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Research Papers

Analytical Evaluation of the Acoustic Behavior of Multilayer Walls When Subjected to Three-Dimensional and Moving 2.5-Dimensional Loads

[+] Author and Article Information
A. Tadeu

e-mail: tadeu@dec.uc.pt

L. Godinho

Department of Civil Engineering,
University of Coimbra,
Pólo II, Rua Luís Reis Santos,
Coimbra 3030-788, Portugal

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received July 6, 2012; final manuscript received March 6, 2013; published online June 19, 2013. Assoc. Editor: Theodore Farabee.

J. Vib. Acoust 135(6), 061001 (Jun 19, 2013) (16 pages) Paper No: VIB-12-1192; doi: 10.1115/1.4024049 History: Received July 06, 2012; Revised March 06, 2013

This paper focuses on the analytical evaluation of the acoustic behavior of multilayer walls when subjected to 3D and moving 2.5D loads. The computations are performed in the frequency domain for a wall system composed of multiple solid and fluid layers. The pressure generated by the 3D load is computed as Bessel integrals, following the transformations proposed by Sommerfeld. The integrals are discretized by assuming the existence of a set of virtual loads equally spaced in a direction perpendicular to the plane of the wall. The expressions presented here allow the pressure field to be computed without discretizing the interfaces between layers. The full interaction between the fluid (air) and the solid layers is taken into account. As the 3D pressure field can also be computed as a summation of spatially sinusoidal harmonic line loads, which can be seen as a moving 2.5D load, this paper studies the contribution made to the global 3D response by the insulation provided by the wall when subjected to each of these loads. To illustrate the main findings, simulated responses are computed in the frequency domains for single and double walls that are subjected to 3D and moving 2.5D loads. Additionally, time responses have been synthesized using inverse Fourier transformations.

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References

Warnock, A., and Fasold, W., 1997, Sound Insulation: Airborne and Impact, Encyclopedia of Acoustics, Vol. 3, Wiley-Interscience Publication, New York, pp. 1129–1161.
Novikov, I., 1998, “Low-Frequency Sound Insulation of Thin Plates,” Appl. Acoust., 54, pp. 83–90. [CrossRef]
London, A., 1950, “Transmission of Reverberant Sound Through Double Walls,” J. Acoust. Soc. Am., 22, pp. 270–279. [CrossRef]
1960, Noise Reduction, L.Beranek, ed., McGraw-Hill Book Company, New York.
Fahy, F., 2001, Foundations of Engineering Acoustics, Academic Press, New York.
Gösele, K., 1980, “Zur Berechnung der Luftschalldämmung von doppelschaligen Bauteilen (ohne Verbindung der Schalen),” Acustica, 45, pp. 218–227.
Panneton, R., and Atalla, N., 1996, “Numerical Prediction of Sound Transmission Through Finite Multiplayer Systems With Poroelastic Materials,” J. Acoust. Soc. Am., 100(1), pp. 346–354. [CrossRef]
Sgard, F., Atalla, N., and Nicolas, J., 2000, “A Numerical Model for the Low Frequency Diffuse Field Sound Transmission Loss of Double-Wall Sound Barriers With Elastic Porous Linings,” J. Acoust. Soc. Am., 108(6), pp. 2865–2872. [CrossRef]
Steel, J., and Craik, R., 1994, “Statistical Energy Analysis of Structure-Borne Sound Transmission by Finite Element Methods,” J. Sound Vib., 178(4), pp. 553–561. [CrossRef]
Craik, R., Nightingale, T., and Steel, J., 1997, “Sound Transmission Through a Double Leaf Partition With Edge Flanking,” J. Acoust. Soc. Am., 101(2), pp. 964–969. [CrossRef]
Craik, R., and Smith, R., 2000, “Sound Transmission Through Double Leaf Lightweight Partitions—Part I: Airborne Sound,” Appl. Acoust., 61, pp. 223–245. [CrossRef]
Coz-Díaz, J., Álvarez-Rabanal, F., García-Nieto, P., and Serrano-López, M., 2010, “Sound Transmission Loss Analysis Through a Multilayer Lightweight Concrete Hollow Brick Wall by FEM and Experimental Validation,” Building and Environment, 45(11), pp. 2373–2386. [CrossRef]
Xin, F., and Lu, T., 2011, “Analytical Modeling of Sound Transmission Through Clamped Triple-Panel Partition Separated by Enclosed Air Cavities,” Eur. J. Mech. A/Solids, 30(6), pp. 770–782. [CrossRef]
2002, Formulas of Acoustics, F.Mechel, ed., Springer-Verlag, Berlin.
Tadeu, A., and António, J., 2002, “Acoustic Insulation of Single Panel Walls Provided by Analytical Expressions Versus the Mass Law,” J. Sound Vib., 257(3), pp. 457–475. [CrossRef]
António, J., Tadeu, A., and Godinho, L., 2003, “Analytical Evaluation of the Acoustic Insulation Provided by Double Infinite Walls,” J. Sound Vib., 263(1), pp. 113–129. [CrossRef]
Tadeu, A., Pereira, A., Godinho, L., and Antonio, J., 2007, “Prediction of Airborne Sound and Impact Sound Insulation Provided by Single and Multilayer Systems Using Analytical Expressions,” Appl. Acoust., 68(1), pp. 17–42. [CrossRef]
Sheng, X., Jones, C., and Petyt, M., 1999, “Ground Vibration Generated by a Load Moving Along a Railway Track,” J. Sound Vib., 228(1), pp. 129–156. [CrossRef]
Adam, M., Pflanz, G., and Schmid, G., 2000, “Two- and Three-Dimensional Modelling of Half-Space and Train-Track Embankment Under Dynamic Loading,” Soil Dynamics and Earthquake Eng., 19(8), pp. 559–573. [CrossRef]
Xia, H., Cao, Y., and De Roeck, G., 2010, “Theoretical Modeling and Characteristic Analysis of Moving-Train Induced Ground Vibrations,” J. Sound Vib., 329(7), pp. 819–832. [CrossRef]
Gao, G., Chen, Q., He, J., and Liu, F., 2012, “Investigation of Ground Vibration Due to Trains Moving on Saturated Multi-Layered Ground by 2.5D Finite Element Method,” Soil Dynamics and Earthquake Engineering, 40, pp. 87–98. [CrossRef]
Tanaka, K., and Ishii, S., 1981, “Acoustic Radiation From a Moving Line Source,” J. Sound Vib., 77(3), pp. 397–401. [CrossRef]
Obrezanova, O., and Rabinovich, V., 1998, “Acoustic Field Generated by Moving Sources in Stratified Waveguides,” Wave Motion, 27(2), pp. 155–167. [CrossRef]
Lee, P., and Wang, J., 2010, “The Simulation of Acoustic Radiation From a Moving Line Source With Variable Speed,” Appl. Acoust., 71(10), pp. 931–939. [CrossRef]
Sommerfeld, A., 1950, Mechanics of Deformable Bodies, Academic Press, Inc., New York.
Ewing, W., Jardetzky, W., and Press, F., 1957, Elastic Waves in Layered Media, McGraw-Hill Book Company, New York.
Tadeu, A., António, J., Godinho, L., and Amado Mendes, P., 2012, “Simulation of Sound Absorption in 2D Thin Elements Using a Coupled BEM/TBEM Formulation in the Presence of Fixed and Moving 3D Sources,” J. Sound Vib., 331, pp. 2386–2403. [CrossRef]
Jensen, F., Kuperman, W., Porter, M., and Schmidt, H., 1994, Computational Ocean Acoustics, American Institute of Physics, New York.
Schwartz, L., 1966, Theorie des Distributions, Hermann, Paris.
Bouchon, M., and Aki, K., 1977, “Discrete Wave-Number Representation of Seismic-Source Wave Field,” Bull. Seismol. Soc. Am., 67, pp. 259–277.
Bouchon, M., 1979, “Discrete Wave Number Representation of Elastic Wave Fields in Three-Space Dimensions,” J. Geophys. Res., 84, pp. 3609–3614. [CrossRef]

Figures

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Fig. 1

The geometry of the problem

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Fig. 2

Definition of potentials for simulation of 3D loads: (a) solid layer; (b) fluid layer

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Fig. 3

Definition of potentials for simulation of 2.5D sinusoidally harmonic line loads: (a) solid layer; (b) fluid layer

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Fig. 4

Verification results in terms of the sound insulation of a double-panel partition wall under the effect of normally incident plane waves

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Fig. 5

Position of the receivers for frequency domain computations: plane yz; plane xz

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Fig. 6

Single wall in the presence of a 3D fixed point load (500.0 Hz). Pressure responses at time instants: (a) t = 15.0 ms; (b) t = 25.0 ms; (c) t = 35.0 ms.

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Fig. 7

Single wall in the presence of a 3D fixed point load (500.0 Hz). Pressure responses in the time domain: (a) receiver in the outer fluid; (b) receiver in the inner fluid.

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Fig. 8

Single wall in the presence of a 3D fixed point load (750.0 Hz). Pressure responses at time instant t = 25.0 ms.

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Fig. 9

Average sound pressure in the inner fluid (left), and sound insulation (right), provided by a single ceramic brick wall 0.1 m thick, when subjected to pressure waves generated by a 3D point load

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Fig. 10

Moving 2.5D load in the presence of a single wall (500.0 Hz). Time signatures when the loads travel at velocities of: (a) cm = 25.0 m/s; (b) cm = 50.0 m/s; (c) cm = 100.0 m/s; (d) cm = 500.0 m/s; (e) cm = 2500.0 m/s.

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Fig. 11

Moving 2.5D load in the presence of a single wall. Time signatures when the load travels at velocity cm = 500.0 m/s and the characteristic frequency of the pulse is 100.0 Hz.

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Fig. 12

Average sound pressure in the inner fluid (left) and sound insulation (right) provided by a single ceramic brick wall 0.1 m thick when subjected to pressure waves generated by moving 2.5D loads traveling at velocities cm = 25.0 m/s, cm = 50.0 m/s, cm = 100.0 m/s, cm = 500.0 m/s, and cm = 2500.0 m/s

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Fig. 13

Double wall in the presence of a 3D fixed point load (500.0 Hz). Pressure responses at time instants: (a) t = 15.0 ms and (b) t = 35.0 ms.

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Fig. 14

Average sound pressure in the inner fluid (left) and sound insulation (right) provided by a double ceramic wall composed of panels 0.1 m and 0.15 thick and an air layer 0.05 m thick, when subjected to pressure waves generated by a 3D point load

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Fig. 15

Moving 2.5D load in the presence of a double wall (500.0 Hz). Time signatures when the load is traveling at a velocity of cm = 500.0 m/s.

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Fig. 16

Average sound pressure in the inner fluid (left) and sound insulation (right) provided by a double ceramic wall composed of panels 0.1 m and 0.15 m thick and an air layer 0.05 m thick, when subjected to pressure waves generated by moving 2.5D loads traveling at velocities cm = 25.0 m/s, cm = 50.0 m/s, cm = 500.0 m/s, and cm = 2500.0 m/s

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