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Research Papers

Sound Radiation From Point Acoustic Sources With Shield of Large Prolate Spheroidal Baffles

[+] Author and Article Information
Xiongtao Cao

Laboratory of Marine Power Cabins,
Shanghai Maritime University,
Haigang Avenue 1550,
Shanghai 201306, China
e-mail: caolin1324@126.com

Mingsheng Wang, Lei Shi

Laboratory of Marine Power Cabins,
Shanghai Maritime University,
Haigang Avenue 1550,
Shanghai 201306, China

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 23, 2017; final manuscript received February 7, 2018; published online March 30, 2018. Assoc. Editor: Sheryl M. Grace.

J. Vib. Acoust 140(4), 041016 (Mar 30, 2018) (14 pages) Paper No: VIB-17-1223; doi: 10.1115/1.4039403 History: Received May 23, 2017; Revised February 07, 2018

Sound radiation from stationary and rotating point acoustic sources with shield of rigid prolate spheroidal baffles is explored in the prolate spheroidal coordinate system. The formulae of far-field sound pressure and acoustic power are derived and acoustic power spectral density (PSD) in terms of circumferential and azimuthal wavenumber is manifested from the low frequency range to high frequency range. Acoustic wave propagation features in the spherical coordinate system as a particular case of the prolate spheroidal coordinate system are presented. Rotating sound sources cause the frequency veering phenomenon and change the patterns of PSD. Some spheroidal harmonic waves with lower and higher wavenumber for the large prolate spheroids cannot contribute to far-field sound radiation in the high frequency range when sound sources are close to the axes of the spheroids. Sound pressure directivity and acoustic power of stationary point sound sources are also analyzed with the variation of source location.

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Figures

Grahic Jump Location
Fig. 1

Sound radiation from several rotating point acoustic sources with shield of large prolate spheroidal baffle

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Fig. 9

(a) Power spectral density of rotating point acoustic sources with shield of rigid prolate spheroid at  fa=0.5 kHz,  s=7, ω0=8π/s and (b) PSD of rotating point acoustic sources with shield of rigid prolate spheroid at  fa=5 kHz,  s=7, ω0=8π/s

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Fig. 13

(a) Power spectral density of point acoustic source on the rigid prolate spheroid at  fa=3 kHz,  s=1,  η=−0.15 and (b) PSD of point acoustic source on the rigid prolate spheroid at  fa=3 kHz,  s=1,  η=cos π/2

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Fig. 2

Deviation of  |∂p1/∂ξ|/Q along the boundary of rigid prolate spheroid defined by  ξ=ξ1 and  θ=0

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Fig. 3

(a) Power spectral density of point acoustic source with shield of rigid prolate spheroid at  fa=0.5 kHz,  s=1,  ω0=0, (b) PSD of point acoustic source with shield of rigid prolate spheroid at  fa=1.5 kHz,  s=1,  ω0=0, (c) PSD of point acoustic source with shield of rigid prolate spheroid at  fa=3 kHz,  s=1,  ω0=0, and (d) PSD of point acoustic source with shield of rigid prolate spheroid at  fa=5 kHz,  s=1,  ω0=0

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Fig. 4

(a) Power spectral density of point acoustic source with shield of rigid sphere at  fa=0.5 kHz,  s=1,  ω0=0, (b) PSD of point acoustic source with shield of rigid sphere at  fa=1.5 kHz,  s=1,  ω0=0, (c) PSD of point acoustic source with shield of rigid sphere at  fa=3 kHz,  s=1,  ω0=0, and (d) PSD of point acoustic source with shield of rigid sphere at  fa=5 kHz,  s=1,  ω0=0

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Fig. 5

(a) Power spectral density of point acoustic source with shield of rigid prolate spheroid at  fa=0.5 kHz,  s=1,  ω0=0,  η=−cos π/4, (b) PSD of point acoustic source with shield of rigid prolate spheroid at  fa=1.5 kHz,  s=1,  ω0=0,  η=−cos π/4, (c) PSD of point acoustic source with shield of rigid prolate spheroid at  fa=3 kHz,  s=1,  ω0=0,  η=−cos π/4, and (d) PSD of point acoustic source with shield of rigid prolate spheroid at  fa=5 kHz,  s=1,  ω0=0,  η=−cos π/4

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Fig. 6

(a) Power spectral density of point acoustic source without shield of rigid prolate spheroid at  fa=3 kHz,  s=1,  ω0=0 and (b) PSD of point acoustic source without shield of rigid prolate spheroid at  fa=5 kHz,  s=1,  ω0=0

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Fig. 7

Sound pressure directivity of point acoustic source with and without shield of rigid prolate spheroid at  fa=0.5 kHz,  s=1,  ω0=0,  ξ=ξ1,  θ=0 and  θ=π, directivity angle  β is related to  η by  η=cos β; (b) Sound pressure directivity of point acoustic source with and without shield of rigid prolate spheroid at  fa=1.5 kHz,  s=1,  ω0=0,  ξ=ξ1,  θ=0 and  θ=π, directivity angle  β is related to  η by  η=cos β

Grahic Jump Location
Fig. 8

Acoustic power level of sound source with shield of the spheroid at  fa=0.5 kHz and  fa=1.5 kHz

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Fig. 10

(a) Power spectral density of rotating point acoustic sources with shield of rigid prolate spheroid in the air at  fa=0.5 kHz,  s=7,  ω0=8π/s, (b) PSD of rotating point acoustic sources with shield of rigid prolate spheroid in the air at  fa=1.1 kHz,  s=7,  ω0=8π/s, (c) PSD of rotating point acoustic sources with shield of rigid prolate spheroid in the air at  fa=0.5 kHz,  s=7,  ω0=16π/s, and (d) PSD of rotating point acoustic sources with shield of rigid prolate spheroid in the air at  fa=1.1 kHz,  s=7,  ω0=16π/s

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Fig. 11

(a) Sound pressure directivity of point acoustic source on the prolate spheroidal baffle at  fa=1.5 kHz with source location  η=−cos π/12,  θ=0, directivity angle  β is related to  η by  η=cos β and (b) Sound pressure directivity of point acoustic source on the prolate spheroidal baffle at  fa=1.5 kHz with source location  η=cos π/2,  θ=0, directivity angle  β is related to  η by  η=cos β

Grahic Jump Location
Fig. 12

Acoustic power level of point acoustic source on the prolate spheroidal baffle

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