 1994, DPG-GmbH, Bad Honnef: 1994. – s. 525-528. [9] Krasnov A.V., Fesina M.I., Baluev A.A. (2012) Razrabotka semejstv universal'nyh shumopogloshhajushhih modulej [Development of a versatile sound-absorbing modules]. Sbornik tezisov dokladov na Mezhdunarodnoj nauchno-tehnicheskoj konferencii s uchastiem molodyh uchenyh «Dinamika i vibroakustika mashin» [Book of Abstracts of the International scientific conference with the participation of young scientists "Dynamics and vibroacoustics machines"], Samara: Izdatel'stvo Samarskogo gosudarstvennogo ajerokosmicheskogo universiteta [Samara: Publisher Samara State Aerospace University] – 5-7 September 2012 – 132-133 pp. (in Russian)
ScienceDirect Procedia Engineering 106 (2015) 296 – 302
Dynamics and Vibroacoustics of Machines (DVM2014)
Sound-insulating linings modified constructions of technical rooms Michael I. Fesina, Alexander V. Krasnov, Larisa N. Gorina * Togliatti State University, Belorusskaya Str., 14 , Togliatti, 445667, Russian Federation
Abstract The article presents the developed concepts of original noise reducing devices, made in the form of sound-insulating linings wall constructions of technical rooms where noise generation technical objects (the engine room of the sea craft, electric transformer substation closed type, compressor or diesel genera-tor station, etc.) are mounted. The technical result, achieved through the using of the developed noise reducing devices is to get rid of "expressed failures" in the frequency characteristics of typical sound-insulating linings constructions due to the resonant excitation of the lower (transversal, longitudinal) acoustic eigenmodes of air cavities formed by the front panels of sound-insulating linings with oppositely placed wall (ceiling) guards technical premises. For this purpose, the relevant quarter and half-wave design of acoustic resonators and/or sound-absorbing groups preformed separate modules, using crushed fragmented sound absorbers. These constructions are arranged at the appropriate spatial zones of air cavities of sound-insulating linings, where sound pressure antinodes of the lowest resonant acoustic eigenmodes are localized. This allows you to improve the technical, cost and environmental properties of used noise reducing devices. © by Elsevier Ltd. This an open access © 2015 2014Published The Authors. Published byisElsevier Ltd. article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014). Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014)
Keywords: Noise reducing devices; sound-insulating lining; technical room; quarter- and half-wave acoustic resonators; briquetted absorbing separate modules; acoustic eigenmodes
The sound insulation of enclosing walls constructions of a technical premise, in particular of a ship engine room, could be increased by using of sound-insulating linings, lightweight solid-state plate aluminum or plywood elements, referred to some of the distance d from the surface of the partition wall. Terminological definition of "soundinsulating linings'' and the features of its embodiment are shown, in particular, on p. 98...99 of the monograph [1]. The use of composite soundproofing constructions of this type, set on the propagation paths of sound waves, triggers two solid-state dense hedges, which provide appropriate acoustic impedance jumps, created by teir own partition
* Corresponding author. Tel.: +7-8482-53-92-36. E-mail address: [email protected], [email protected], [email protected]
1877-7058 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014)
doi:10.1016/j.proeng.2015.06.038
297
Michael I. Fesina et al. / Procedia Engineering 106 (2015) 296 – 302
wall premises or extra plate mounted solid-state element - sound insulating linings. At the same time, the presence of the air gap d, formed between the solid-state barriers, makes some influence on the physical process of acoustic energy transfer (transformation) through these barriers. These features are characterized not only by mechanically excited vibrational resonance of plate solid-state barriers mass, but also by emerging elastic air mass acoustic resonance centered in the solid state formed between the plate cavity barriers. In particular, these resonant acoustic phenomena are pronounced when the thickness of the air gap d fits the integer (fold) number of half of the sound waves length (λв/2), with corresponding formation of resonating transversal eigentones f md. The arising air acoustic resonances of such type cause a significant loss of sound insulating effect in the applied composite sound insulating construction, appearing at the frequencies of lower transversal eigentones (f md) of the formed the air cavity. As it follows from the work results [2], even the sound radiation enhancing effect appearance (of 1.7 ... 7.7 dB) in the high frequency region of the audio spectrum is possible. At the same time, there are not only the high frequency resonating transversal eigentones f md, but also longitudinal eigentones fmL, fmB, fmH, arising in locked air cavities of sound insulating linings. They are formed along the dimensions (length L, width B and height H) of wall and ceiling panels, formed by technical premise partition walls and sound insulating linings, and attachable end surfaces of bearing elements of floor, walls and ceiling of technical premises (see. Fig. 1). Due to a large size of produced deadlock acoustic waveguides, coinciding with the dimensions of technical premises, resonant longitudinal eigentones are located mainly in the low and medium frequency sound range. As it is known, efficient low-frequency acoustic resonance suppression, produced through monolithic layers of porous sound-absorbing material, in most cases is not sufficiently productive and / or requires the use of a sufficiently sophisticated, time-consuming and expensive techniques (use of thick layers of costly porous soundabsorbing substance, the increase of air gaps dimensions). Arising under the thin-walled sound insulating linings, transversal and longitudinal acoustic resonances of the air cavity at their lower eigentones make intensive strength structural influence on thin-walled plate sound insulating linings. This may be responsible for secondary reradiation of its own structural acoustic radiation, with negative "gaps", occurred in the frequency response of a used sound insulation construction. That is why a formed bulky deadlock acoustic waveguide, characterized by dimensions of sound insulating lining thin front panel and by an oppositely disposed at a distance d bearing element of a technical premise, requires proper design and technological upgrading. In general terms, the elastic fluctuating on its own frequencies air mass, placed in a closed three-dimensional cavity (which is defined by the dimensions of length L, width B, height H and is limited by hard sound-reflecting walls), is characterized by a spectrum of natural frequencies of vibrations (eigentones), whose discrete values are determined according to [3…8] the expression (1):
fm
c
L , mB ,mH
= ට( 2
mL 2 L
) +(
mB 2 B
) +(
mH 2 H
) , Hz
(1)
where c - the speed of sound in air m/s (c= 344.057 m/s at 20 ° C); mL, mB, mH = 1,2,3 ... (integers). Air space closed three-dimensional cavities (see. Fig. 1b), presented in the form of elastic vibrating at its own frequency of air masses and formed deadlock acoustic waveguides, defined by their dimensions, are characterized by the corresponding spectrum of the natural vibration frequencies of f md, fmL, fmB, fmH (eigentones), whose discrete values can be determined from the corresponding expression (2), (3), (4): x when mounting a sound insulating lining to the side walls (left and right) of technical premises
2
2
2
c m m m fmd,mB,mH = ටቀ d ቁ + ቀ Bቁ + ቀ H ቁ , Hz 2
d
B
H
(2)
298
Michael I. Fesina et al. / Procedia Engineering 106 (2015) 296 – 302
x
when installing sound insulating linings to the front and back wall of a technical room
2
2
2
c m m m fmL,md,mH = ටቀ L ቁ + ቀ d ቁ + ቀ H ቁ , Hz 2
x
L
d
(3)
H
when mounting a sound insulating lining to a ceiling of a technical room
2
2
2
c m m m fmL,mB,md = ටቀ Lቁ + ቀ B ቁ + ቀ d ቁ , Hz 2
L
B
(4)
d
1 1
1
1
2
(а) 1
4
B
4
3 4
d
3
d 1
3 4
1
5
H
4
L
1
5
(b) (б) Figure 1 - General view of the technical room with noise-generating technical object (a) and calculation scheme of the technical room with mounted elements of sound insulating linings (b) 1 - bearing elements - walls, ceiling, interior partitions; 2 - generating noise technical object; 3 - faceplate sound insulating linings; 4 - separate bricketed absorbing modules; 5 - sound insulating linings
Michael I. Fesina et al. / Procedia Engineering 106 (2015) 296 – 302
As technical devices of attenuation of acoustic energy resonant amplification process that occurs at discrete frequencies of eigentones of the air volume of the cavities, formed by the enclosing panel sound reflecting surfaces of bearing elements and oppositely placed soundproof front flat sheet and / or front nonflat soundproof panels of sound insulating linings; appropriate types of acoustic resonators R - quarter wave acoustic resonators R' and halfwave acoustic resonators R'', shown in the diagrams in Fig. 2 (a, b) are used.
d 1
1 6
6 6 3
1
6
6 B
5 L
(а)
B 1 dmin dmax
3
8 H
7
9
7 7
5
(б) (b) (b)
Figure 2 - Detail of the technical room cavity with sound insulating linings and set quarter-R' (a) half-wave and R'' (b) acoustic resonators 1 - bearing elements - walls, ceiling, interior partitions; 3 - sound insulating linings faceplate; 5 - sound insulating linings of bearing elements; 6 a quarter-acoustic resonator R'; 7 - half wave acoustic resonator R''; 8 - the throat portion of the acoustic resonator R' or R''; 9 - the tubular portion of the acoustic resonator R' or R''
299
300
Michael I. Fesina et al. / Procedia Engineering 106 (2015) 296 – 302
The geometric length of the tubular portion lrd of quarter acoustic resonators R', intended in particular for suppressing of the lowest resonant transversal eigentone with frequencies fd, is determined by expression (5):
d
4ST
2
π
l'rd= -(0,1…0,3)ට
,m
(5)
where ST is a flow area in m2 of the tubular portion of the quarter acoustic resonator R'. Design of quarter acoustic resonators R' (see. Fig. 3a) is represented by a hollow tubular element, limited by reflecting rigid walls - a tubular part, one of the ending parts of which is overlapped by a reflecting hard bottom, forming its bottom portion. Pref2 Ротр2
11
12
Рпад3 P
11 RmB' 9
l RmB'
inc3
l RmL'
10
9
отр2 PРref2
9 Рпад4
Pinc4
Pref4
12
10 RmH'
РPпад2 inc2
10
RmL' PР ref1 отр1
inc4 РPпад4
PРref4 отр4
l RmB'/2
Rmd'
inc2 РP пад2
8
8
l RmL'/4
l Rmd'/2 PРref3 отр3
РPпад1 inc1
l RmH'
13
8
l Rmd'
отр1 PРref1
inc3 РPпад3
Pref3 Ротр3
Pinc1 Рпад1 10
(а) 8
13
8
РPпадinc
Рпад Pinc 4
12
Rmd ''
12
11 RmH ''
11
9
4
l RmB ''/4
l RmL ''/4
l Rmd ''/2 l Rmd ''
lR311/4
11
l RmH ''
9
l RmL ''/2
9 l RmB ''
l RmB ''
RmL '' l RmL '' 9 11
(b) Figure 3 – Schemes of interlocked modular units, composed of four acoustic resonators R (a - quarter Rmd', RmL', RmB', RmH', b - half-wave Rmd'', RmL'', RmB'', RmH'') with set damping elements 8 - neck portion; 9 - tubular portion; 10 - the bottom part (sound reflecting rigid bottom); 11 – air-swept porous plugs; 12 – perforation holes; 13 footer layer of sound transparent material
301
Michael I. Fesina et al. / Procedia Engineering 106 (2015) 296 – 302
The open end area of the tubular portion with a visco connected thereto a part of an oscillating air column (located behind the plane of the tubular part open cut) forms a neck portion of the quarterwave acoustic resonator R'. Formation of the set values of physical and structural parameters of the quarter-wave acoustic resonators R' made by a choice of their own (resonant) frequency fR', the geometric length of the tubular portion - lr', dynamic length - lR', the given hydraulic diameter of the flow cross section of the tubular part – dfl, the wall perforation coefficient of the tubular part – Kper, the total cross sectional area nhl perforations - Fper made in the wall of the tubular portion. The use of damping porous air-swept plugs of a tubular part, the use of protective footer damping layers of material, mounted on the throat and / or the area of the perforated zone of the tubular portion wall, are also considered . Similar conditions and requirements for supplementing and / or the alternative use of acoustic resonators R constructions, apply to the half-wave acoustic resonator R''. In this case, the geometric length of the tubular portion lrd'' of half-wave acoustic resonators R'', intended to suppress the lowest resonant transversal eigentone with a frequency fd may be determined by the expression (6):
4ST
l''rd=d-(0,2…0,6)ට
π
,m
(6)
Supplementing, taken into account structural parameter of the implement of effective facilities of half-wave acoustic resonators R'' is the need to respect the maximum possible access of their neck portions to each other, according the constructive-technological reasons. It is carried out by appropriate choice of the U-shaped curved geometric shape, providing a selection of the shortest distance ɣ between contours of passage sections in a half-wave acoustic resonator R'' neck portion plane. This provides a common-mode ingress and subsequent terms of in-phase spreading of sound waves in both open neck portion of the tubular part towards each other in every individual sample of a half wave acoustic resonator R''. Their further effective antiphase compensation is carried out in the medial zone of the tubular portion with the opposite spreading of sound pressure impulse towards each other in both areas of their U-shaped tubular portion. The above is also true of other complementary and / or alternative modification upgrading of half-wave acoustic resonators R'' constructions, it was already mentioned above, concerning quarter-wave acoustic resonators R'. The condition of the resonant amplification suppression (removal) of radiation of sound energy, concentrated on air volume eigentones, formed through the thickness of the air gap d, length L, width B and height H of edges technical room 1 - fmd, fmL, fmB, fmH (where m = 1, 2, 3, ...), based on the frequency tuned combination of values of its own (resonant) frequency of sound vibrations of different types of acoustic resonators R - fRd, fRL, fRB, fRH with the specified frequency of eigentones of the sound insulating lining air cavity - fmd, fmL, fmB, fmH. This is achieved by the conditions of providing the multiplicity of dimensions of the air cavity through the thickness of the air gap d, length L, width B and height H with the corresponding values of ulcer-quarter length sound waves (λ/4), and half the length of the sound waves (λ/2), complying (multiple) the given overall dimensions of air cavities of the acoustic resonators R' and R'' tubular parts (dynamic lengths l' R and l''R). Suppression of natural acoustic resonances of the cavity air at the higher harmonic components of multiple (overtones) eigentones, when m> 1 (m= 2, 3, 4, 5, 6 ...) can be carried out through selecting of appropriate values of geometrical lengths lr'' and lr', this type of half- R'' and quarter R', acoustic resonators R (Rmd, RmL, RmB, RmH), which will be a multiple number shorter by 2, 3, 4, ..., according to their basic geometrical length lr'' and lr', defined for the case m = 1. As an alternative and / or complementary technological solution, used for attenuation the acoustic energy resonant amplification process, that occurs at discrete frequencies of eigentones of sound insulating lining air cavities in spatial localization zone of the eigentone sound pressure antinodes, separate briquetted sound absorbing modules, containing separate crushed fragmented sound absorbing elements (which are placed in the cavities of closed separate containers of bearing sound transparent covers (see. Fig. 1b)) can be installed. Features of structural and technological implement of briquetted sound absorbing modules are presented in the monograph [9]. Special limited localized spatial zones in the air cavities, in which separate briquetted absorbing modules are mounted,
302
Michael I. Fesina et al. / Procedia Engineering 106 (2015) 296 – 302
mainly located in the peripheral angle and / or in the ending parts, and / or in the central spatial zones of air cavities, formed under a sound insulating lining. Conclusion Proposed modifications of structural and technological implement of sound insulating linings of wall (ceiling) enclosing constructions of noisy technical premises can eliminate the acoustic resonance impulse of air cavities, formed under sound insulating linings. As a consequence, it allows to increase the sound insulation capacity of enclosing elements of technical premises. Nomenclature 1 2 3 4 5 6 7 8 9 10 11 12 13
bearing elements - walls, ceiling, interior partitions generating noise technical object faceplate sound insulating linings separate bricketed absorbing modules sound insulating linings a quarter-acoustic resonator R' half wave acoustic resonator R'' the throat portion of the acoustic resonator R' or R'' the tubular portion of the acoustic resonator R' or R'' the bottom part (sound reflecting rigid bottom) air-swept porous plugs perforation holes footer layer of sound transparent material
References [1] Nikiforov А.S. (1990) Akusticheskoe proektirovanie sudovyh konstrukcij: Spravochnik. [Acoustic design of ship structures: Directory]. – L.: Sudostroenie. – 200 p. (in Russian) [2] Nurova E.N., Fesina M.I. (2013) K voprosu opredelenija potencialov uvelichenija zvukoizoljacii ograzhdajushhih peregorodok mashinnogo otdelenija plavuchego zemlesosnogo snarjada. [On the determination of the potential increase in soundproofing walls enclosing the engine room of the floating dredge]. Vektor nauki Tol'jattinskogo gosudarstvennogo Universiteta [Vector science Togliatti State University], №2 (24). – pp. 183-186. (in Russian) [3] Tupov V.B. (2005) Snizhenie shuma ot jenergeticheskogo oborudovanija: uchebnoe posobie dlja vuzov po napravleniju «Teplojenergetika» [Reduction of noise from power equipment: a textbook for high schools in the direction of "Thermal Engineering"], М.: Izdatel'stvo Moskovskogo jenergeticheskogo instituta [Publishing House of Moscow Power Engineering Institute]. – 232 p. (in Russian) [4] Helmut V.Fuchs. Shallabsorber und Shalldampfer. Springer-Verlag Berlin Heidelberrg. – 2007. – 546 p.. [5] Cummings A. The effect of a resonator array on the sound field in a cavity. J. Sound Vib. 154, H.1, 1992, S. 25-44. [6] Fücker P. Reflexionsschalldämpfung mittels Reihenresonator. In:Schirmer W (Hrsg) Lärmbekämpfung, Kap. 13. Tribune, Berlin. – 1979. [7] Galaitsis A.G., Ver I.L. Passive Silencers and Lined Ducts. In: L. L. Beranek and I. L. Ver, Eds., Noise and Vibration Control Engineering: Principles and Application, Wiley Interscience, New York. – 1992. [8] Spannheimer H., Freymann R., Fastf H. Aktiver Helmholtz-Resonator zur Daempfung von Hohlraumeigenschwingungen. Fortschritte der Akustik - DAGA 1994, DPG-GmbH, Bad Honnef: 1994. – s. 525-528. [9] Krasnov A.V., Fesina M.I., Baluev A.A. (2012) Razrabotka semejstv universal'nyh shumopogloshhajushhih modulej [Development of a versatile sound-absorbing modules]. Sbornik tezisov dokladov na Mezhdunarodnoj nauchno-tehnicheskoj konferencii s uchastiem molodyh uchenyh «Dinamika i vibroakustika mashin» [Book of Abstracts of the International scientific conference with the participation of young scientists "Dynamics and vibroacoustics machines"], Samara: Izdatel'stvo Samarskogo gosudarstvennogo ajerokosmicheskogo universiteta [Samara: Publisher Samara State Aerospace University] – 5-7 September 2012 – 132-133 pp. (in Russian)