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 as@nadwork.at http://www.nadwork.at
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 Computational Acoustics by Means of
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NADwork Simulation Suite Overview 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 preand postprocessors Computational Acoustics by Means of
NADwork Acoustics Overview 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 Computational Acoustics by Means of
Basic Theory Structure-borne Sound Equations of motion for dynamic, elastic structures via FEM in the frequency domain K s... stiffness matrix D s... damping matrix M s... mass matrix... displacements (vector) u s f s... force (vector) ( s s 2 s s K + iωd ω M ) u = 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) Computational Acoustics by Means of f s
Basic Theory Air-borne Sound Calculation of air-borne sound in the frequency domain via solving the Helmholtz equation by means of BEM p + k p = γ B q = 2 2 f f f p... sound pressure B f... coefficient matrix k= /c... wave number q f... sound pressure (vector)... frequency f f... 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) f Computational Acoustics by Means of
Basic Theory Fluid-Structure Coupling Coupling structure-borne sound (FEM) with air-borne sound (BEM) K s + iωd C s fs 2 ω M s C B sf f u q s f = f f ss fi Structure has influence on surrounding air and vice versa Sound radiation (with diffusor, etc) and effects of cabinets (closed and vented) can be calculated Computational Acoustics by Means of
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 Computational Acoustics by Means of
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) Computational Acoustics by Means of
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 Computational Acoustics by Means of
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 Computational Acoustics by Means of
Practical Applications (Noise Engineering) 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) Computational Acoustics by Means of
Practical Applications (Noise Engineering) 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) Computational Acoustics by Means of
Practical Applications (Noise Engineering) 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) Computational Acoustics by Means of
Practical Applications (Noise Engineering) 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 Computational Acoustics by Means of
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 Computational Acoustics by Means of
Practical Applications (eacoustic) 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 Computational Acoustics by Means of
Practical Applications (eacoustic) 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) Computational Acoustics by Means of
Practical Applications (eacoustic) 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 Computational Acoustics by Means of
Practical Applications (eacoustic) 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 Computational Acoustics by Means of
Practical Applications (eacoustic) Tweeter for HI-FI application Objective: Optimize tweeter acoustics Two-sided fluid-structure interaction using NADwork Chassis Wizard and NADwork Acoustics Computational Acoustics by Means of
Practical Applications (eacoustic) Horn adapter for PA application Objective: Optimize horn acoustics Frequency response Directivity Pure acoustic analysis using NADwork Acoustics Computational Acoustics by Means of
Practical Applications (eacoustic) Small transducer for cell phone Objective: Optimize THD Nonlinear acoustic analysis using NADwork Acoustics Computational Acoustics by Means of
Practical Applications (eacoustic) Cabinet for professional audio application Objective: Calculate sound radiated by cabinet (excluding loudspeaker) based on measurement data NADwork Polytec Connection Computational Acoustics by Means of
Practical Applications (eacoustic) 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 Computational Acoustics by Means of
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) Computational Acoustics by Means of
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) Computational Acoustics by Means of
Thank you very much for your kind attention! Please let s discuss further requirements in audio industry! Computational Acoustics by Means of