Modeling acoustic resonators using higher-order equivalent circuits

2019 ◽  
Vol 67 (6) ◽  
pp. 456-466
Author(s):  
Caleb B. Goates ◽  
Mathew F. Calton ◽  
Scott D. Sommerfeldt ◽  
David C. Copley
Keyword(s):  
Higher Order ◽  
Side Branch ◽  
Equivalent Circuits ◽  
One Dimensional ◽  
Acoustic Resonators ◽  
Helmholtz Resonators ◽  
Lumped Element ◽  
Classical Models ◽  
The One ◽  
Dimensional Wave

Helmholtz resonators are widely used, but classical models for the resonators, such as the lumped-element equivalent circuit, are inaccurate for most geometries. This article presents higher-order equivalent circuits for describing the resonators based on the one-dimensional wave equation. Impedance expressions are also derived. These circuits and expressions are given for various constituent resonator components, which may be combined to model resonators with curved, tapered, and straight necks. Resonance frequency predictions using this theory are demonstrated on two realistic resonators. The higher-order predictions are also applied to the theory of side branch attenuators in a duct and the theory of resonator coupling with a mode of an enclosure.

scholarly journals Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea
Keyword(s):  
Applied Sciences ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Second Order ◽  
Dimensional Case ◽  
Moduli Of Continuity ◽  
One Dimensional ◽  
Multidimensional Generalization ◽  
The One

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

Thermally corrected solutions of the one-dimensional wave equation for the laser-induced ultrasound

2021 ◽  
Vol 130 (2) ◽  
pp. 025104
Author(s):  
Misael Ruiz-Veloz ◽  
Geminiano Martínez-Ponce ◽  
Rafael I. Fernández-Ayala ◽  
Rigoberto Castro-Beltrán ◽  
Luis Polo-Parada ◽  
...  
Keyword(s):  
Wave Equation ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

scholarly journals Сlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

2020 ◽  
Vol 64 (6) ◽  
pp. 657-662
Author(s):  
V. I. Korzyuk ◽  
J. V. Rudzko
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Smooth Boundary ◽  
Analytical Form ◽  
Initial Condition ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.

scholarly journals THE ONE-DIMENSIONAL WAVE SPECTRA AT LIMITED FETCH

1972 ◽  
Vol 1 (13) ◽  
pp. 13
Author(s):  
Hisashi Mitsuyasu
Keyword(s):  
Similarity Theory ◽  
Wind Waves ◽  
Laboratory Data ◽  
Peak Frequency ◽  
Wave Spectra ◽  
One Dimensional ◽  
Wide Range ◽  
Laboratory Tank ◽  
The One ◽  
Dimensional Wave

The data for the spectra of wind-generated waves measured in a laboratory tank and in a bay are analyzed using the similarity theory of Kitaigorodski, and the one-dimensional spectra of fetch-limited wind waves are determined from the data. The combined field and laboratory data cover such a wide range of dimensionless fetch F (= gF/u2 ) as F : 102 ~ 10 . The fetch relations for the growthes of spectral peak frequency u)m and of total energy E of the spectrum are derived from the proposed spectra, which are consistent with those derived directly from the measured spectra.

scholarly journals Exact statistical properties of the Burgers equation

2000 ◽  
Vol 417 ◽  
pp. 323-349 ◽  
Author(s):  
L. FRACHEBOURG ◽  
Ph. A. MARTIN
Keyword(s):  
White Noise ◽  
Large Distance ◽  
Burgers Equation ◽  
Higher Order ◽  
Statistical Properties ◽  
Inviscid Limit ◽  
Initial Condition ◽  
Spatial Correlations ◽  
One Dimensional ◽  
The One

The one-dimensional Burgers equation in the inviscid limit with white noise initial condition is revisited. The one- and two-point distributions of the Burgers field as well as the related distributions of shocks are obtained in closed analytical forms. In particular, the large distance behaviour of spatial correlations of the field is determined. Since higher-order distributions factorize in terms of the one- and two- point functions, our analysis provides an explicit and complete statistical description of this problem.

scholarly journals Bilateral Laplace multipliers on spaces of distributions

1990 ◽  
Vol 33 (3) ◽  
pp. 461-474 ◽  
Author(s):  
S. E. Schiavone
Keyword(s):  
Wave Operator ◽  
Fractional Integrals ◽  
Fréchet Spaces ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

A bilateral Laplace multiplier theory, based on Rooney's class , is developed for certain operators defined on the Fréchet spaces Dp,μ. The theory is applied to Riesz fractional integrals associated with the one-dimensional wave operator.

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