Chapter 11
Acoustic Coatings for Water-Filled Tanks 1
1
2
2
Robert D. Corsaro , Joel F. Covey , Rose M. Young , and Gregory Spryn 1
Naval Research Laboratory, Washington, DC 20375-5000 SFA, Inc., Lanham, MD 20785 2
Applications requiring underwater sound absorption usually make use of the high damping capability of polymeric materials. This paper describes the trade-offs necessary in selecting materials for sound absorbing coatings for use in reducing extraneous wall echoes in water filled pools and tanks. Coatings for this purpose are called anechoic, literally meaning no echoes, or non-reflective. Satisfactory anechoic coatings have been developed using a variety of different approaches including: simple and multi-layer absorbers; wedge– shaped designs; and resonant cavity approaches. This paper reviews the advantages of each and the material requirements involved. Data is presented on various commercially available underwater sound absorbing coatings, including three new coatings which have been only recently developed. Two examples of typical coating applications are presented: a tank for use in medical studies at ultrasonic frequencies (0.5 to 10 MHz) and one designed for calibration use at lower frequencies (6 to 100 kHz). Underwater acoustics is routinely used in laboratory-scale test facilities for flaw detection, transducer calibration, material property evaluations, and acoustic visualization. In a typical underwater acoustic study, an object of interest is submerged in a water filled tank and acoustically illuminated (insonified). The acoustic signals scattered by the object are then measured and analyzed. If the tank used is not sufficiently large, these measured acoustic signals will include spurious echo components due to extraneous wall reflections. Since the effect of these contaminating echoes usually cannot be removed from the resulting data set by post analysis, they must be prevented from occurring at their source. One cost 0097-6156/90/0424-O208$O6.25/0 © 1990 American Chemical Society
11. CORSARO ET AL.
Acoustic Coatings for Water-Filled Tanks
209
effective approach toward reducing these extraneous echoes is to apply sound absorptive treatments to the tank walls. Several anechoic coatings are commercially obtainable for this purpose. Because their availability is not widely recognized, their characteristics are reviewed in this paper. We also include consideration of coatings which are not immediately commercially available but whose construction and performance is sufficiently documented in the literature to be reproduced on demand. Some general design principals for each coating class are also included here to provide physical insight as to the operating principles of each coatings class. These can also be used for feasibility estimates of coating dimensions and properties. However it must be emphasized that in the final stages of a coating design, such model calculations are no substitute for direct measurements on candidate materials and structures.
ReflextiQELat_a Boundary In this section we very briefly review the principles of sound reflection. Additional introductory material is presented in the preceeding papers in this publication, and a more complete analysis appears in standard acoustics textbooks such as that of Kinsler and Frey (1), or Pierce (2), or on a broader introductory level that of Crawford (3). An acoustic wave is a traveling periodic pressure disturbance. This wave travels at a speed c dependent on the properties of the medium and the type of motion associated with the wave. The periodic nature of the acoustic wave is (for present purposes) taken to be a sinusoidal oscillation occurring at a frequency f. At any location x and instant in time t, the pressure associated with this traveling wave can be expressed as a cosine wave, or in a mathematically equivalent form as the real part of a complex exponential: P = P cos(kx - u;t) = P Re{exp j (kx - art)} G
u
(1)
The terminology used here is conventional: k is the wavenumber (k = 27r/A = u>/c) ijj is the angular frequency in radians (w = lid) \ is the wavelength, (A=c/f) and where P is the maximum sound pressure amplitude, which is considered to occur at location x=0 and time t=0. u
For plane waves propigating in an isotropic homogeneous medium, three acoustic properties are important: the speed of sound, the attenuation coefficient (to be discussed), and the characteristic impedance of the media. This impedance z is defined as the ratio of the acoustic pressure to the particle velocity associated with the wave motion in the material. For simple free-field plane waves, this is simply the product of the sound speed and density p.
210
SOUND AND VIBRATION DAMPING WITH POLYMERS z = pc
(2)
When sound traveling in media 1 strikes an interface with another material, media 2, a portion is reflected while the remainder is transmitted into media 2. As shown in Figure 1, if Pi is the incident pressure, P is the reflected pressure, and P is the transmitted pressure, then the reflectivity R and the transmissibility T are defined: r
R = P / Pj,
t
T = P / Pj
t
(3)
t
The property of the interface which controls the relative amounts reflected and transmitted is termed the "specific acoustic input impedance" Z which is defined as the ratio of the acoustic pressure to the particle velocity associated with the wave motion at the boundary. Note that this definition is similar to that used previously in defining the specific impedance of the media z. The use of the term impedance for both "input impedance at the boundary" and "specific impedance of the media" occasionally leads to some confusion if care is not taken. Considering perpendicular sound incidence, the specific acoustic input impedance Z at the boundary is simply 2
Z =z. 2
(4)
2
Hence in this case it is immaterial whether we refer to impedance as Z or z . It can then be shown that the reflectivity and transmissibility are simply related to the ratio of the impedance of media 1 and the input impedance of the boundary: 2
R = ( l - z ^ z p / (l+zj/zp,
T = 2 / (l+z^zp
2
(5)
For consistency with latter equations, we will also express these two in the form: R = M /Jvf,
T = 2 / M'
(6)
where in this case, M = (l-z /Z ) and where (in general) M ' is simply M but with the sign of z changed. While this usage is not common, it is preferred by this author since it simplifies the subsequent analysis of more complicated cases. 1
2
x
From equation 5 we see that if Z > z then R is positive and the incident acoustic signal simply reflects with a reduced amplitude. If Z < z the sign of R is negative indicating that the incident signal is inverted (180° phase shift) on reflection. Finally, if Z = Zj there is then no reflection at the boundary and all acoustic energy striking the surface is transmitted into medium 2. This latter case is of particular interest here, since it indicates that we can eliminate reflections from a surface by properly selecting or adjusting the density and sound speed of the material of medium 2. 2
l
2
x
2
While reflectivity and transmissibility are simple ratios, it is more common to present these parameters in decibel units. The corresponding parameters are then echo reduction (ER) and transmission loss (TL): ER = -20 LoglRl,
T L = -20 LoglTl
(7)
11. CORSARO ET AL.
Acoustic Coatings for Water-Filled Tanks
211
where the logarithms are base 10 and where the absolute values of R and T are used. Note that in Equation 3, both R and T are defined in terms of pressure ratios. While this is unimportant for reflectivity (because both P and P exist in the same media), it can lead to difficulties in interpreting transmissibility. Consider, for example, the case of sound in water impinging on a steel surface. Since the density and speed of sound in steel are 7.7 g/cc and 6.1 x 10 cm/s, the impedance ratio z IZ is 0.032. Then R = 0.938, indicating most (93.8%) of the incident pressure was reflected. But T = 1.94 indicating a pressure increase upon transmission to steel. While this may at first appear unclear, it is understandable if one considers that the impedance of water is much less than that of steel; hence although only a small fraction (12%) of the acoustic energy was transferred across the water-steel boundary, that small energy fraction corresponds to a much higher acoustic pressure in steel then it would in water. For following acoustic signals across boundaries, it is safer to use acoustic intensity rather than pressure, where intensity is proportional to the pressure squared. It can be shown that the intensity transmission coefficient and its corresponding transmission loss are: f
r
5
x
2
Tj = 4 ( / Z ) / (1+ /Z )2, Zl
2
Zl
T L = 10 Log (T,).
2
(8)
As mentioned previously, the reflectivity and transmissibility of the surface is entirely controlled by the ratio of the specific impedance of media 1 and the input impedance at the boundary with media 2. As additional complexities are included in the formulation, they simply present themselves as modifications to these impedances. For example, the previous discussion was for sound incident "normal" or perpendicular to the media boundary. If the acoustic signal strikes the surface at some other angle, as shown in Figure 1, the effect can be included simply as an increase in impedance. Hence, for an angle of sound incidence the effective impedance of media 1 can be represented as: 1
(
Zl
) = Zj / cos( /k*
=c /(l - ja/k). G
(13)
Thus, in an attenuating media, we see that sound speed is no longer a simple quantity. It will be frequency dependent, its magnitude being: lc*l = c / (1+72)1/2, D
7
= 0.0183 a'X.
(14)
where a' is the attenuation coefficient now expressed in dB units. Since sound speed is a frequency dependent complex quantity, it therefore follows that the characteristic impedance of the media will also be frequency dependent and complex. If the frequency dependence of sound speed is not known, it can be estimated from the attenuation coefficient as follows. For the rubber composites of interest here, usually a'A is essentially independent of frequency. Using Kramers-Kronig relationships (5) it can then be shown that: 2
c = c [1+ ( a ' t y * ) ln(f/f )l G
(15)
()
where c is the sound speed at any reference frequency f . Q
0
Anechoic Treatments ayer The simplest anechoic wall treatment available involves covering the wall with a layer of absorptive material. Such a case is shown in Figure 2. To be effective in absorbing the incident sound without reflection, the reflected echos labeled (A and (B must both be small. Here echo cA is called the specular or front face reflectivity (described in the previous section), echo © is the first internal reflection, and echo Q is the first multiple internal reflection. If echo © is small then all multiple internal reflections (such as echo Q) will be even smaller and can be neglected.. The material used must therefore perform two functions: it must allow all incoming sound to pass into the coating, and it must absorb this acoustic energy before it can be re-emitted.
CORSARO ET AL.
Acoustic Coatings for Water-Filled Tanks
213
. • /•/// i I / / / / /•/• /////•// /• /• //•////// //•///•/.
'/////• > //.'//////////////
1
/ ////'•//////
^ •'///////////////^/y////////////////
MEDIUM 1 Pl.c,, z,. o,
/
MEDIUM 2 p, c, 2
2
z .
