Application of 'steady' state finite element and transient finite difference theory to sound propagation in a variable duct - A comparison with experiment

1981 ◽  
Author(s):  
K. BAUMEISTER ◽  
W. EVERSMAN ◽  
R. ASTLEY ◽  
J. WHITE
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Finite Difference ◽  
Sound Propagation ◽  
Comparison With Experiment

Systematic Characterization of Coupled Structural-Acoustic Systems With the Aid of Temporal and Spectral (Complex) Proper Orthogonal Decomposition

2008 ◽  
Author(s):  
Christos I. Papadopoulos ◽  
Ioannis T. Georgiou
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Proper Orthogonal Decomposition ◽  
Transient Response ◽  
Degrees Of Freedom ◽  
Sound Propagation ◽  
Orthogonal Decomposition ◽  
Pod Analysis ◽  
Proper Orthogonal ◽  
Spectral Complex

We extend the application of temporal and spectral Proper Orthogonal Decomposition (POD) to study the sound propagation and sound-structure interaction of systems combined of acoustic and structural subsystems. We consider a prototypical system consisted of two adjacent rooms separated by a sound insulating plate. Approximation to the steady-state and transient response is obtained with the aid of the finite element method. We define the temporal (real) and spectral (complex) variations of POD to tackle acoustical and structural degrees of freedom. We apply the method to process the numerical databases of the finite element solutions. It is shown that the steady-state and transient response may be represented by a small number of dominant POD modes. The extracted frequencies and spatial shapes are evaluated and linked to the modal properties of the system. It is shown that POD analysis may provide significant insight on the properties of coupled structural-acoustic systems.

scholarly journals Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

1996 ◽  
Vol 118 (4) ◽  
pp. 622-629 ◽  
Author(s):  
K. J. Baumeister ◽  
K. L. Kreider
Keyword(s):  
Wave Equation ◽  
Steady State ◽  
Finite Difference ◽  
Frequency Domain ◽  
Sound Propagation ◽  
Time Dependent ◽  
Frequency Domain Method ◽  
Impedance Boundary ◽  
Frequency Domain Methods ◽  
Time Marching

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Steady State Heat Conduction Modeling by the Generalized Finite Element Method

2018 ◽  
Author(s):  
Humberto Alves da Silveira Monteiro ◽  
Guilherme Garcia Botelho ◽  
Roque Luiz da Silva Pitangueira ◽  
Rodrigo Peixoto ◽  
FELICIO BARROS
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Steady State ◽  
Generalized Finite Element Method ◽  
State Heat ◽  
Steady State Heat ◽  
Generalized Finite Element ◽  
Element Method
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