The equivalent translational stiffness of steel studs

Transcription

1 Poceedings of th Intenational Congess on Acoustics, ICA August 1, Sydney, Austalia The equivalent tanslational stiffness of steel studs John L. Davy (1) (), Catheine Guigou-Cate (3) and ichel Villot (3) (1) School of Applied Sciences, RIT Univesity, GPO Box 476V elboune, Victoia 1, Austalia () CSIRO ateials Science and Engineeing, PO Box 56 Highett, Victoia 319, Austalia (3) CSTB Dépatement Acoustique et Éclaiage, 4 Rue Joseph Fouie, 38 Saint atin d Hèes, Fance PACS: Rg, Ti, 43..Rj, 43..Rz ABSTRACT The effect of the esilience of the steel studs on the sound insulation of steel stud cavity walls can be modelled as an equivalent tanslational stiffness in simple models fo pedicting the sound insulation of walls. Numeical calculations (Poblet-Puig et al., 9) have shown that this equivalent tanslational stiffness vaies with fequency. Vigan (1a) has deived a best-fit thid ode polynomial appoximation to the logaithm of these numeical values as a function of the logaithm of the fequency fo the most common type of steel stud. This pape uses an invese expeimental technique. It detemines the values of the equivalent tanslational stiffness of steel studs which make Davy s (1) sound insulation theoy agee best with expeimental sound insulation data fom the National Reseach Council of Canada (NRCC) (Halliwell et al., 1998) fo 16 steel stud cavity walls with gypsum plasteboad on each side of the steel studs and sound absobing mateial in the wall cavity. These values ae appoximately constant as a function of fequency up to Hz. Above Hz they incease appoximately as a non-intege powe of the fequency. The equivalent tanslational stiffness also depends on the mass pe unit suface aea of the cladding on each side of the steel studs and on the width of the steel studs. Above Hz, this stiffness also depends on the stud spacing. The equivalent tanslational stiffness of steel studs detemined in this pape and the best-fit appoximation to that data ae compaed with that detemined numeically by Poblet-Puig et al. (9) and with Vigan s (1a) best-fit appoximation as a function of fequency. The best-fit appoximation to the invesely expeimentally detemined values of equivalent tanslational stiffness ae used with Davy s (1) sound insulation pediction model to pedict the sound insulation of steel stud cavity walls whose sound insulation has been detemined expeimentally by NRCC (Halliwell et al., 1998) o CSTB (Guigou-Cate and Villot, 6). INTRODUCTION Heckl (1959a; b) deived fomulae fo the sound powe adiated on one side of an infinite plate excited by a point foce and the sound powe pe unit length adiated fom one side of an infinite plate excited by an infinite line souce. These fomulae only apply below the citical fequency of the plate. He used these esults to pedict the impovement in sound insulation obtained by attaching a lightweight panel at a distance fom heavyweight wall with point o line connections to the heavy weight wall and filling the esulting wall cavity with sound absobing mateial. Heckl s theoy and those theoies based on it, ignoe the mass of the connecting studs and assume that the behaviou of each stud is independent of the othe studs. Shap (1973; 1978) and Shap et al. (198) applied Heckl s esults to pedict the sound insulation of lightweight cavity walls with igid studs o igid point connections. Gu and Wang (1983) modelled esilient steel studs as spings with an equivalent tanslational stiffness of 9 o 1 Pa. Davy (199b; a) stated that Gu and Wang s fomulae ae not obviously an extension of Shap s fomulae and intoduced an equivalent mechanical compliance (the invese of equivalent mechanical stiffness) of /Pa into Fahy s (1985) vesion of Shap s theoy. Notice that Davy s value of equivalent mechanical stiffness is a facto of 9 o 1 less than Gu and Wang s value. Because Fahy had not integated ove angle of incidence, Davy pefomed the integation. The esults mentioned above only apply below the citical fequency. Davy (1991) extended his theoy to above the citical fequency. Both Shap s and Davy s theoies included empiical coection factos below the citical fequency. Davy (1993) eplaced his empiical coection facto with the effects of esonant vibation in both panels. He also found and coected an eo in his theoy above the citical fequency. Unfotunately this pape intoduced an appaent asymmety into the theoy. Davy was able to explain that the appaent asymmety in panel citical fequency was due to total intenal eflection. If this total intenal eflection is taken into account, the appaent asymmety in panel citical fequency is emoved. Heckl pointed out that thee is still an asymmety in panel total damping loss factos. Howeve this asymmety will only aise if the panels have identical citical fequencies and diffeent total damping loss factos. The ecommended appoach in this case is to use the aveage total damping loss facto fo both panels. Vigan (1b) gives a good summay of Shap s method of modelling sound tansmission due to igid studs and point connections. Vigan extends Shap s theoy to above the citical fequency using a diffeent appoach to that of Davy. Hongisto (6) showed that Davy s theoy ageed well with measuements on steel stud walls with sound absoption in ICA 1 1

2 3-7 August 1, Sydney, Austalia Poceedings of th Intenational Congess on Acoustics, ICA 1 the cavity while Gu and Wang s theoy did not. Unfotunately Davy s theoy only ageed well because as Hongisto also showed Davy s theoy fo the sound tansmission via a wall cavity with sound absobing mateial poduced esults which wee too high. It tuned out that Davy s theoetical ai bone esults wee appoximately the same as the expeimental steel stud stuctue bone esults and thus poduced excellent ageement. Davy (1998) modified his aibone theoy by limiting the uppe angle of integation to a maximum value of 61. He also set the equivalent mechanical compliance of the steel studs to 1/Pa and intoduced an empiical steel stud stuctue bone attenuation of 1 db elative to wooden studs. In 9, Davy (9) ecommended a stud attenuation facto in the ange fom. to.. He actually used a stud attenuation facto of.4 to compae his theoy with expeimental esults. Davy (1) used an equivalent mechanical compliance of /Pa fo steel studs but limited the pedicted steel stud tansmission to be geate than a minimum value of.5. Guigou-Cate et al. (1998) modelled the sound insulation of 1 mm plasteboad mounted by igid o esilient line connections mm fom a heavyweight wall. The mm cavity was filled with glass wool. Thei esilient line connectos wee assumed to have an equivalent tanslational stiffness of 1 Pa. Poblet-Puig et al. (6) calculated the vibational level diffeence between 9 mm and 13 mm gypsum plaste boad wall leaves connected via steel studs and compaed these diffeences with those calculated fo a line connections with a ange of equivalent tanslational stiffnesses o a ange of equivalent otational stiffness. Guigou-Cate and Villot (6) used this infomation to calculate the sound insulation at low fequencies of two gypsum plaste boad steel stud cavity walls with sound absobing mateial in the wall cavity. At highe fequencies they modelled the steel studs as esilient point connections situated at the positions of the scews used to attach the gypsum plaste boad to the steel studs. Reseach by Poblet-Puig (8) and Poblet-Puig et al. (9) has shown that a steel stud can be modelled as a tanslational sping with an equivalent tanslational stiffness which vaies with fequency in the ange fom 1 5 to 1 8 Pa. The constant value of equivalent mechanical compliance used in Davy (1) coesponds to an equivalent tanslational stiffness of Pa which lies towads the bottom end of the above ange. The value of the minimum stud tansmission used in Davy (1) is -3 db. This also lies in the to - db stud tansmission ange detemined by Poblet-Puig et al. (9) fo a standad steel stud. Vigan (1a) has deived a best-fit thid ode polynomial appoximation to the logaithm of Poblet-Puig s numeical values as a function of the logaithm of the fequency fo the most common type of steel stud. USE OF POBLET-PUIG S STIFFNESS VALUES Initially, the equivalent tanslational stiffness values of Poblet-Puig et al. (9) fo standad TC steel studs wee used with Davy s (1) theoy to pedict the aveage of nine expeimental measuements by the NRCC (Halliwell et al., 1998). These nine measuements wee made on walls consisting of two layes of 16 mm gypsum plasteboad on each side of 9 mm steel studs at 6 mm spacing. Thee was sound absobing mateial in the wall cavity. This type of wall constuction is denoted as in this pape. Fo walls whee the thicknesses of gypsum plaste boad on each side of the steel studs ae diffeent, the second leaf thicknesses ae included in backets. An example is 13+16(16+16)-9-6. Some of the walls only had one laye athe than two layes of gypsum plasteboad on one side o both sides of the steel studs. An example is Walls with fie ated and non fie ated gypsum plaste boad (with slightly diffeent masses pe unit aea) wee gouped togethe, as wee walls with diffeent sound absobing mateial in the cavity. The NRCC epot gives the actual mass pe unit aea of the gypsum plaste boad. Because of the combination of diffeent densities of gypsum plaste boad into the same goup, gypsum plaste boad is assumed to have a density of 7 kg/m in this pape and the nominal thickness of the gypsum plasteboad is used with this density to calculate the mass pe unit aea. The sound absoption coefficient of the cavity sound absobing mateial is assumed to be 1. Note that Davy s (9) theoy limits the actual value of the sound absobing mateial at low fequencies depending on the width of the cavity. A single laye of gypsum plaste boad is assumed to have a Young s modulus of. GPa. Because two layes of gypsum plaste boad on one side of the steel studs ae only fastened at points by the scews, they can slide elative to each othe when being bent by the sound. The esult is that the citical fequency of two equal thicknesses of gypsum plaste boad is almost the same as that of a single thickness. In the theoetical esults of this pape this esult is achieved by assuming that two thicknesses behave as a single thickness of the same total thickness with a Young s modulus of appoximately one quate of one of the oiginal single layes. In this pape two layes of gypsum plaste boad ae assumed to have a Young s modulus of.6 GPa. The Poisson s atio of gypsum plaste boad is assumed to be expeiment theoy Figue 1. Compaison of the aveage of five NRCC expeimental esults with theoetical calculations fo a 16-9-none type wall using Davy s (1) theoy. Based on the compaison between Davy s (1) theoy and the aveage of 5 NRCC measuements on walls with 16 mm of gypsum plaste boad on each side of mm double steel studs, the in-situ damping loss facto of gypsum plaste boad is assumed to be.3. Thee was a 1 mm gap between the mm double steel studs giving a cavity width of 9 mm. The cavity was filled with sound absobing mateial. This wall type is denoted 16-9-none in this pape and the compaison is shown in figue 1. The compaison between theoy and the aveage of the nine expeimental esults fo the type is shown in figue. It is appaent that the stud only and the combined theoetical esults ae much moe iegula that the expeimental o studless theoetical esults. This is due to the iegulaity of the numeically calculated equivalent tanslational stiffness. Nevetheless, the compaison was encouaging enough to poceed futhe. ICA 1

3 Poceedings of th Intenational Congess on Acoustics, ICA August 1, Sydney, Austalia DERIVING COPLIANCE FRO NRCC DATA One way fowad would have been to fit a smooth cuve to the numeically calculated values of equivalent tanslational stiffness as has been done by Vigan (1a). Instead the decision was made to detemine the values of the equivalent tanslational compliance which would make Davy s (1) theoy agee with NRCC sound insulation measuements on steel stud walls (Halliwell et al., 1998). The 16 steel stud walls wee gouped into 8 diffeent classes of wall. These types of wall wee labelled as descibed at the stat of the pevious section. Fo each wall type and thid octave band cente fequency, the value of equivalent tanslational compliance which made zeo o minimised the diffeence between theoy and expeiment was detemined if possible. Davy s (1) theoy does not use the stud bone tansmission theoy below the mass-ai-mass esonance fequency because in that fequency ange the ai cavity igidly couples the two wall leaves. Thus an equivalent tanslational compliance could not be detemined fo fequencies below the mass-ai-mass esonance fequency. In some situations, the theoetical ai bone sound insulation was less than the expeimental sound insulation. In these situations, it was also not possible to detemine a meaningful value of equivalent stud compliance expeiment studless stud only combined Figue. Compaison of the aveage of nine NRCC expeimental esults (Halliwell et al., 1998) with theoetical calculations fo a type wall using Poblet-Puig et al. s (9) equivalent tanslational stiffness values fo TC steel studs in Davy s (1) theoy. Figue 3 shows the equivalent tanslational compliance detemined using this method fo a type of wall. Examination of figue 3 suggests that the equivalent tanslational compliance is appoximately constant up to about Hz. Above Hz, the elationship between the logaithm of the equivalent tanslational compliance and the logaithm of the fequency is appoximately linea. In this fequency ange, this lineaity is vey sensitive to the value of the citical fequency. The values of Young s modulus given above fo both double and single layes of gypsum plaste boad wee detemined by choosing the values which made the above elationship as linea as possible. Also shown in figue 3 ae the equivalent tanslational compliances deived fo the aveage of eleven type NRCC measuements. These esults show moe vaiability than those deived fom the type walls because thee is less diffeence between the theoetical studless sound insulation and the stud only sound insulation in this case. Since these ae all geate than the compliances deived fom the type walls, it appeas that the equivalent tanslational compliance depends on the popeties of the gypsum plaste boad leaves. Compliance (1/Pa) 1.E-5 1.E-6 1.E-7 1.E Figue 3. The equivalent tanslational compliance equied to make Davy s (1) theoy agee with the aveage of nine type and eleven type NRCC expeimental esults (Halliwell et al., 1998). Compliance (1/Pa) 1.E-5 1.E-6 1.E-7 1.E-8 1.E-9 maximum minimum Figue 4. The maximum and minimum values of equivalent tanslational compliance of steel studs deived by making Davy s (1) theoy fit NRCC expeimental data (Halliwell et al., 1998). BEST FITTING TO COPLIANCE VALUES Figue 4 shows the maximum and minimum values of equivalent tanslation compliance deived by making Davy s (1) theoy fit the 8 diffeent wall type aveages of the 16 NRCC (Halliwell et al., 1998) measuements on steel stud walls with sound absobing mateial in thei wall cavities. Because the equivalent tanslational compliance appeas to decease as a function of fequency above o Hz, a linea egession in the fequency ange fom to Hz was conducted of the natual logaithm of the compliance C as a function of the natual logaithms of the fequency f, the educed mass of the gypsum plasteboad wall leaves m, the steel stud spacing b and the steel stud (cavity) width d. ICA 1 3

4 3-7 August 1, Sydney, Austalia Poceedings of th Intenational Congess on Acoustics, ICA 1 The educed mass m is given by mm m 1 = m m 1+ whee mi is the mass pe unit aea of the ith wall leaf. It was chosen because it appeas in the equation fo the nomal incidence mass-ai-mass esonance angula fequency ω, ρ c (1) ω =. () dm In this equation ρ is the ambient density of ai, c is the speed of sound in ai and d is the cavity (steel stud) width. Accoding to Davy (1), the stud tansmission atio J is given by whee J = 4ω mmcc G 3/ / 1/ 1 c c1 (3) G = mω + mω (4) (Davy, 9). The stud tansmission atio J is the atio of the vibational enegy tansmitted fom wall leaf 1 to wall leaf by a esilient stud with an equivalent tanslation compliance of C to that tansmitted by a igid stud ( C = ). ci ω is the angula citical fequency of the ith wall leaf and ω is the angula fequency of the sound. Inseting equation (4) into equation (3) gives If ωc 1 ωc ωc J =. (5) 3/ 4ω mmcc / 1/ m1ωc + mωc 1 = =, then equation (5) becomes J = 3/ 4ω mcc / ωc. (6) The appeaance of the educed mass m in equation (6) is anothe eason fo using it in the linea egession. Using each side of the linea egession equation as the agument of the exponential function poduces the following equation. x f xm xb xd C = Af m b d. (7) The linea egession poduced the values and 95% confidence limits shown in table 1 fo the constants in equation (7). Notice that at the 95 % confidence level, A is statistically diffeent fom 1 and all fou x s ae statistically diffeent fom. Because the equivalent tanslational compliance appeas to be appoximately constant as a function of fequency below o Hz, a linea egession in the fequency ange fom 63 to Hz was conducted of the natual logaithm of the compliance C as a function of the natual logaithms of the same vaiables used in the pevious linea egession. This linea egession poduced the values and 95% confidence limits shown in table fo the constants in equation (7). Table 1. Values and confidence limits fo the constants in equation (7) in the fequency ange fom to Hz. Constant Value 95% Uppe 95% Lowe A x f x m x b x d Table. Values and confidence limits fo the constants in equation (7) in the fequency ange fom 63 to Hz. Constant Value 95% Uppe 95% Lowe A 8.5 x x x 1-5 x f x m x b x d At the 95 % confidence level, A is statistically diffeent fom 1, x m and x d ae statistically diffeent fom and x f and x b ae not statistically diffeent fom. The fact that x f is not statistically diffeent fom zeo confims the visual obsevation that the equivalent tanslational compliance is not a function of fequency in the fequency ange fom 63 to Hz. Because x f and x b ae not statistically diffeent fom, a new linea egession in the fequency ange fom 63 to Hz was conducted of the natual logaithm of the compliance C as a function of the natual logaithms of the educed mass of the gypsum plasteboad wall leaves m and the steel stud (cavity width) d. Using each side of this linea egession equation as the agument of the exponential function poduces the following equation. C xm xd = Am d. (8) The linea egession poduced the values and 95% confidence limits shown in table 3 fo the constants in equation (8). Table 3. Values and confidence limits fo the constants in equation (8) in the fequency ange fom 63 to Hz. Constant Value 95% Uppe 95% Lowe A 9.3 x x x 1-5 x m x d Table 4. Values and confidence limits fo the constants in equation (7) in the fequency ange fom to Hz. Constant Value 95% Uppe 95% Lowe A x f x m x b x d ICA 1

5 Poceedings of th Intenational Congess on Acoustics, ICA August 1, Sydney, Austalia Looking at figue 4, the values of equivalent tanslational compliance ae much moe tightly gouped in the fequency ange fom to Hz. Thus it is of inteest to epeat the oiginal linea egession esticted to this fequency ange. The esults ae shown in table 4. Given that the confidence intevals fo x f and x m in table 1 ae less than -1.5 and -1 espectively, while they ae geate than -1.5 and -1 espectively in table 4, it is inteesting to speculate that the tue values of x f and x m in the high fequency ange ae -1.5 and -1 espectively. Also x b in table 4 is not statistically significantly diffeent fom -.5 and it is also inteesting to speculate that the tue value of x b in the high fequency ange is -.5. These speculations lead to an inteesting conclusion. They imply that fo a constant value d, the equivalent tanslational compliance is given by C = Bb ω m (9) 1/ 3/ 1 in the high fequency ange whee B is a constant. Substituting equation (9) into equation (6) gives J = 4Bc 1+ 1 b ω 1/ 1/ c. (1) This implies that fo constant angula citical fequency ω c constant stud spacing b and constant speed of sound c, the stud tansmission atio J is constant. This speculative esult agees with the assumption of a constant o a minimum stud tansmission atio made by Davy (1998; 9; 1). If the magnitude of the second tem in the backets of equation (1) is much geate than one, equation (1) becomes bω c J =. (11) 8B c Equation (9) of Davy (1) gives the stud bone tansmission coefficient τ as 3 3ρcHJ τ = (1) Gbω whee H is the D of equation () of Davy (9). Substituting equation (11) into equation (1) gives 4ρcωc H τ =. (13) GBω Thus the speculative assumptions suggest that the stud bone sound insulation of a steel stud gypsum plaste boad cavity wall with sound absobing mateial in the wall cavity is independent of the stud spacing at medium and high fequencies. This is not the case at low fequencies whee table shows that the equivalent tanslational compliance is independent of the stud spacing and thus that equation (1) etains its invese dependence on the stud spacing b. Anothe conclusion to be dawn fom an examination of tables 1 to 4 is that the equivalent tanslational compliance depends moe stongly on the stud (cavity) width at low fequencies than at medium and high fequencies. Some caution should be execised with egad to the dependence on stud spacing and stud (cavity) width. Only two stud spacings (6 and 61 mm) wee consideed. All but two of the walls whose esults wee analysed had 65 o 9 mm stud widths. The othe two had 1 mm stud widths. On the othe hand the values analysed ae the most common used in pactice. Compliance (1/Pa) 1.E-4 1.E-5 1.E-6 1.E-7 1.E-8 1.E-9 Poblet-Puig et al. Davy et al. Vigan Figue 5. Compaison of the best fit equations of this pape (Davy et al.) and that of Vigan (1a) fo the equivalent tanslational compliance with the Poblet-Puig et al. s (9) data fo mm wide TC steel studs spaced at mm with 13 mm gypsum plasteboad on each side. Stud tansmission atio (db) Davy et al. Vigan Poblet-Puig et al. Figue 6. Compaison of stud tansmission atio (db) calculated using equation (3) and the best fit equations fo the equivalent tanslational compliance of this pape (Davy et al.), the best fit equation of Vigan (1a) and Poblet-Puig et al. s (9) numeical data fo mm wide TC steel studs spaced at mm with 13 mm gypsum plasteboad on each side. In this pape the equivalent tanslational compliance C will be calculated as the minimum of equation (7) calculated using the constant values in table 1 and equation (8) using the constant values in table 3. The equivalent tanslational stiffness is calculated by inveting of the value of the equivalent tanslational compliance. Define ICA 1 5

6 3-7 August 1, Sydney, Austalia Poceedings of th Intenational Congess on Acoustics, ICA 1 ( f ) x = log 1. (14) Then Vigan s (1a) best fit thid ode polynomial appoximation, to Poblet-Puig et al. s (9) numeically calculated equivalent tanslational stiffness data fo TC steel studs, is given by the following equation. 3 ( C ) x log1 = x 1.333x 7.7. (15) Figue 5 compaes the best fit equations of this pape (Davy et al.) and that of Vigan with the Poblet-Puig et al. data fo mm wide TC steel studs spaced at mm with 13 mm gypsum plasteboad on each side. The equivalent tanslation compliance of /Pa ecommended by Davy (1) is in ough ageement with the low fequency value of this pape of /Pa shown in figue 5. USE OF THE BEST FIT EQUATIONS Figue 6 shows the compaison of the stud tansmission atio J (db) calculated using equation (3) and the best fit equations fo the equivalent tanslational compliance of this pape (Davy et al.), the best fit equation of Vigan (1a) and Poblet-Puig et al. s (9) numeical values fo mm wide TC steel studs spaced at mm with 13 mm gypsum plasteboad on each side. The minimum value of the stud tansmission atio of -3 db ecommended by Davy (1) is in ough ageement with the high fequency esults of this pape shown in figue 6. Table 5. The mean, standad deviation, maximum and minimum of sound insulation theoy (Davy, 1) minus expeiment (Halliwell et al., 1998) fo the thid octave fequency bands fom to Hz fo diffeent wall types. Wall Type mean (db) std dev (db) max (db) min (db) (13+13) (13+13) (13+13) (13+13) (16+13) (16+16) (16+16) (16+16) (16+16) (16+16) Oveall none Table 5 shows the mean, standad deviation, maximum and minimum of sound insulation theoy (Davy, 1) minus expeiment (Halliwell et al., 1998) fo the thid octave fequency bands fom to Hz fo the 8 diffeent wall types using the best fit equations deived in this pape fo equivalent tanslational compliance. The oveall ow in table 5 shows the aveage value of the mean diffeences, the oot mean squae of the standad deviations of the diffeences, the maximum of the maximum diffeences and the minimum of the minimum diffeences. Fo compaison, the last ow of table 5 shows the values fo the 16-9-none wall type whose theoetical and expeimental esults ae gaphed in figue 1. This last wall type is without studs which bidge the wall cavity. The oveall standad deviation of.4 db is not excessively geate than the 1.9 db standad deviation of the 16-9-none wall type without bidging studs expeiment studless stud only combined Figue 7. Compaison of the aveage of nine NRCC expeimental esults (Halliwell et al., 1998) with theoetical calculations fo a type wall using the equivalent tanslational compliance best fit equations fo steel studs in Davy s (1) theoy. Figue 7 shows the compaison of the aveage of nine NRCC expeimental esults (Halliwell et al., 1998) with theoetical calculations fo a type wall using the equivalent tanslational compliance best fit equations fo steel studs in Davy s (1) theoy. This figue should be compaed with figue. Fom Table 5, it can be seen that the mean, standad deviation, maximum and minimum of the combined theoy minus expeiment fo figue 7 ae -.8, 1.8, 3.1 and db espectively. The equivalent numbes fo figue ae 3., 5.7, 11. and -8.4 db. Thus it can be seen fom both these sets of numbes and the figues that the best fit equations deived in this pape pefom bette oveall than the numeical calculations of Poblet-Puig et al. (9). This is thought to be due the vey complicated vibational situation that the numeical calculations of Poblet-Puig et al. (9) ae attempting to analyse fom fist pinciples. Nevetheless, the calculations of Poblet-Puig et al. (9) ae vey impotant because they povide a fist pinciples theoetical explanation of why steel studs behave vibationally in the way that they do. Of couse, the eal test of the best fit equations deived in this pape is how they pefom when used to pedict expeimental sound insulation data othe than that fom which they wee deived and when they ae used with theoies othe than Davy s (1) theoy. As a fist step in this diection, CSTB measuements (Guigou-Cate and Villot, 6) ae compaed with Davy s (1) theoy using the best fit equations deived in this pape. 6 ICA 1

7 Poceedings of th Intenational Congess on Acoustics, ICA August 1, Sydney, Austalia Figue 8 shows a compaison of CSTB expeimental esults (Guigou-Cate and Villot, 6) with theoetical calculations fo a 9(13)-175- type wall using the equivalent tanslational compliance best fit equations fo steel studs in Davy s (1) theoy. The mean, standad deviation, maximum and minimum of the combined theoy minus expeiment ae -.6, 4.4, 6. and -9.8 db espectively expeiment studless stud only combined Figue 8. Compaison of CSTB expeimental esults (Guigou-Cate and Villot, 6) with theoetical calculations fo a 9(13)-175- type wall using the equivalent tanslational compliance best fit equations fo steel studs in Davy s (1) theoy. 1 expeiment studless stud only combined Figue 9. Compaison of CSTB expeimental esults (Guigou-Cate and Villot, 6) with theoetical calculations fo a type wall using the equivalent tanslational compliance best fit equations fo steel studs in Davy s (1) theoy. Figue 9 shows a compaison of CSTB expeimental esults (Guigou-Cate and Villot, 6) with theoetical calculations fo a type wall using the equivalent tanslational compliance best fit equations fo steel studs in Davy s (1) theoy. The mean, standad deviation, maximum and minimum of the combined theoy minus expeiment ae 1.4, 5.6, 6.5 and -8.7 db espectively. Fom to 1 Hz in figue 8 and fom 1 to Hz in figue 9, the expeimental cuve is in easonable ageement with the stud only cuve. Ove most of these two fequency anges, the studless cuve and hence the combined cuve ae less than the expeimental cuve. Thus although the aibone sound insulation is unde pedicted by Davy s (1) theoy in these fequency anges fo easons which ae not clea at this stage, the stud bone sound insulation pedictions appea to be in good ageement with the expeimental esults in these fequency anges. At most of the highe fequencies the expeimental esults ae less than the pedicted esults and the diffeences ae lage in figue 9. At fist sight, it appeas that thee may be some systematic diffeence between these two CSTB esults and the 16 NRCC esults. Howeve it should be bone in mind that the 175 mm cavity width of figue 8 is lage than any of the 16 NRCC cavity widths and that the 15 mm cavity width of figue 9 is lage than all but of the 16 NRCC cavity widths. It should also be noted that Guigou-Cate and Villot (6) modelled the expeimental esults in figues 8 and 9 as point connections due to the scews above about 1 o 1 Hz. Howeve the NRCC walls also used scews to attach the gypsum plaste boad to the steel studs. Clealy moe compaisons between Davy s (1) theoy, othe theoies and expeiment ae needed. CONCLUSIONS This pape has deived empiical best fit fomulae fo the equivalent tanslational compliance of standad steel studs by making Davy s (1) sound insulation theoy agee with the expeimental measuements of the National Reseach Council of Canada (NRCC) on 16 diffeent gypsum plaste boad steel stud walls with sound absobing mateial in thei wall cavities. The values of the equivalent tanslational stiffness of standad steel studs ae easily obtained by inveting the calculated values of equivalent tanslational compliance. The equivalent tanslational compliance o stiffness depends on the masses pe unit aea of gypsum plaste boad fastened to each side of the steel studs and the width of the steel studs (which is also the cavity width). Above o Hz, it also depends on the fequency and the spacing between the steel studs. The values of equivalent tanslational compliance deived in this pape and the stud velocity tansmission atios deived fom them ae in ough ageement with values poposed peviously by Davy. When used with Davy s (1) sound insulation theoy, the empiical best fit fomulae fo equivalent tanslational stud compliance ae easonably successful at pedicting the NRCC expeimental sound insulation esults fom which the empiical best fit fomulae wee deived. They ae less successful when pedicting two CSTB expeiment sound insulation esults. Thus moe compaisons between expeimental sound insulation esults, Davy s (1) sound insulation theoy and othe sound insulation theoies using the empiical best equations deived in this pape ae needed. Othe theoies of sound insulation with which the empiical best fit equations of this pape could be used include those of Caik and Smith (a; b), Wang et al. (5), Legault and Atalla (9; 1), Poblet-Puig (8) and Vigan (1b; a). REFERENCES Caik, R. J.., and Smith, R. S. (a). "Sound tansmission though double leaf lightweight ICA 1 7

8 3-7 August 1, Sydney, Austalia Poceedings of th Intenational Congess on Acoustics, ICA 1 patitions pat I: aibone sound," Appl. Acoust. 61, Caik, R. J.., and Smith, R. S. (b). "Sound tansmission though lightweight paallel plates. Pat II: stuctue-bone sound," Appl. Acoust. 61, Davy, J. L. (199a). "A model fo pedicting the sound tansmission loss of walls," in The Austalian Vibation and Noise Confeence 199 (Institution of Enginees, Austalia, elboune, Austalia), pp Davy, J. L. (199b). "Pedicting the sound tansmission loss of cavity walls," in Inteio noise climates: National Confeence of the Austalian Acoustical Society (Austalian Acoustical Society, Peth, Austalia), pp Davy, J. L. (1991). "Pedicting the sound insulation of stud walls," in Costs of Noise: Poceedings of Inte- Noise 91 : Intenational Confeence on Noise Contol Engineeing, edited by A. Lawence (Austalian Acoustical Society, Sydney, Austalia), pp Davy, J. L. (1993). 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