work.at Alfred J. Svobodnik Transducers

Computational Acoustics by Means of Finite and Boundary Elements for Woofers, Tweeters, Horns and Small

Transducers

Alfred J. Svobodnik

NAD - Numerical Analysis and Design GmbH & Co KG [email protected]

http://www.NADwork.at

“Computational Acoustics by Means of Finite and Boundary Elements for Woofers,

Tweeters, Horns and Small Transducers”

Numerical Analysis and Design (NAD)

• NAD – An essential part of concurrent engineering• Founded 1990• Since 1994 acoustics• Departments

⇒NADwork⇒Software Technology⇒Consulting Services⇒Business Consulting⇒R&D Cooperations



Numerical Analysis and Design (Customers)



NADwork® Simulation SuiteOverview

• Advanced analysis software for computational mechanics⇒NADwork® Structural is designed for simulating general

structural phenomena⇒NADwork® Acoustics is designed for simulating arbitrary

structures interacting with an acoustic fluid ⇒NADwork® Chassis Wizard is designed to calculate fully

automated the 3D sound field radiated by a chassis (loudspeaker)based on a section cut defined via a 2D CAD file

⇒NADwork® Polytec® Connection is designed for simulations based on measurement data from Polytec® Scanning Vibrometers

⇒NADwork® High Performance Computing is designed for large scale simulations on parallel systems via the use of external pre-and postprocessors



NADwork® AcousticsOverview

• Computational acoustics for⇒Structure-borne sound (structural dynamics)⇒Air-borne sound (fluid)

• radiation• reflection• diffraction• transmission

of sound waves• Uncoupled acoustic analyses (including single-sided coupling)• Fluid-structure coupling (two-sided coupling)• Elastoacoustic coupling



Basic TheoryStructure-borne Sound

• Equations of motion for dynamic, elastic structures via FEM in the frequency domain

Ks . . . stiffness matrixDs . . . damping matrixMs . . . mass matrixus . . . displacements (vector)fs . . . force (vector)

• Special shell finite elements (“assumed strain formulation”) for thin-walled structures as used e.g. in loudspeakers⇒ Specific tuning for dynamic loudspeakers with combination of soft (e.g.

rubber) and stiff (e.g. titanium) materials⇒ Special damping model for structures with combination of high damping

(e.g. rubber) and low damping (e.g. titanium) materials• Forces can be defined in the time domain (FFT)

sssss fuMDiK =−+ )( 2ωω



Basic TheoryAir-borne Sound

• Calculation of air-borne sound in the frequency domain via solving the Helmholtz equation by means of BEM

p . . . sound pressure Bf . . . coefficient matrixk=�/c . . . wave number qf . . . sound pressure (vector) � . . . frequency ff . . . incident waves (vector)c . . . Speed of sound� . . . Excitation

• Analytical solutions for Helmholtz equation in general exist only for simple geometries and simple boundary conditions⇒Numerical procedures like FEM (Finite Element Method) or

BEM (Boundary Element Method)

γ=+∇ pkp 22 fff fqB =



Basic Theory Fluid-Structure Coupling

• Coupling structure-borne sound (FEM) with air-borne sound (BEM)

• Structure has influence on surrounding air and vice versa• Sound radiation (with diffusor, etc) and effects of cabinets (closed and

vented) can be calculated

=

−+fi

ss

f

s

ffs

sfsss

ff

qu

BCCMDiK 2ωω



Boundary Element Method (BEM)

• Well tried method for computational acoustics• Automatically fulfills Sommerfeld-condition (Radiation to ∞)• Very robust, for interior and exterior problems• Automatic detection of intersections and bifurcations• Boundary conditions

⇒ Impedance/admittance⇒Velocity⇒Sound pressure⇒Transfer-impedance/-admittance



Finite Element Method for Viscothermal Effects

• Viscoelements based on FEM for viscothermal effects (sound energy converts to thermal energy due to viscous behavior of air)

• Viscotube⇒Line element for viscothermal losses in small tubes⇒Can be coupled with BEM acoustic elements

• Viscolayer⇒Surface element for viscothermal losses in narrow gaps⇒Can be coupled with FEM structural elements (panel speaker)



Integration into Development Process

• Standalone application• Simple CAD integration (NADwork® Chassis Wizard)• Tight integration into CAD/CAE

⇒ Existing FEM structural mechanics models can be fast and reliable adapted for acoustic analyses

⇒ Specific tuning for various CAD/CAE-systems• Pro/ENGINEER• SolidWorks• Autodesk Inventor• UGS NX (I-deas)• CATIA (V4, V5)• HyperMesh• MSC.Patran• …



Practical Applications(Noise Engineering)

• Hard disk drive• Objective: Optimization of radiated noise due to vibrating housing• Coupled analysis (FEM/BEM)• FEM beams, shells and solids for structure• BEM mid-plane elements for fluid• Detailed model based on CAD-solids








• Floor construction of railway chassis• Objective: Optimization of sound transmission• Two-sided fluid-structure interaction• FEM beams, shells and solids for structure• BEM mid-plane and surface elements for fluid• Admittance boundary condition for carpet (frequency dependent)• Baffle (3-zones)






• Test assembly of railway chassis• Objective: Evaluation of FEM and BEM for computational acoustics

via comparison with measurements• Two-sided fluid-structure interaction• FEM beams, shells and solids for structure• BEM mid-plane and surface elements for fluid• Admittance boundary condition for interior surface of chassis (special

sound absorbing materials)






• Oil pan of truck diesel engine• Objective: Optimization of sound radiation• Threefold fluid-structure coupling• FEM beams, shells and solids for structure• BEM surface elements for fluid (air, exterior, single-sided coupling with

oil pan)• FEM for fluid (oil, interior, two-sided coupling with oil pan)• Problem: Characteristic excitation of oil pan

⇒Modeling of engine block⇒Definition of forces due to combustion in time domain (FFT ->

frequency domain)






• Complete truck assembly• Objective: Optimization of air-borne sound radiation due to pass-by

noise (exterior to surface of engine)• Uncoupled acoustic analysis (only air-borne sound)• BEM mid-plane and surface elements for fluid• Frequency dependent admittance boundary conditions for sound

absorbing panels near engine• Hard reflecting half-space condition• Unit velocity for engine block













Practical Applications(eacoustic)

• Transducer assembly for telecom application (cell phone)• Objective: Optimization of sound quality

⇒As small as possible (mobile phone)⇒As loud as possible (for multimedia applications)⇒Excellent sound quality (high fidelity quality)

• Different types of analyses⇒Structural mechanics models⇒Fluid-structure models




• Structural mechanics models (linear and nonlinear)⇒All analyses in vacuum (fluid is not being considered)⇒Stiffness analysis⇒Eigenfrequency analysis of free vibrations

• Used for calibrating material properties• Results (eigenfrequencies and mode shapes) can be used for a

first design step⇒Forced vibrations

• Results (displaced volume) can be used for a first design step⇒Stability analysis (linear and nonlinear)

• Results can be used for calculation of mechanical harmonic distortions




• Fluid-structure models⇒Reuse of previous models (just add “back volume”)⇒Two-sided fluid-structure interaction⇒FEM shells and solids for structure⇒BEM mid-plane and surface elements⇒Transfer-admittance for woven material (acoustic friction)








• Woofer for HI-FI application• Objective: Optimize driver acoustics and study influence of cabinet• Driver acoustics

⇒Two-sided fluid-structure interaction without cabinet using NADwork® Chassis Wizard “Base”

⇒Nonlinear force-displacement relationship via NADwork® Chassis Wizard “Nonlinear” (and calculate mechanical THD)

• Influence of cabinet⇒Two-sided fluid-structure interaction using NADwork® Chassis

Wizard “Advanced”














• Woofer for HI-FI application• Objective: Optimize driver acoustics in baffle• Chassis acoustics

⇒Two-sided fluid-structure interaction without cabinet using NADwork® Chassis Wizard “Base”

• Influence of cabinet⇒Two-sided fluid-structure interaction using NADwork® Chassis

Wizard “Advanced”






















• Tweeter for HI-FI application• Objective: Optimize tweeter acoustics

⇒Two-sided fluid-structure interaction using NADwork® Chassis Wizard and NADwork® Acoustics






• Horn adapter for PA application• Objective: Optimize horn acoustics

⇒Frequency response⇒Directivity

• Pure acoustic analysis using NADwork® Acoustics










• Small transducer for cell phone• Objective: Optimize THD• Nonlinear acoustic analysis using NADwork® Acoustics




















• Cabinet for professional audio application• Objective: Calculate sound radiated by cabinet (excluding

loudspeaker) based on measurement data⇒NADwork® Polytec® Connection








• Benchmark application for viscothermal effects in narrow tubes• Objective: Verify implementation of viscothermal effects• Two-sided fluid-structure interaction• FEM shells and trusses (vibrating single mass system)• BEM mid-plane elements for two volumes• Viscotubes (connector for the two BEM volumes)

⇒Circular cross-section⇒Rectangular cross-section





Limitations• Modeling of glue

⇒ Currently only in NADwork® Acoustics possible⇒ Very soon: Automatic modeling of glue in NADwork® Chassis Wizard

• Material properties⇒ Modulus of elasticity

• Solution: Polytec Laser Scanning Vibrometer in combination with NADwork® Polytec® Connection and NADwork® Acoustics (provided by Fink Audio-Consulting)

⇒ Damping• Solution: Polytec Laser Scanning Vibrometer in combination with NADwork® Polytec® Connection and NADwork® Acoustics (Fink Audio-Consulting)

⇒ Influence of manufacturing process• Solution: Currently no solution for predictive engineering (possible

solution: calibration of analysis model based on measurements)



Limitations

• Transient vibrations⇒ Solution: Currently neglecting viscoelastic effects (creep/relaxation)⇒ In the near future: Viscoelasticity will be included

• Turbulent flow in vented cabinets and horn adapters (nonlinear acoustics)⇒ Solution: Currently no solution (I.e. neglecting turbulence)

• No coupling to motor system⇒ Coupling possibilities to external magnetic programs⇒ Very soon: Lumped motor model in NADwork® Acoustics and NADwork®

Chassis Wizard • Large scale models (complete cabinet with woofers and tweeters)

⇒ Simulation only possible in 64-bit mode on UNIX/LINUX⇒ Will be possible on PC with availability of Windows 64-bit (to be

expected mid 2005)



Thank you very much for your kind attention!

Please let‘s discuss further requirements in audio industry!

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