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Dept. of Mech. Engineering University of Kentucky 1 Acoustic BEM ME 599/699 Vibro- Acoustic Design THE BOUNDARY ELEMENT METHOD
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Dept. of Mech. EngineeringUniversity of Kentucky
1
Acoustic BEM
ME 599/699 Vibro-Acoustic Design
THE BOUNDARY ELEMENT METHOD
Dept. of Mech. EngineeringUniversity of Kentucky
2
Acoustic BEM
ME 599/699 Vibro-Acoustic Design
The Boundary Element Method
üConceptual description of the BEM
üPreprocessingvMeshvBoundary Conditions
üSolution
üPost-Processing
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
FEM BEM
Domain method
Boundary method
Discretization volume (3-D) surface (2-D)
Calculation of modes easy expensive
Sound radiation only with I-FEM easy
Interior problems easy easy
Comparison of Features: Acoustic FEM/BEM
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Overview of Numerical Methods: Definitions
Interior Noise Analysis Radiation Analysis
Acoustic boundary elements(these are 2-D surface elements only)
Interior Noise Analysis Radiation Analysis
Acoustic boundary elements(these are 2-D surface elements only)
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
The Point Monopole Source – Key to the BEM
r
Sound pressure a distance r from the point source
r
p(r)
Phase
Q = source strength
jkrerQ
rp −=)(
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Mathematical Formulation of the Direct BEM*
*Boundary Element Acoustics, T. W. Wu, WIT Press, 2000
v, psr
pθ
Using Green’s Second Identity
Helmholtz Integral Equation
p pe
rikr i v
er
dSs
ikr
o
ikr
S= + −
− −
∫ 41
4πθ ρ ω
π( )cos
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
üDirect BEM
ü Indirect BEM
üFEM
Overview of Solution Options
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Direct BEM (DBEM) - Two Types of Problems
Exterior (radiation)
v specified
Boundary mesh(2-D surface mesh)
p unknown
Interior (cavity)
v z
p
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Disadvantages of the DBEM
• 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
ODP’s
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Indirect Boundary Element Method (IBEM)
vz
p
Noise source
vp
Openings
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Features of the IBEM
• more general than DBEM
• more difficult to use andto 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. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Starting SYSNOISE
• Type SYSNOISE
• Create a New Model
• Input a Name
• Filename Extension .sdb
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
SYSNOISE Solution Options
Model
Option
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
SYSNOISE Solution Options
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Input the Mesh
• File > Import
In ANSYSFile > Archive > Write
File Format
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Viewing the Mesh
• From the toolbar
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Viewing the Mesh
• From the menus
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Check the Normals
• Directü Point towards the acoustic domain
• Indirectü Define boundary condition side
• Viewing normals
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Correcting the Normals
• Geometry > Reverse Elements
Select All
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Automatic Normal Correction
• Geometry > Check Mesh
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Viewing the Reversed Normals
• Toggle display to see inside
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Applying Fluid Properties
• Model > Fluid Properties
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Is the BEM Mesh Fine Enough?
vLinear Elements – at least 6 elements/wavelength
vParabolic Elements – at least 2 elements/wavelength
vAcoustic wavelength is a function of frequency
BEM solution time: (Nodes)3
fc
=λ
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Checking the Maximum Frequency
• Inquire > fmaximum …
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Selecting Sets for Boundary Condtions
• From the toolbar
Select Elements
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Viewing Sets
• View > Sets
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Viewing Sets
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Boundary Conditions for BEM
• Particle Velocity- Default is vn = 0
• Pressure
• Impedance
nvp
z =
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Applying Velocity Boundary Conditions
• Model > Vibrating Panels > Manual …
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Element Set Selection
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Importing Velocities from ANSYS
BEM – Coarse MeshFEM – Fine Mesh
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Importing Velocities from ANSYS
• Model > Vibrating Panels … > FEA …
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Applying Impedance Boundary Conditions
• Model > Absorbent Panels …Enter as Impedance
Or Admittance
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Applying Pressure Boundary Conditions (Rare)
• Model > Pressure B.C. > Manual
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Point Sources
• Model > Sources
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Additional Boundary Conditions for IBEM
• Jump Boundary Conditions
• Discontinuous Pressure, Velocity, and Impedance
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
IBEM Jump Boundary Condition
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Select Free Edges
• Geometry > Sets > Envelope Generation …
Use Whole Model
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Set the Jump Condition
• Model > Free Edges …
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Discontinuous Boundary Condition
• Model > Vibrating Panel >
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Rigid Halfspace
• Geometry > Symmetry … >
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Solution Parameters
• Analysis > Parameters … > Quadrature …
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Quadrature Options
Linear Elements (3 3 2)
Parabolic Elements (4 4 2)
• Quadrature Guidelines
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Solving the BEM
• Analysis > Solve …> Frequency Selector …
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Select the Frequency Range
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Postprocessing Boundary Pressures (DBEM Only)
• Postprocess > Color Map …
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Creating Field Points
• Geometry > Field Point > Sphere
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Processing Field Points
• Analysis > Process Field Points … >
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Displaying Field Point Results
• Postprocess … > Color Map …
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Surface Pressure Results
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Examining the Sound Power
• Postprocess … > Power Function … (Converts to RMS)
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Exporting the Sound Power in ASCII Format
• File > Export …
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Point Sources
Be sure that you switch to power
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Importing the Impedance Files
• Model > Table > From File …
File with absorption properties
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Convert the Impedance Table to Admittance
• Tools > Combine …
Read in Impedance Table
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Convert the Impedance Table to Admittance
Take Reciprocal X-1 then Write Table
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Use Admittance Table for Boundary Condition
• Model > Absorbent Panels …Enter as Admittance
Dept. of Mech. EngineeringUniversity of Kentucky
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Acoustic BEM
ME 599/699 Vibro-Acoustic Design
Create Automatic Junctions
Model > Automatic Junctions
T-Junctions
