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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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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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