scholarly journals NUMERICAL SIMULATION OF ACOUSTIC STREAMING WITHIN THE COCHLEA

2013 ◽  
Vol 21 (04) ◽  
pp. 1350019 ◽  
Author(s):  
CHRISTIAN GERSTENBERGER ◽  
FRANZ-ERICH WOLTER
Keyword(s):  
Outer Hair Cell ◽  
Basilar Membrane ◽  
Order Approximation ◽  
Acoustic Streaming ◽  
Biomechanical Properties ◽  
Mean Flow ◽  
Outer Hair Cell Motility ◽  
Physiological Impact ◽  
First Order Approximation

This paper is concerned with the numerical examination of acoustically driven flows within the inner ear on the basis of a computational model. For this purpose, a comprehensive system of differential equations and boundary conditions is deduced, which takes, to a satisfactory extent, the complexity of the main biophysical mechanisms of the cochlea into account. Beside an appropriate representation of the fluid dynamics, also the biomechanical properties of the basilar membrane as well as the internal amplification mechanism caused by the outer hair cell motility are considered in order to get realistic estimates of the structure and magnitude of the mean flow field. The present paper introduces a two-stage approach for the numerical evaluation of the solutions on the basis of the finite element method. The first step deals with the calculation of the linear acoustic reaction whereas the second step is associated with the determination of a first-order approximation of the acoustic streaming field. It is shown that the results are essentially consistent with measurements as well as analytical and experimental considerations. In addition, the numerical estimates of the acoustically driven flows provide an instrument for a more profound discussion on their physiological impact.

Direct Prediction of the Effects of Mistuning on the Forced Response of Bladed Disks

1998 ◽  
Vol 120 (3) ◽  
pp. 626-634 ◽  
Author(s):  
M. P. Mignolet ◽  
W. Hu
Keyword(s):  
Structural Model ◽  
Order Approximation ◽  
Forced Response ◽  
Blade Vibration ◽  
First Order ◽  
Bladed Disk ◽  
Novel Approach ◽  
Error Terms ◽  
First Order Approximation

In this paper, a novel approach to determine reliable estimates of the moments of the steady-state resonant response of a randomly mistuned bladed disk is presented, and the use of these moments to accurately predict the corresponding distribution of the amplitude of blade vibration is described. The estimation of the moments of the response is accomplished first by relying on a “joint cumulant closure” strategy that expresses higher order moments in terms of lower order ones. A simple modeling of the error terms of these approximations is also suggested that allows the determination of an improved, or accelerated, estimate of the required moments. The evaluation of the distribution of the amplitude of blade response is then accomplished by matching the moments computed by the cumulant closure with those derived from a three-parameter model recently derived. A first order approximation of the moments obtained for a simple structural model of a bladed disk yields a new parameter that can be used as a measure of the localization of the forced response. Then, numerical results demonstrate that the method provides extremely accurate estimates of the moments for all levels of structural coupling which in turn lead to a description of the amplitude of blade response that closely matches simulation results. Finally, a comparison with existing perturbation techniques clearly shows the increased accuracy obtained with the proposed joint cumulant closure formulation.

Calculation of the Uncertainty in the Determination of the Equilibrium Moisture Content of Pumpkin Seed Flour

2007 ◽  
Vol 3 (1) ◽  
Author(s):  
Wilton P. S. da Silva ◽  
Jürgen W. Precker ◽  
Cleide M. D. P. S. Silva ◽  
Cleiton D. P. S. Silva ◽  
Diogo D. P. S. Silva ◽  
...  
Keyword(s):  
Moisture Content ◽  
Equilibrium Moisture Content ◽  
Order Approximation ◽  
Computer Code ◽  
Indirect Measurement ◽  
Pumpkin Seed ◽  
Seed Flour ◽  
First Order Approximation ◽  
Fitting Parameters

Empiric equations for the determination of the equilibrium moisture content as a function of temperature and relative humidity of air are normally obtained from experimental data by curve fitting. Once the fitting parameters of a function for a given product are determined, the value of that function for specific values of temperature and humidity of air is obtained by substituting these values into the function, which represents an indirect measurement. Generally, the results of these modelings are stated without the uncertainties inherent in the measurement. This article proposes a method for the determination of these uncertainties. For that, a computer code was developed which calculates the error propagation in first order approximation from the obtained fitting parameters and their covariances. The code was used for the determination of the uncertainties of the equilibrium moisture content of pumpkin seed flour, both for adsorption and desorption. This procedure allows a report of the measurement in agreement with the rules established by international standardization organizations.

scholarly journals Direct Prediction of the Effects of Mistuning on the Forced Response of Bladed Disks

1997 ◽  
Author(s):  
Marc P. Mignolet ◽  
Wei Hu
Keyword(s):  
Structural Model ◽  
Order Approximation ◽  
Forced Response ◽  
Blade Vibration ◽  
First Order ◽  
Bladed Disk ◽  
Novel Approach ◽  
Error Terms ◽  
First Order Approximation

In this paper, a novel approach to determine reliable estimates of the moments of the steady state resonant response of a randomly mistuned bladed disk is presented and the use of these moments to accurately predict the corresponding distribution of the amplitude of blade vibration is described. The estimation of the moments of the response is accomplished first by relying on a “joint cumulant closure” strategy that expresses higher order moments in terms of lower order ones. A simple modeling of the error terms of these approximations is also suggested that allows the determination of an improved, or accelerated, estimate of the required moments. The evaluation of the distribution of the amplitude of blade response is then accomplished by matching the moments computed by the cumulant closure with those derived from a three-parameter model recently derived. A first order approximation of the moments obtained for a simple structural model of a bladed disk yields a new parameter that can be used as a measure of the localization of the forced response. Then, numerical results demonstrate that the method provides extremely accurate estimates of the moments for all levels of structural coupling which in turn lead to a description of the amplitude of blade response that closely matches simulation results. Finally, a comparison with existing perturbation techniques clearly shows the increased accuracy obtained with the proposed joint cumulant closure formulation.

Approximation for the Effect of Twist on the Vibration of a Turbine Blade

1957 ◽  
Vol 8 (3) ◽  
pp. 291-308 ◽  
Author(s):  
A. I. Martin
Keyword(s):  
Turbine Blade ◽  
Order Approximation ◽  
Turbine Blades ◽  
First Order ◽  
Flexural Vibrations ◽  
First Order Approximation ◽  
Kirchhoff Theory

SummaryModern turbine blades are generally twisted about their axes, the shape resembling that of a helicoid. This makes the determination of their overtone frequencies much more difficult. The equations governing the flexural vibrations may be obtained from the Clebsch-Kirchhoff theory for rods which are naturally twisted. By using these equations, this paper considers a first-order approximation for the effect of uniform twist.

Improved first-order approximation of eigenvalues and eigenvectors

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 1721-1727
Author(s):  
Prasanth B. Nair ◽  
Andrew J. Keane ◽  
Robin S. Langley
Keyword(s):  
Order Approximation ◽  
Eigenvalues And Eigenvectors ◽  
First Order ◽  
First Order Approximation

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

FIRST-ORDER APPROXIMATION OF THE NUMBER-PROJECTED SO(2N) TAMM-DANCOFF EQUATION AND ITS REDUCTION BY THE SCHUR FUNCTION

1999 ◽  
Vol 08 (05) ◽  
pp. 461-483
Author(s):  
SEIYA NISHIYAMA
Keyword(s):  
Wave Function ◽  
Order Approximation ◽  
Approximate Equation ◽  
Variation Principle ◽  
Schur Function ◽  
Soliton Theory ◽  
First Order ◽  
Fermion Systems ◽  
Group Manifold ◽  
First Order Approximation

First-order approximation of the number-projected (NP) SO(2N) Tamm-Dancoff (TD) equation is developed to describe ground and excited states of superconducting fermion systems. We start from an NP Hartree-Bogoliubov (HB) wave function. The NP SO(2N) TD expansion is generated by quasi-particle pair excitations from the degenerate geminals in the number-projected HB wave function. The Schrödinger equation is cast into the NP SO(2N) TD equation by the variation principle. We approximate it up to first order. This approximate equation is reduced to a simpler form by the Schur function of group characters which has a close connection with the soliton theory on the group manifold.

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