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Research Papers

A Novel Method of Designing Quiet Zones in Diffuse Fields

[+] Author and Article Information
Wen-Kung Tseng

Graduate Institute of Vehicle Engineering,
National Changhua University of Education,
No.1, Jin-De Road,
500 Changhua City, Taiwan, ROC
e-mail: andy007@cc.ncue.edu.tw

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received January 3, 2011; final manuscript received June 26, 2012; published online February 4, 2013. Assoc. Editor: Lonny Thompson.

J. Vib. Acoust 135(1), 011001 (Feb 04, 2013) (9 pages) Paper No: VIB-11-1001; doi: 10.1115/1.4007451 History: Received January 03, 2011; Revised June 26, 2012

This paper presents the analysis of quiet zones in broadband diffuse fields using two- and three-channel systems. An optimization method combining a neural network with a search algorithm has been used to design quiet zones in broadband diffuse fields. Simulation results using the proposed method are presented. Experiments are also carried out to validate the simulation results. The results show that a good attenuation in the desired zone of quiet over space and frequency is achieved using a two-channel system. However, a better performance could be achieved using a three-channel system. Also, the shape and location of quiet zones over space and frequency could be controlled by using the proposed method. The results also show that the shape and size of 10-dB quiet zones are both similar in simulations and experiments. The main contributions of the paper are that a novel method of designing quiet zones in broadband diffuse fields is proposed and the performance of the active systems is analyzed through computer simulations and experiments.

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Figures

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Fig. 1

Definition of spherical coordinates r, θ, φ for an incident plane wave traveling along line r direction

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Fig. 2

The plane perpendicular to lines A and B and parallel to line r

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Fig. 4

Two-channel feedback control system with two internal model controllers

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Fig. 3

Configuration of acoustic pressure minimization over space and frequency with a two-channel feedback system

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Fig. 5

A flow chart of the optimization method combining a neural network with a search algorithm

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Fig. 6

Architecture of the neural network

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Fig. 7

Flow chart of the search algorithm

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Fig. 8

Attenuation in decibels as function of space and frequency for two-channel system with two FIR filters without constraints

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Fig. 9

Attenuation in decibels as function of space and frequency for a two-channel system with two FIR filters and with constraints on amplification not exceeding 20 dB at spatial axis from r = 0.09 m to r = 0.2 m for all frequencies and constraints on robust stability with B1 = B2 = 0.3

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Fig. 10

Attenuation in decibels as a function of space and frequency for a three-channel system with FIR filters without constraints

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Fig. 11

Attenuation in decibels as a function of space and frequency for a three-channel system with FIR filters and constraints on robust stability for B1 = B2 = B3 = 0.3 and amplification not to exceed 20 dB at the spatial axis from r = 0.09 m to r = 0.2 m for all the frequencies

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Fig. 12

Attenuation in decibels as a function of space and frequency for a three-channel system with FIR filters without constraints for the different minimization shape represented by a rectangular frame. (a) The rectangular frame is narrow in the frequency axis direction and longer in the space axis direction. (b) The rectangular frame is narrow in the space axis direction and longer in the frequency axis direction.

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Fig. 13

Configuration of experimental setup

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Fig. 14

The reduction contour of the zones of quiet created by two secondary sources located at positions (0,0) and (–0.05, 0) using the optimization method combining a neural network with a search algorithm. (a) Computer simulations. (b) Experiments.

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