Study on Characteristics of Sound Absorption of Underwater Visco-elastic Coated Compound Structures

Transcription

1 Vol. 3, No. Modern Alied Science Study on Characteristics of Sound Absortion of Underwater Visco-elastic Coated Comound Structures Zhihong Liu & Meiing Sheng College of Marine Northwestern Polytechnical University Xi an 77, China Abstract Visco-elastic daming materials containing kinds of air-filled, fluid-filled microsheres or cylindrical cavities have been widely used in various areas involving the coating of water-borne structure to reduce acoustic echoes to active sonar systems. As a secial daming material, rubber has attracted great interest in the field of vibration and noise for its low Young s modulus and high strain recovery features. Based on wave transfer roagation theory in infinite layered medium, sound absortion erformance for underwater comound daming structures is investigated using transfer matrix method. A new anechoic coating containing different varying sectional cavities is roosed. Simulation results show that the new anechoic coating kees good absortion erformance in high frequency and its sound absortion coefficient is increased notably in low frequency. Simulations also show that the roerty of rubber material influences structural sound absortion greatly. Soft rubber as well as those with large loss factor may imrove sound absortion erformance of the whole structure remarkably. New anechoic coating containing varying sectional cavities have great advantages over the uniform comound structures. It's a good way to make different varying sectional cavities inside multi-layered rubber comound structures for imroving sound absortion roerty. The sound absortion coefficient can be modulated by changing the thickness of the three different varying sectional cavities, and not the more the cavities are, the better sound absortion will achieve. As a new kind of comlex multilayered rubber comound structures, comound structure containing varying sectional cavities has better sound absortion roerty than rubber interlayer with cylindrical cavities comound structure and homogeneous rubber comound structure. Keywords: Visco-elastic material, Sound absortion, Comound structure, Varying sectional cavities. Introduction Visco-elastic daming materials have been widely used in many areas involving the coating of water-borne structure to reduce the acoustic echoes to avoid active sonar systems. As a articular kind of daming material, rubber has lower Young s modulus and better strain recovery ability comared to metal material, and so it can revent structure from noise transmission more effectively. In this aer, the study of sound absortion erformance of underwater comound daming structures with varying sectional cavities is carried out, which can rovide a guidance for underwater structure sound absortion research and engineering alications. There are four imortant analysis methods for sound absortion: Transfer matrix method, FEM, BEM and statistical energy analysis (SEA). Transfer matrix method is a classical aroach to solve sound absortion, which is adoted in literatures. The results of literatures show that there are some differences between redicted values and measuring ones in low frequency range because the infinite late theory does not consider the influence of geometrical dimensions. But the limitation can be modified in a certain extent by considering structure finite sizes. SEA method in literature can simlify comlex vibration-acoustic daming system and change its energy transmission to a set of linear equations solution. But in general, SEA is commonly alied to calculate for the roblem of high frequencies and it is also limited when solving non-resonance roblems of sound and energy. Numerical method referred in literature is not restricted by structure geometrical dimensions and material roerties, and can be alied to solve non-linear roblems. But when the frequency increases, the necessary divided mesh number manifolds raidly, calculating the highest frequency is then confined. To break the limitations of single aroaches, combination of two kinds of methods is considered. For instance, FEM together with BEM is used to treat with low frequency diffusing field of double-wall sound barriers with elastic orous linings in literature; while the combination of FEM and SEA is used to disose of multilayered anels in 3

2 Modern Alied Science January, 9 literature. Nevertheless there are some roblems in the combinations. Comaratively, Transfer matrix method is the better method, which has a long investigation history and mature theory analysis. Therefore, based on wave transfer theory of infinite layered medium in literature, Transfer matrix method is adoted as a theoretical analysis method. In condition of normal incidence, the sound absortion roerties of homogeneous underwater coatings and underwater coatings containing uniform cylindrical cavities are researched and their shortages of frequency resonse roerties are ointed out in our early studies. Secondly, on the basis of the studies mentioned, a new tye of underwater sound absortion coatings is roosed, whose sound absortion erformances are also investigated and comared with the cylindrical cavities comound structure and homogeneous rubber comound structure. The theoretical formulation and results are described in Sec., the results obtained with different structures are shown and discussed in Sec.3, and finally summarized in Sec.4. For reading conciseness, homogeneous rubber comound structure is simlified to HRCS rubber with cylindrical cavities comound structure is simlified to RWCCS, and rubber with varying sectional cavities comound structure is simlified to RVWCCS.. Theoretical Formulation and Solution When lane wave transmits from one medium to another in normal incidence, two kinds of sound wave are roduced because of the imedance difference between the two media. One is the reflection wave, the other is the transmission wave. At the interface of the two kinds of media, it satisfies: () ressure is continuous; and () article vibration velocity in vertical direction is also continuous. Formulations of multi-layered HRCS and multi-layered RWCCS have been given in our early researches, so here only the formulation of multi-layered RVWCCS is given. RVWCCS is a secial multi-layered HRCS. This aer uts forward the kind of new coating structure on the basis of HRCS and RWCCS structure, and brings it into underwater noise control field and discusses its sound absortion erformance in condition of normal incidence. New varying sectional coating s structure in the aer is constituted of different sectional structures among rubber layers. A whole RVWCCS includes the surface layer, varying sectional layers and the bottom layer. In this way, varying sectional rubber layer is made u of three different rubber varying sectional layer, which is catenary shae structure, taer shae structure, and exonential shae structure layer. The RVWCCS sketch is illustrated in Figure. Hence, it is a five-layer structure. Underwater non-homogeneous comound structure illustrated in this aer is to add RVWCCS onto double-layer shells, which is a comound sound absortion structure comosed by eight layers, seen in Figure. The governing equation of sound in non-homogeneous layered rubbers containing varying sectional cavities is written as follows ln s () x x x c t Let xe ( ) jwt be the solution of the above equation. It is simlified to ' ds Where s, k, when sx ( ) satisfies dx c i s '' Where K k. Aly Eq.(3)to Eq.(4),,the solution of Eq.(4) is shown as d ( x) s d( x) dx s dx ' k x x ( ) ( x) s Aly Eq.(3) to Eq.(), Eq.(4) is yielded d ( x) K ( x) dx ( ) Total ressures and article velocity in unit sections of non-homogeneous layers are formulated as s x ( ) e ia e sx ( ) j k x j k x ra () (3) (4) (5) 33

3 Vol. 3, No. Modern Alied Science Where, s reresents the initial area of varying sectional structure, reresents the arameter which determines the change of sectional area, reresents the extend sloe ratio. The underwater non-homogeneous comound structure is the model shown in Figure. It models the underwater large samle exeriment environment. Transfer matrices of the sound wave in Multi-layered structures are denoted as when x when x se sx ( ) s cos h( x) s ( x) x d F( x) s( x) ( x) c s( x) x vx ( ) j x ( ) s s v ra z z F ia (6) (7) (8) When x d jk d jk d jkd ' e s ( ) ( ) ( ) e s e s z c s xds xd jk jk ia d jkd e e jkd ra e j z z s jkd ' e s( zc) ( s ) xds ( ) xd jk ia jkd e j ra s (9) when x d 3 jkd ' e s( zc) ( s ) xd s ( ) xd jk jkd e j s e s z c s s jk e s e s jkd ' ( ) ( ) ( ) jk d jk d xd xd ia jk 3ia d jkd jkd e e e j ra 3ra z z s () When x d 4 jkd3 jkd3 jkd3 jkd3 e s e s e s e s jk 3ia 4ia d3 jkd 3 jkd3 jkd 3 e e e e 3ra 4ra z z z z () jkd4 jkd4 e s e s 4ia jkd F jkd4 jkd 4 4 e e e () 4ra v z z So the Transfer matrices of multi-layered RVWCCS which is made u of n rubber layers can be exressed as follows 34

4 Modern Alied Science January, 9 F F jkd n n AA AA 3 4 AA 5 6 An Ane v v n (3) Where that K k is the wave number of non-homogeneous multi-layered RVWCCS. And then it can be obtained jkd4 jkd c 4 ta e s ( ia ra ) s c ta e s z ia ra jkd4 jkd c 4 ta e s z z c ta e s z Ultimately, the sound ressure coefficient of transmission, reflection and absortion can be written resectively as ta t c ia c c z sc z s r c c c z sc ia z s c ra c c z sc z s t r where k is the water wave number, z is the characteristic imedance of water. 3. Numerical simulation analysis In order to understand the rules of the influences of material roerty and anel s thickness of coating on sound absortion erformance, a hyothesis about the arameters of the material which will be used in the analysis is given below: 3 The thickness of steel shell and steel shell is mm and 3mm, resectively. The density of steel late is 78 kg / m, 3 Young s modulus is.6 Pa, Poisson ratio is.8. The density of sea water is 6 kg / m, the thickness of water-layer is.3m, and the sound seed in water is 5 m/ s. 3 The rubber layer is made of certain daming material as in literature. Its density is kg / m, and its Poisson s ratio is.49. Its Young s modulus and corresonding loss factor roerties, which deend uon the frequency and temerature. The temerature is equal to C. Influence of the thickness of surface layer on sound absortion coefficient is illustrated in Fig.3. The figure shows that the absortion eak value moves to low frequency with the increasing of thickness of surface layer, and absortion erformance in low frequency is imroved significantly, but the sound absortion coefficient becomes surged in about khz frequency range. When the thickness increases, the absortion erformance in high frequency range changes less than that in other frequency range. If the thickness of the surface layer increases too much, there will be a great effect on the absortion erformance, esecially in about such a frequency range from khz to khz. Figure 4 shows the curve of sound absortion coefficient versus frequency, when the thickness of catenary layer is altered. With the increasing of the thickness of catenary layer, the absortion eak value remains constant before 63Hz frequency, and the sound absortion coefficient isn t imroved yet. On the contrary, the sound absortion coefficient decreases with the increasing of the thickness of the catenary layer in the ~63Hz frequency range. In the frequency band between 63Hz and 8kHz, sound absortion coefficient increases while the thickness of the catenary layer become thicker. And beyond 8kHz frequency, the influence on absortion erformance is not notable with the increasing of the thickness of the catenary layer. Therefore, the thickness of the catenary layer deends on the frequency range which is concerned in the ractical engineering roblems. Figure 5 shows the sound absortion coefficient curve verses frequency, while the thickness of the taer layer is altered. It is seen from the figure, the sound absortion coefficient in low frequency doesn t increase with the thickness of the taer layer, and there will be an otimal value, which can imrove the sound absortion coefficient greatly in low frequency range, it is not necessary to increase the total thickness of anechoic coating for getting the otimal design. The higher the frequency, the smaller the influence on absortion erformance, esecially beyond 5kHz. It is seen from figure 6 that the influence on sound absortion coefficient by the thickness of the exonential layer is small before 4Hz frequency. With the increasing of the frequency and the thickness of the exonential layer, the (4) (5) (6) (7) 35

5 Vol. 3, No. Modern Alied Science sound absortion coefficient increases also in about such a frequency range from 4Hz to khz.. But comared to the extent that the thickness of the exonential layer, the sound absortion coefficient doesn t increase remarkbly. And there is almost no influence on sound absortion coefficient in high frequency range(beyond 5kHz) with the increasing of the thickness of the exonential layer. Influence of the thickness of bottom layer on sound absortion coefficient is given in figure 7. As is shown in the figure, there is almost no effect on sound absortion coefficient before 4Hz with the increasing of the thickness of the bottom layer. With the increasing of the thickness of the bottom layer, sound absortion coefficient increases accordingly in about such a frequency range from 4Hz to 3kHz. But influence on sound absortion erformance isn t great in high frequency, esecially beyond 7kHz. Figure 8 shows that the frequency-resonse curve of sound absortion coefficient, when the erforation ratio is altered. It is seen from figure 8 that there is almost no effect on sound absortion coefficient with the change of the erforation ratio in such a frequency range from khz to khz. But influence on sound absortion coefficient is notable before khz frequency. In addition, there will be an otimal erforation ratio value which can imrove the sound absortion coefficient greatly in low frequency range. Figure 9 shows the sound absortion coefficient curve verses frequency, while the loss factor is altered. It can be seen from the figure that the sound absortion coefficient increases with the increasing of the loss factor of rubber material. It also can be seen from the figure that there is almost no effect on eak value of the frequency of sound absortion coefficient, but influence on eak value of sound absortion coefficient is notable. From the figure, we can see that sound absortion coefficient will be decreased beyond khz frequency range when loss factor becomes too large. Hence, there will be an otimal value for loss factor. When the Young s modulus is altered, the sound absortion coefficient curve verses frequency is shown in Figure. It can be seen from the figure that the sound absortion coefficient decreases if the Young s modulus is too large. It is because that if the Young s modulus becomes too large, imedance of rubber layer will not match the imedance of water well. It is also found that when the Young s modulus becomes small, sound absortion coefficient imroves greatly in low frequency. Similarly, there will be an otimal value for Young s modulus. Figure shows the sound absortion coefficient curve verses frequency, while the thickness of the water layer is altered. It is seen from the figure that there is almost no effect on the form of the sound absortion coefficient, when the thickness of the water layer is changed. When the thickness of the water layer increases, eak value of sound absortion coefficient moves to low frequency. It is because that the sound seed diminishes in water, and at the same time the thickness of the water increases, and therefore the resonance henomena occurs in water layer. Figure shows the sound absortion coefficient curve verses frequency with three different coating structures. As a articular kind of comlex multilayered rubber comound structures, comound structure containing varying sectional cavities has better sound absortion roerty than rubber with cylindrical cavities comound structure and homogeneous rubber comound structure. 4. Conclusions In condition of normal incidence, sound absortion erformance of multi-layered RVWCCS is analyzed by the transfer matrices method in the manuscrit. For multi-layered RVWCCS, the influence on sound absortion erformance by rubber material roerties and the thickness of varying sectional comound structure is mainly investigated. The sound absortion effect on different anechoic coating is also discussed. The following results can be obtained by the above investigations. (). The roerties of rubber material have a large influence on sound absortion coefficient of the structure. Rubber with small Young s modulus and large loss factor is adoted in order to imrove sound absortion coefficient obviously. Sound absortion coefficient of RVWCCS develos with the increasing of rubber thickness, but there is limitation on increasing sound absortion coefficient of RVWCCS at the cost of increasing the thickness of rubber. (). Multilayered RVWCCS can combine advantages of HRCS, and achieve better sound absortion effect. It is of advantageous imroving sound absortion erformance by erforation on inside rubber. But not the larger erforation ratio of inside rubber is, the better sound absortion erformance will be achieved. (3). Because of comlex inner toology, with the same thickness of these structures, sound absortion erformance of RVWCCS is much better than that of both RWCCS and HRCS. References Alberto Di Meglio, Lian Sheng Wang. (), A variational method for identification of viscoelastic arameters from exerimental data, JASA, 8(6), Brekhovski L M, Waves in Layered Media, nd Edition, New York, Academic Press,

6 Modern Alied Sciencee January, 9 Craik RJM, Nightingale TR, Steel JA (997), Sound transmissionn through a double leaf artition with edge flanking, JASA,, (), Du, gonghuan, Zhu, zhemin, Gong, xiufen. (3), Acoustic Foundation, Pressed in Nan Jing University, (in Chinese). Liu, Zhihong, Sheng, MeiPing. (6), Analysis of Absortion Characteristics of an Oblique Incidence Plane Wave on Isotroic Symmetric Plate, Noise and Vibration, 6(), (in Chinese). Liu, Zhihong, Sheng, MeiPing. (5), Analysis of Absortion Characteristics of a Normal Incidence Plane Wave on Isotroic Symmetric Plate in Water, Noise and Vibration Control, 5(), -3. (in Chinese). Liu, Zhihong, Sheng, MeiPing. (5), Study on Absortion Characteristics of visco-elasticc multi-layered comound structure. Acoustic Technica., (), -5(in Chinese). Michael EI-Raheb. (997), Frequency resonse of a two-dimensional trusslike eriodic anel, JASA, (6), Panneton R, Atalla N. (996), Numerical rediction of sound transmission through finite multilayer systems with oroelastic materials, JASA, (), Sgard FC, Atalla N, Nicolas J. (), A numerical model for the low frequency diffuse field sound transmission loss of double-wall sound barriers with elastic orous linings, JASA, 8( 6), Steel JA, Craik RJM. (994), Statistical energy analysis of structure-borne sound transmission by finite element methods, Journal of Sound Vibration, 78(4), Wang, Man. (4). Theoretical and Exerimental Study of Underwater Anechoic Coating[D], Harbin Engineering University. (in Chinese). Wang, Man, He, ZuoYong. (996). Theory study on absortion erformancee of water non-homogeneous structure, Aly Acoustic, 5(5),. (in Chinese). Figure. model of RVWCCS 37

7 Vol. 3, No. Modern Alied Science Figure. Sound absortion model of multi-layered RVWCCS in normal incidence. Figure 3. Sound absortion coefficient versus frequency for thickness of surface layer Figure 4. Influence on sound absortion coefficient of thickness of catenary layer 38

8 Modern Alied Science January, 9 Figure 5. Influence on sound absortion coefficient of thickness of taer layer Figure 6. Influence on absortion erformance by the thickness of the exonential layer Figure 7. Influence on absortion erformance by the thickness of the bottom layer 39

9 Vol. 3, No. Modern Alied Science Figure 8. Influence on sound absortion coefficient of erforation ratio Figure 9. Influence on sound absortion coefficient of loss factor Figure. Influence on sound absortion coefficient of Young s modulus 4

10 Modern Alied Science January, 9.. Figure. Influence on sound absortion coefficient of the thickness of the water layer Figure. Influence on sound absortion coefficient of the different multi-layered coating structure 4