Research on sound insulation of multiple-layer structure with porous material and air-layer

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1 Reearch on ound inulation o multiple-layer tructure with porou material and air-layer Guoeng Bai 1 ; Pei Zhan; Fuheng Sui; Jun Yang Key Laboratory o Noie and Vibration Reearch Intitute o Acoutic Chinee Academy o Science China ABSTRACT Sound inulation perormance o multiple-layer tructure i inetigated which conit o elatic olid luid and porou material. The Biot theory o ound propagation in elatic porou medium and the method o traner matrix are ued to derie the tranmiion lo o typical layered-tructure. The inluence o air-layer and porou material on ound inulation perormance o multiple-layer tructure had been dicued by numerical calculation and experimental teting. The reult indicate that the air-layer and porou material can improe ound inulation perormance o multiple-layer tructure and their ditribution alo ha great inluence on the ound inulation perormance. Keyword: ound tranmiion lo; traner matrix; porou material I-INCE Claiication o Subject Number(: 51.4 (See INTRODUCTION Sound inulation perormance o ingle plate depend on not only it tine internal lo and ma but alo the incident wae requency and incident angle etc. Acoutic characteritic cure o thin plate i diided into our region: the tine control damping control ma control and coincident eect area. Becaue mot o acoutical tranmiion lo cure i ma control area ma law i the mot important inluence on ound inulation propertie. Although in recent year the ingle plate ha changed into bilayer or multilayer inulation tructure in order to attenuate noie energy a much a poible it i diicult to increae ound inulation perormance and reduce urace denity at the ame time or ma law. Thereore a compromie mut be made when chooing the ound inulation material. There i a preing need to oercome the hortcoming o acoutical material in order to reduce the tranport noie epecially the high-peed train. The traner matrix method(tmm wa irt propoed to analyze multilayer medium by Thomon[1]. Brekokikh once decribed plane wae propagation in elatic olid by the traner matrix which greatly deelop TMM o the luid and olid[2]. Biot theory i a ery claical method to analyze wae propagation in porou material[]. According to Biot theory there are three kind o wae propagation in porou media: two dilatation wae and one hear wae. All kind o wae propagation in porou material the luid and elatic layer can be repreented by the traner matrix which are compoed o the inal matrix ytem to acquire acoutical inulation perormance. Becaue too many parameter o Biot theory make it ery complex Allard Brouard and Atalla deeloped TMM to decribe to normal or oblique plane wae propagating in ariou media[4-6]. In thi paper we introduce air layer to deign light compoite material or ound inulation. TMM and acoutic meaurement are ued to reearch on ound inulation perormance o compoite material containing air layer. 2. THE TRANSFER MATRIX OF LAYERED COMPOSITE MATERIALS Figure 1 i ingle layer with h thickne when plane wae i incident. The two point M and on the medium urace are deined. Figure 2 i multi-layer compoite medium when plane wae i incident. The two point A and B on the incident and tranmiion urace are deined. M ' 1 bg@mail.ioa.ac.cn Inter-noie 2014 Page 1 o 6

2 Page 2 o 6 Inter-noie 2014 Figure 1 Plane wae incidence o ingle layer medium with h thickne Figure 2 Plane wae incidence o multi-layer compoite medium 2.1 The Air Layer When the air layer i included in compoite media The M point in ound ield i determined by V ( M [ p( M ( M] T (1 where p and are preure and particle elocity the lower index i coordinate direction k i complex wae number and V ( ( ' i denity. Baed on M T V M or luid medium the ound preure and particle elocity can be repreented by the 2 2 tranmiion matrix. T j co( kh in( kh k jk in( kh co( kh (2 2.2 The elatic olid A inite medium i elatic olid layer in Figure 1 1 ( M 2( M ( M 1( M ound propagation in an elatic olid and can be written a ollow are decribed the V ( M [ ( M ( M ( M ( M] T ( where (M 1 and (M are the elocity component o point M x in 1 x and direction (M and (M 1 are repectiely the normal and tangential tre o point M. Page 2 o 6 Inter-noie 2014

3 Inter-noie 2014 Page o 6 A [ A A A A A A A A ] T Let V ( M ( x A Combining with equation ( it can be obtained a ollow k1c1 jk11 jk kc jk1 1 k1c1 k1c jk1 D1c 1 jd1 1 jd2k D2kc jd2k1 1 D2k1c 1 D1c jd1 ( where D1 ( k1 k1 2 k1 ( k1 k1 D2 2k1 c1 co( k1 x 1 in( k1 x c co( kx in( kx x. The traner matrix o elatic olid can be obtained when are equal to h and 0 in equation (4 repectiely. [ T ] [ ( h][ (0] 1 (5 2. The porou material According to Biot' theory 1 and the deinition o the two elocity and component ramework in a porou material i component elocity o the luid and 1 are the two tre component and ramework i tre component o luid the ound ield in the point o porou material layer can be expreed a V p ( M [ ] T (6 Let A A1 A 1 A1 A 1 A2 A 2 A2 A 2 A A A A 1 1 then [ ] T p and V ( M [ ( x] A ktc1 jkt 1 ktc2 jkt 2 jk kc jk1 1 k1c1 jk22 k2c2 ktc jkt jk1 11 1k1c 1 jk222 2k2c2 ktc jkt [ ( x ] D1c 1 jd1 1 D2c2 jd22 2jNkkt 2Nkktc jnktk 2Nktk c 2 jnktk 2 Nktk c N( k kt c jn( k kt E1c1 je11 E2c2 je where c2 co( k2x 2 in( k 2 x x Let material in the equation (7 be repectiely h and 0 we can get the traner matrix or porou p [ T ] [ ( h ][ (0] 1 (7 2.4 Tranmiion lo o compoite material When it i a emi-ininite air medium at the end o multiple-layer tructure we can derie the tranmiion lo o typical compoite material by uing traner matrix. The impedance at B point o Figure 2 can be expreed a Z co p ( B ( B (8 B There i a relationhip between the tranmiion coeicient t and relection coeicient r p( A p( B 1 r t (9 Combined with traner matrix o multiple-layer tructure we can obtain tranmiion lo with incident angle or plane wae. TL 10log ( (10 Inter-noie 2014 Page o 6

4 Page 4 o 6 Inter-noie 2014 where 2 ( t (. RESULTS AND DISCUSSIONS.1 Simulation Veriication Sound inulation or aluminum and gla wool compoite material in Figure are compared between experimental reult in the Re. [4] and the imulation reult. The legend o G i gla cotton AL tand or aluminum plate. The two cure in Fig. are agreement which how that the model i uitable or the prediction o compoite material..2 Computational reult Figure 4 i tranmiion lo (TL cure o dierent thickne o porou material between double aluminum panel which panel thickne i 1mm. TL o aluminum panel with 2mm thickne i compared with melamine oam with 0mm 50mm and 70mm thickne repectiely. The legend P repreent the melamine oam. It can be een that porou material between double aluminum panel play a good role in increaing TL and the thickne o porou material are poitiely correlated. Porou material hae a great inluence on compoite tructure and are mainly concentrated in the high requency. In general the inluence o porou material i limited in low requency. Figure Simulation Veriication Figure 4 TL o dierent thickne o porou material (a70mmg+1mmal(imulation reult (b70mmg+1mmal(experimental reult in Re. [4] (c1mmal+1mmal (d1mmal+0mmp+1mmal (e1mmal+50mmp+1mmal ( 1mmAL+70mmP+1mmAL Figure 5 TL o dierent thickne o air layer Figure 6 TL o dierent multiple-layer tructure (g 1mmAL+1mmAL (h 1mmAL+1mmAir+1mmAL (i 1mmAL+2mmAir+1mmAL (j 1mmAL+mmAir+1mmAL (k1mmal+70mmp+1mmal (l1mmal+0mmp+10mmair+0mmp+1mmal (m1mmal+20mmp+10mmair+ 40mmP+ 1mmAL (n 1mmAL+10mmP+10mmAir+50mmP+1mmAL Figure 5 i tranmiion lo cure o dierent thickne o air-layer between double aluminum panel which panel thickne i 1mm. TL o aluminum panel with 2mm thickne i compared with Page 4 o 6 Inter-noie 2014

5 Tranmiion Lo(dB Inter-noie 2014 Page 5 o 6 air-layer with 1mm 2mm and mm thickne repectiely. From the imulation reult we can ee that the air-layer o thee tructure ha a good role in high requency but in the peciic requency generate acoutic alley or the caity reonance. It can be een that with increaing the air-layer thickne TL i increaing in high requency and acoutic alley i moing to low requency at the ame time. In general the preence o air layer improe ound inulation perormance or thi kind o tructure becaue o the air icou diipation eect. At the ame time the preence o air-layer make the impedance mimatch trengthened between panel and air. Figure 6 i tranmiion lo cure o dierent multiple between double aluminum panel which panel thickne i 1mm. The compoite tructure contain air-layer and porou material whoe thickne i 70mm. By comparing eeral cure in Figure 6 we can get the ollowing concluion: (1 TL can be igniicantly improed in low requency while reducing a portion o porou material and increaing air-layer appropriately which lead to maller the oerall weight and urace denity o compoite material. (2 When the total thickne o compoite material i contant the dierent ditribution mean or porou material and air-layer ha great inluence on the ound inulation perormance. Good optimization combination can increae impedance mimatch and improe the ound inulation perormance obiouly epecially retrain reonant ound alley in low requency.. The experimental teting Figure 7 i the tranmiion lo cure o experimental teting in reerberation room or dierent material between aluminium extruion and ceiling panel which are ued in the high-peed train. The tranmiion lo o compoite material containing air layer i increaed greatly than the other material in low requencie and the weighted tranmiion lo i improed.5db. It how that the air-layer can improe the ound inulation perormance and reduce quality o compoite material at the ame time P 6A+50P+6A Frequency(Hz Figure7. Tranmiion lo cure o experimental teting in reerberation room or dierent material 4. CONCLUSIONS Thi paper dicue the theory o ound propagation in layered compoite material and ound inulation perormance o compoite material i calculated baed on the traner matrix method o the porou material elatic olid and luid layer. The imulation and experimental reult how that ound inulation perormance i greatly improed ater the air-layer i ued appropriately or compoite material which proide a new way or deigning light acoutical inulation material. The air-layer in the compoite tructure make impedance mimatch between the dierent medium while ound aborption o porou material make acoutical energy urther attenuation. The ditribution method or porou material and the air-layer alo aect ound inulation perormance and noie reduction. We hould elect dierent tructural parameter and the optimization combination or peciic requency band. ACKNOWLEDGEMENTS Thi work wa upported by the National Nature Science Foundation o China under Grant No. Inter-noie 2014 Page 5 o 6

6 Page 6 o 6 Inter-noie the National key Baic Reearch Program o China (97 Program under Grant No. 201CB62900 and the National High Technology Program o China (86 Program under Grant No. 2011AA11A10. REFERENCES 1. Thomon W.T. Tranmiion o elatic wae through a tratiied olid medium. Journal o applied Phyic ( Brekokikh L.M. Wae in layered media. Academic Pre ( Biot M.A. The theory o propagation o elatic wae in a luid aturated porou olid. Journal o the Acoutical Society o America 28 : ( Allard J.F. Propagation o Sound in Porou Media: Modelling ound Aborbing Material CHAPMAN & HALL London( Brouard B. Laarge D. & Allard J.F. A general method o modeling ound propagation in layered media J. Sound Vib 18 (1: ( Atalla N. Panneton R. Debergue P. A mixed diplacement-preure ormulation or poroelatic material Journal o the Acoutical Society o America 104 ( : (1998. Page 6 o 6 Inter-noie 2014