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Descrição: Tutorial de Geoprocessamento tendo como base aplicativo ArcGis/ Desktop 9.3. Desenvolvido por: Osvaldo José Ribeiro Pereira Graduado em Geografia pela UNESP e mestre em Ciências do Solo pela USP.
The Boundary Element Method Acoustic BEM ü Conceptual
description of the BEM
ü Preprocessing vMesh vBoundary
Conditions
ü Solution ü Post-Processing
Dept. of Mech. Engineering University of Kentucky
2
ME 599/699 VibroAcoustic Design
Comparison of Features: Acoustic FEM/BEM Acoustic BEM
Discretization Calculation of modes Sound radiation Interior Inter ior problems probl ems
Dept. of Mech. Engineering University of Kentucky
FEM FE M
BE M
Domain method
Boundary method
volume (3 (3-D) -D)
surface (2-D)
easy
expensive
only with I-FEM
easy
easy
easy
3
ME 599/699 VibroAcoustic Design
Overview of Numerical Methods: Definitions Acoustic BEM Interior Noise Analysis
Radiation Analysis
Acoustic boundary elements (these are 2-D surface elements only)
Dept. of Mech. Engineering University of Kentucky
4
ME 599/699 VibroAcoustic Design
The Point Point Monopo Monopole le Source Source – Key to to the BEM BEM Acoustic BEM
Sound pressure a distance r from the point source p (r )
r
=
Q jkr e r −
Phase
p(r)
r Q = source strength Dept. of Mech. Engineering University of Kentucky
5
ME 599/699 VibroAcoustic Design
Mathematical Formulation of the Direct BEM* Acoustic BEM
Using Green’s Second Identity p r
θ
v, ps
Helmholtz Integral Equation e − ikr e − ikr p = ∫ p s (1 + ikr ) cos θ − iρ o ω v dS S π 4 r 4π r
*Boundary Element Acoustics, T. W. Wu, WIT Press, 2000
Dept. of Mech. Engineering University of Kentucky
6
ME 599/699 VibroAcoustic Design
Overview of Solution Options Acoustic BEM
ü Direct
BEM
ü Indirect
BEM
ü FEM
Dept. of Mech. Engineering University of Kentucky
7
ME 599/699 VibroAcoustic Design
Direct BEM (DBEM) - Two Types of Problems Acoustic BEM Interior (cavity)
Exterior (radiation) p unknown
p v
z
v specified
Boundary mesh (2-D surface mesh) Dept. of Mech. Engineering University of Kentucky
8
ME 599/699 VibroAcoustic Design
Disadvantages of the DBEM Acoustic BEM
• boundary must be closed - can’t model open systems such as partial enclosures
• matrix is non-symmetric - coupling to FEM not efficient - inefficient for large meshes
• non-uniqueness problem (radiation only) - must add interior points Dept. of Mech. Engineering University of Kentucky
9
ODP’s
ME 599/699 VibroAcoustic Design
Indirect Boundary Element Method (IBEM) Acoustic BEM
Openings p
v
Noise source
p
Dept. of Mech. Engineering University of Kentucky
z
v
10
ME 599/699 VibroAcoustic Design
Features of the IBEM Acoustic BEM
• more general than DBEM • more difficult to use and to interpret results • symmetric matrix - efficient for large meshes - efficient coupling with FEM
• non-existence problem (radiation from closed bodies) - must add absorbing elements Dept. of Mech. Engineering University of Kentucky
11
ME 599/699 VibroAcoustic Design
Starting SYSNOISE Acoustic BEM
• Type SYSNOISE
• Input a Name
• Create a New Model
• Filename Extension .sdb
Dept. of Mech. Engineering University of Kentucky
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ME 599/699 VibroAcoustic Design
SYSNOISE Solution Options Acoustic BEM Model
Option
Dept. of Mech. Engineering University of Kentucky
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ME 599/699 VibroAcoustic Design
SYSNOISE Solution Options Acoustic BEM
Dept. of Mech. Engineering University of Kentucky
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ME 599/699 VibroAcoustic Design
Input the Mesh Acoustic BEM
• File > Import
In ANSYS File > Archive > Write
Dept. of Mech. Engineering University of Kentucky
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File Format
ME 599/699 VibroAcoustic Design
Viewing the Mesh Acoustic BEM
• From the toolbar
Dept. of Mech. Engineering University of Kentucky
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ME 599/699 VibroAcoustic Design
Viewing the Mesh Acoustic BEM
• From the menus
Dept. of Mech. Engineering University of Kentucky
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ME 599/699 VibroAcoustic Design
Check the Normals Acoustic BEM
• Direct ü Point towards the acoustic domain
• Indirect ü Define boundary condition side
• Viewing normals
Dept. of Mech. Engineering University of Kentucky
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ME 599/699 VibroAcoustic Design
Correcting the Normals Acoustic BEM
• Geometry > Reverse Elements
Select All
Dept. of Mech. Engineering University of Kentucky
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ME 599/699 VibroAcoustic Design
Automatic Normal Correction Acoustic BEM
• Geometry > Check Mesh
Dept. of Mech. Engineering University of Kentucky
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ME 599/699 VibroAcoustic Design
Viewing the Reversed Normals Acoustic BEM
• Toggle display to see inside
Dept. of Mech. Engineering University of Kentucky
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ME 599/699 VibroAcoustic Design
Applying Fluid Properties Acoustic BEM
• Model > Fluid Properties
Dept. of Mech. Engineering University of Kentucky
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ME 599/699 VibroAcoustic Design
Is the BEM Mesh Fine Enough? Acoustic BEM vLinear
Elements – at least 6 elements/wavelength
vParabolic vAcoustic
Elements – at least 2 elements/wavelength
wavelength is a function of frequency
λ
c =
f BEM solution time: (Nodes)3 Dept. of Mech. Engineering University of Kentucky
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ME 599/699 VibroAcoustic Design
Checking the Maximum Frequency Acoustic BEM
• Inquire > fmaximum …
Dept. of Mech. Engineering University of Kentucky
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ME 599/699 VibroAcoustic Design
Selecting Sets for Boundary Condtions Acoustic BEM
