Research Papers: Fundamental Issues and Canonical Flows

Acoustic Boundary Layer Attenuation in Ducts With Rigid and Elastic Walls Applied to Cochlear Mechanics

[+] Author and Article Information
Frank Böhnke

Department of Otorhinolaryngology,
Technische Universität München
Ismaningerstr. 22,
München 81664, Germany
e-mail: frank.boehnke@tum.de

Sebastian Semmelbauer

Department of Otorhinolaryngology,
Ludwig Maximilian University Munich,
Marchioninistr. 15,
München 81377, Germany
e-mail: Sebastian.Semmelbauer@med.uni-muenchen.de

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 5, 2016; final manuscript received April 21, 2017; published online July 10, 2017. Assoc. Editor: Satoshi Watanabe.

J. Fluids Eng 139(10), 101202 (Jul 10, 2017) (6 pages) Paper No: FE-16-1658; doi: 10.1115/1.4036674 History: Received October 05, 2016; Revised April 21, 2017

The cochlea is the most important part of the hearing system, due to the fact that it transforms sound guided through air, bone, and lymphatic fluid to vibrations of the cochlear partition which includes the organ of Corti with its sensory cells. These send nerve impulses to the brain leading to hearing perception. The work presents the wave propagation in rigid ducts filled with air or water including viscous-thermal boundary layer damping. In extension, a mechanical box model of the human cochlea represented by a rectangular duct limited by the tapered basilar membrane at one side is developed and evaluated numerically by the finite element method. The results match with rare experiments on human temporal bones without using the physically unfounded assumption of Rayleigh damping. A forecast on the concept of the traveling wave parametric amplification is given to potentially explain the high hearing sensitivity and otoacoustic emissions.

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Grahic Jump Location
Fig. 1

Rectangular duct with arbitrary segmentation in the longitudinal direction. The evaluation of the pressure distribution along the duct is either conducted for an air (low density, low viscosity) or water (high density, high viscosity) filled duct with different geometrical dimensions.

Grahic Jump Location
Fig. 2

Box model of the cochlea derived from the rigid duct by extension of a tapered elastic wall on top of the duct. The transverse dimensions are 2 mm × 2 mm and length 34 mm. On top of the duct, the geometry of the orthotropic elastic solid with expanding width from 100 μm to 500 μm is visible.

Grahic Jump Location
Fig. 3

(a) The lateral view of a midplane slice of the duct of Fig. 2 presents the longitudinal velocity vx coded changing from maximum positive 13.76 nm/s to maximum negative −13.04 nm/s values for an input velocity of 1 nm/s and frequency f = 2 kHz at the front area. For illustration of the vibrating elastic structure's movement, its vz component is included by gray areas above the duct. (b) The corresponding pressure distribution using the same stimulation value of 1 nm/s at the front area of the duct. The minimum pressure of −97.5 μPa occurs at the base of the cochlea, and the maximum value is 80.16 μPa.

Grahic Jump Location
Fig. 4

Frequency-dependent pressure at the end area of an air-filled rigid duct. A maximum pressure resonance is found as shown in Ref. [21].

Grahic Jump Location
Fig. 5

Frequency-dependent pressure at the end area of a water-filled rigid duct. A maximum pressure resonance is found at a high frequency f = 22.5 kHz caused by the lower size of the duct and the different material parameters of water.

Grahic Jump Location
Fig. 6

The displacements of the vibrating solid (bm) show the characteristic traveling wave for the input signal with frequency f = 2 kHz at a fixed time. After reaching a maximum displacement of nearly 6 pm at x = 17 mm in the longitudinal direction of the duct, amplitudes diminish because of boundary layer damping. If the boundary layer damping is set to zero, the structure continues to vibrate with displacement amplitudes of 6 pm.

Grahic Jump Location
Fig. 7

Absolute values and phases of velocities at the centerline of the elastic solid (bm) recorded along the length of the duct. A wide dynamic range of amplitudes (53 dB) and a phase shift of 600 deg or −1.66 cycles at the location of maximum velocity at 18 mm distance from the base occurs.



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