Simulation of the 3D Sound Pressure Level Inside Closed Absorbing Acoustic Rooms Bounded by Non-Parallel Floor and Ceiling Surfaces, and Parallel Sidewalls

Tadeu, A.; Simões, I.; António, Julieta; Sousa, Laura

doi:10.3813/aaa.918573

Cited by 3 publications

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“…They are frequently combined to simulate heat conduction in the time domain or in a transform space defined by the Laplace transform, in half-spaces, infinite plates, rectangular 2D spaces, wedges, and rectangular 3D spaces [1][2][3]. Solutions have also been proposed to deal with multilayer systems, and they include the matrix method [1], the thermal quadrupole method [3], the thin layer method [4], and methods based on the definition of potentials [5][6][7]. Chen et al have described the use of image method to solve 2D and 3D problems in unbounded and half-space domains containing circular or spherical shaped boundaries [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions

Simões

Tadeu

Simões

2016

Journal of Applied Mathematics

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This paper presents a set of fully analytical solutions, together with explicit expressions, in the time and frequency domain for the heat conduction response of homogeneous unbounded and of bounded rectangular spaces (three-, two-, and one-dimensional spaces) subjected to point, line, and plane heat diffusion sources. Particular attention is given to the case of spatially sinusoidal, harmonic line sources. In the literature this problem is often referred to as the two-and-a-half-dimensionalfundamental solutionor 2.5D Green’s functions. These equations are very useful for formulating three-dimensional thermodynamic problems by means of integral transforms methods and/or boundary elements. The image source technique is used to build up different geometries such as half-spaces, corners, rectangular pipes, and parallelepiped boxes. The final expressions are verified here by applying the equations to problems for which the solution is known analytically in the time domain.

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Section: Introductionmentioning

confidence: 99%

Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions

Simões

Tadeu

Simões

2016

Journal of Applied Mathematics

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“…As a numerical experiment, we compute the sound field in an ultrasonic homogenizer where our parameter to be studied is the boundary condition at the glass walls. Other examples of the use of the BEM in interior problems can be found in Suzuki et al (1989), Utsuno et al (1990) or Tadeu et al (2012).…”

Section: Introductionmentioning

confidence: 99%

Acoustical Boundary Elements: Theory and Virtual Experiments

Piscoya

Ochmann

2015

Archives of Acoustics

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This paper presents an overview of basic concepts, features and difficulties of the boundary element method (BEM) and examples of its application to exterior and interior problems. The basic concepts of the BEM are explained firstly, and different methods for treating the non-uniqueness problem are described. The application of the BEM to half-space problems is feasible by considering a Green's Function that satisfies the boundary condition on the infinite plane. As a special interior problem, the sound field in an ultrasonic homogenizer is computed. A combination of the BEM and the finite element method (FEM) for treating the problem of acoustic-structure interaction is also described. Finally, variants of the BEM are presented, which can be applied to problems arising in flow acoustics.

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Effects of the convergence tolerance of iterative methods used in the boundary element method on the calculation results of sound fields in rooms

2020

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Simulation of the 3D Sound Pressure Level Inside Closed Absorbing Acoustic Rooms Bounded by Non-Parallel Floor and Ceiling Surfaces, and Parallel Sidewalls

Cited by 3 publications

References 0 publications

Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions

Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions

Acoustical Boundary Elements: Theory and Virtual Experiments

Effects of the convergence tolerance of iterative methods used in the boundary element method on the calculation results of sound fields in rooms

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