scholarly journals An Influence of the Wall Acoustic Impedance on the Room Acoustics. The Exact Solution

2017 ◽  
Vol 42 (4) ◽  
pp. 677-687 ◽  
Author(s):  
Adam Branski ◽  
Anna Kocan-Krawczyk ◽  
Edyta Predka
Keyword(s):  
Boundary Conditions ◽  
Rectangular Cross Section ◽  
Fourier Method ◽  
Room Acoustics ◽  
Acoustic Boundary Conditions ◽  
Impedance Boundary ◽  
Sturm Liouville ◽  
Third Dimension ◽  
Robin Boundary ◽  
Theoretical Considerations

Abstract The Fourier method is applied to the description of the room acoustics field with the combination of uniform impedance boundary conditions imposed on some walls. These acoustic boundary conditions are expressed by absorption coefficient values In this problem, the Fourier method is derived as the combination of three one-dimensional Sturm-Liouville (S-L) problems with Robin-Robin boundary conditions at the first and second dimension and Robin-Neumann ones at the third dimension. The Fourier method requires an evaluation of eigenvalues and eigenfunctions of the Helmholtz equation, via the solution of the eigenvalue equation, in all directions. The graphic-analytical method is adopted to solve it It is assumed that the acoustic force constitutes a monopole source and finally the forced acoustic field is calculated. As a novelty, it is demonstrated that the Fourier method provides a useful and efficient approach for a room acoustics with different values of wall impedances. Theoretical considerations are illustrated for rectangular cross-section of the room with particular ratio. Results obtained in the paper will be a point of reference to the numerical calculations.

scholarly journals An inverse spectral problem for Sturm-Liouville-type integro-differential operators with robin boundary conditions

2019 ◽  
Vol 50 (3) ◽  
pp. 207-221 ◽  
Author(s):  
Sergey Buterin
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Boundary Conditions ◽  
Differential Operators ◽  
A Priori ◽  
Sufficient Conditions ◽  
Robin Boundary Conditions ◽  
Sturm Liouville ◽  
Necessary And Sufficient ◽  
Robin Boundary

The perturbation of the Sturm--Liouville differential operator on a finite interval with Robin boundary conditions by a convolution operator is considered. The inverse problem of recovering the convolution term along with one boundary condition from the spectrum is studied, provided that the Sturm--Liouville potential as well as the other boundary condition are known a priori. The uniqueness of solution for this inverse problem is established along with necessary and sufficient conditions for its solvability. The proof is constructive and gives an algorithm for solving the inverse problem.

Determination of the impulsive Sturm–Liouville operator from a set of eigenvalues

2020 ◽  
Vol 28 (3) ◽  
pp. 341-348 ◽  
Author(s):  
Ran Zhang ◽  
Xiao-Chuan Xu ◽  
Chuan-Fu Yang ◽  
Natalia Pavlovna Bondarenko
Keyword(s):  
Boundary Conditions ◽  
Interior Point ◽  
Liouville Operator ◽  
Inverse Spectral Problem ◽  
Liouville Problem ◽  
Robin Boundary Conditions ◽  
Jump Conditions ◽  
Sturm Liouville ◽  
Robin Boundary

AbstractIn this work, we consider the inverse spectral problem for the impulsive Sturm–Liouville problem on {(0,\pi)} with the Robin boundary conditions and the jump conditions at the point {\frac{\pi}{2}}. We prove that the potential {M(x)} on the whole interval and the parameters in the boundary conditions and jump conditions can be determined from a set of eigenvalues for two cases: (i) the potential {M(x)} is given on {(0,\frac{(1+\alpha)\pi}{4})}; (ii) the potential {M(x)} is given on {(\frac{(1+\alpha)\pi}{4},\pi)}, where {0<\alpha<1}, respectively. It is also shown that the potential and all the parameters can be uniquely recovered by one spectrum and some information on the eigenfunctions at some interior point.

scholarly journals Ambarzumyan-type theorems on a time scale

2018 ◽  
Vol 26 (5) ◽  
pp. 633-637 ◽  
Author(s):  
Ahmet Sinan Ozkan
Keyword(s):  
Boundary Conditions ◽  
Dynamic Equation ◽  
Time Scale ◽  
Robin Boundary Conditions ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
Sturm Liouville ◽  
Robin Boundary

Abstract In this paper, we give Ambarzumyan-type theorems for a Sturm–Liouville dynamic equation with Robin boundary conditions on a time scale. Under certain conditions, we prove that the potential can be specified from only the first eigenvalue.

Filter-Based Time-Domain Impedance Boundary Conditions for CFD Applications

2008 ◽  
Author(s):  
Andreas Huber ◽  
Philipp Romann ◽  
Wolfgang Polifke
Keyword(s):  
Boundary Conditions ◽  
Time Domain ◽  
Problem Formulation ◽  
Mean Flow ◽  
Acoustic Boundary Conditions ◽  
Impedance Boundary ◽  
Filter Model ◽  
Impedance Boundary Conditions ◽  
Computational Fluid Dynamics Cfd ◽  
New Formulation

For flow simulations, proper boundary conditions are essential for realizing a well-posed, physically meaningful and numerically stable problem formulation. This is particularly difficult for compressible flow, where in general boundary conditions have to be imposed both for mean flow and acoustic quantities. For the acoustic variables, boundary conditions can be formulated in terms of the acoustic impedance or alternatively the reflection coefficient, which are general a complex-valued, frequency dependent quantity. The present work presents a novel, efficient and flexible approach to impose time-domain impedance boundary conditions (TDIBC) for computational fluid dynamics (CFD): The acoustic boundary conditions are represented as a discrete filter model with appropriately optimized filter coefficients. Using the z-transformation the filter model is transferred to a time-domain formulation and applied to the CFD environment in form of advanced filter realizations. Validation studies using various acoustic boundary conditions have been carried out with the new formulation. The results demonstrate that the method works in an accurate and robust manner.

Homogeneous robin boundary conditions and discrete spectrum of fractional eigenvalue problem

2019 ◽  
Vol 22 (1) ◽  
pp. 78-94 ◽  
Author(s):  
Malgorzata Klimek
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Eigenvalue Problems ◽  
Liouville Problem ◽  
Continuous Functions ◽  
Real Spectrum ◽  
Robin Boundary Conditions ◽  
Schmidt Operator ◽  
Sturm Liouville ◽  
Robin Boundary

Abstract We discuss a fractional eigenvalue problem with the fractional Sturm-Liouville operator mixing the left and right derivatives of order in the range (1/2, 1], subject to a variant of Robin boundary conditions. The considered differential fractional Sturm-Liouville problem (FSLP) is equivalent to an integral eigenvalue problem on the respective subspace of continuous functions. By applying the properties of the explicitly calculated integral Hilbert-Schmidt operator, we prove the existence of a purely atomic real spectrum for both eigenvalue problems. The orthogonal eigenfunctions’ systems coincide and constitute a basis in the corresponding weighted Hilbert space. An analogous result is obtained for the reflected fractional Sturm-Liouville problem.

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