Technical Brief

Optimized Finite Element Method for Acoustic Scattering Analysis With Application to Head-Related Transfer Function Estimation

[+] Author and Article Information
Mahdi Farahikia

Vibrations and Acoustics Laboratory,
Department of Mechanical Engineering,
Binghamton University (SUNY),
Binghamton, NY 13902
e-mail: mfarahi1@binghamton.edu

Quang T. Su

Vibrations and Acoustics Laboratory,
Department of Mechanical Engineering,
Binghamton University (SUNY),
Binghamton, NY 13902
e-mail: qsu@binghamton.edu

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 15, 2016; final manuscript received January 5, 2017; published online April 13, 2017. Assoc. Editor: Sheryl M. Grace.

J. Vib. Acoust 139(3), 034501 (Apr 13, 2017) (4 pages) Paper No: VIB-16-1351; doi: 10.1115/1.4035813 History: Received July 15, 2016; Revised January 05, 2017

Obtaining head-related transfer functions (HRTFs) is a challenging task, in spite of its importance in localizing sound in a three-dimensional (3D) environment or improving the performance of hearing aids, among their various applications. In this paper, an optimized finite element method through adaptive dimension size based on wavelength (frequency) for acoustic scattering analyses using ansys is presented. Initial investigation of the validity of our method is conducted by simulating scattered sound field for a solid sphere exposed to a far-field plane sound wave at 100 (equally spaced in logarithmic scale) frequencies between 20 and 20 kHz. Comparison of the equivalent HRTF results between the two methods shows a maximum deviation of less than 0.6 dB between our method and the analytical solution depending on the angle of rotation of the sphere with respect to sound source.

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Fig. 1

Two-dimensional schematic of the model

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Fig. 2

Meshed FEM for 3495 Hz frequency

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Fig. 3

Schematic of the orientation of the head rotation angle

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Fig. 4

Normalized head-related transfer function versus ka: (a) 0 deg versus 180 deg, (b) 30 deg versus 210 deg, (c) 60 deg versus 240 deg, and (d) 90 deg versus 270 deg—comparison between analytical and ansys data shows very good agreement

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Fig. 5

Deviation of pressure magnitude given by ansys from the analytical solution (dB) versus ka: (a) 0 deg versus 180 deg, (b) 30 deg versus 210 deg, (c) 60 deg versus 240 deg, and (d) 90 deg versus 270 deg—it is observed that the maximum difference is less than 0.6 dB, which occurs at very high frequency for the contralateral position for θ = 0 deg and θ = 30 deg due to shadowing

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Fig. 6

Magnitude of pressure (Pa) on the surface of the sphere at 15,129 Hz—comparison between the analytical and ansys results shows very good agreement

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Fig. 7

Deviation of pressure magnitude (dB) on the surface of the sphere at 15,129 Hz—the maximum difference of less than 0.6 dB is observed in the contralateral direction. This is a relative error in reporting near zero pressure values.



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