etienne balmès - sdtools · stiffness dynamic stiffness equal at resonance ⇒ response is the...
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Damping : devices, modeling, design.
Etienne BalmèsSDToolsEcole Centrale Paris
IMAC 23, Orlando
Outline• Dissipation devices and
mechanismsViscoelastic devices, Friction, Active
systems, particles, …• Where are the problems ?
– Physical models– Inaccurate methods and typical
software limitations• How to incorporate damping in the
design process
•Simple resonance splitting
•Countless applications : helicopters, buildings, lamp posts, cars, …
Tuned mass dampersDevicesMechanismsProblems
CharacteristicsModelsMeshes
Design •Extension of tuned mass damper
•No moving parts
Fluid Sloshing
www.multitech-fr.com
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Dampers with fluid cavities•Dampers or shock absorbers
•Automotive, aerospace, …
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Friction dampers•Traditional vehicle suspension
•Custom high-tech applications (Ariane SARO from Jarret)
•Aircraft engine
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
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Viscoelastic point to point connections
+ Rugged, efficient, fairly simple design
- Operating temperature
www.artec-spadd.com
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Active control•Coupling with active system allows enhanced dynamic behavior
•But active “damping” is only part of the picture
www.csaengineering.comwww.onera.fr
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Viscoelastic layer treatments•Traditional free and constrained layer viscoelastic treatments
•Constrained layer more efficient for relatively soft damping materials
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Viscoelastic rib designs•Mechanical amplification can be used to enhance constrained layer treatment effectiveness
www.artec-spadd.com
DevicesMechanismsProblems
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Design
Damping mechanisms
Damping : mechanism by which the energy in the considered system is diminished
• Non elastic behavior– Material : viscoelastic, plastic, …– Joint friction– Inter-frequency coupling through non-
linearities• Coupling with other systems
– Fluid/structure, particle, soil, … interactions– Active control systems– Rotating parts
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Viscoelastic materials
ε
σΕsη
−Εsη
−1 1ElasticViscoelastic
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
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Non linear devices/connections•Non linear point to point connection : force-state mapF = f(q,t)
•Friction model
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Fluid / structure coupling•Classical fluid/structure coupling
Damped if fluid is moving or dissipative
•Damping in coupling : surface impedance, porous media (Biot model), …
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Where are the problems ?•Physical characteristics
• Viscoelastic constitutive laws• Friction: how to test friction coefficient and its dependence to environmental factors
• Tests of acoustic wall impedance• …
•Dominant software implements too simple methods
•Numerical design methods still needed
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Viscoelastic constitutive relations
• Stress is a function of strain history • Complex modulus in Laplace domain
DevicesMechanismsProblems
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Reduced frequency nomogramsDevicesMechanismsProblems
CharacteristicsModelsMeshes
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Viscoelastic constitutive laws
Viscous Hysteretic Standard viscoelastic
Alternatives : • More relaxation constants• Fractional derivatives• Direct use of experimental master curve
K
DevicesMechanismsProblems
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Material damping models
Stress/strain curveSimple models
K+iB
DevicesMechanismsProblems
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Constitutive model order1 pole model (3 parameter) loss factor is wrong3 pole model : better match in band but not very good outside
•Good models require high order
•Fractional derivatives : high order with few parameters
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Process influenceBent sandwich plate
.75mm/50µm/.75mm
Significant effect of viscoelasticstiffening in the bend
Accounting for forming process can be crucial
E(ε0,ω)
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Initial stress, friction coefficient, …
Friction depends on
•Contact stress
•Friction coefficient
Z.Abbadi ISMA 04Session 18 (structural joints)
DevicesMechanismsProblems
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Design
Where are the problems ?•Physical characteristics
•Dominant software implements too simple methods
• Modal damping : widespread but insufficient when you are really interested in damping
• New solvers needed for frequency dependent and independent models
• Utilities are needed to handle the modeling detail
•Numerical design methods still needed
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
• Nominal model (elastic + viscous damping)
• Conservative eigenvalue problem
• M>0 & K≥0 ⇒ φ real
Normal modes of elastic structureDevicesMechanismsProblems
CharacteristicsModelsMeshes
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Normal modes of elastic structure
• Orthogonality• Scaling conditions
• Unit mass• Unit amplitude
• Principal coordinates
DevicesMechanismsProblems
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Modal damping assumption• Assume Γ diagonal
• Leads to second order spectral decomposition
Mode shape Participation factor Residue
DevicesMechanismsProblems
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Modal damping assumptionThis is the only widespread damping modelWhy ?• Compellingly practical for system damping• Easy combination of test and analysis• Sufficient mathematical conditions
• Rayleigh• Caughey
Modal also called proportional damping
DevicesMechanismsProblems
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Small damping ⇒small error on system behavior
System vs. local
• System models (dynamic behaviour)
• FEM models (geometry/material knowlege)
• Each objective requires different assumptions
DevicesMechanismsProblems
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System damping. 1 DOF example.
a) Bodeb) Nyquistc) 1DOF modeld) Dynamic stiffness
dynamic stiffness equal at resonance ⇒Response is the same
DevicesMechanismsProblems
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Different local models, same system response
Experimental modes are often “real”
“Complex modes” Residues have a phase spreadPoor modes Have complex residues
“Real modes” Residues for I/O pairs line up
Garteur SM-AG19 test
DevicesMechanismsProblems
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When are complex modes nearly real ?
• Uncoupling criterion (Hasselman) ei<<1 ⇔
corresponds to non overlap of peaks• Proof based on damping matrix positiveness
• When damping is enhanced by design, modes are often complex
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
MSE / Non proportional dampingMSE (modal strain energy) is a common extension
using elastic modes and general damping
NASTRAN• SOL110 modal complex modes• SOL111 modal frequency response• SOL112 modal transient
DevicesMechanismsProblems
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DevicesMechanismsProblems
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Approximation validity• Patch, driving point
MSE, reasonable trends, difficulties when too much deviation from origin
MSE 1st order
MSE Approximation validity
• Complex modes, damped joint
Mode Erreur en % Erreur en %
élastique SOL107 / SDT SOL107 / SOL1101 -2,07 -7,32
2 -1,53 -44,67
3 0,14 -30,40
4 -3,98 -7,65
5 -1,06 -13,32
6 -0,09 -0,93
7 -0,64 -1,13
8 -1,89 -8,23
9 -0,26 -0,66
10 -0,26 -0,87
DevicesMechanismsProblems
CharacteristicsModelsMeshes
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Non proportional damping model
• Modal & MSE loose localization of damping• Good for system, not local analysis
•Forced response around a resonance
DevicesMechanismsProblems
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Intermediate conclusion
• Current practice (Modal damping, MSE, or test derived modal damping ratio)only sufficient for system level damping models
• More general models needed for damping design : predict where the energy is dissipated
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Systems and material level tests
• Based on system level test, you get test derived damping ratio for system model they– are difficult/impossible to extrapolate to other system
configurations– require matching of test/FEM modes– can rarely be translated in local damping information
• Based on materials/components tests, you get– damped FEM models, which are still difficult to solve– are only valid if almost all damping comes from well
characterized parts
• In most current applications damping models are system level design parameters
DevicesMechanismsProblems
CharacteristicsModelsMeshes
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Where are the problems ?•Physical characteristics
•Dominant software implements simple methods
• Modal damping : widespread but insufficient when you are really interested in damping
• New solvers needed for frequency dependent and independent models
• Utilities are needed to handle the modeling detail
•Numerical design methods still needed
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Frequency dependent modelsProblem : dynamic stiffness linear
combination of fixed matrices
Target predictions
• Frequency response• Poles• Complex modes
DevicesMechanismsProblems
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A major computational challenge
• Viscoelastic windshield joint• 118 999 nodes, 122 721 elements• First order : improved SOL110 implemented as a
DMAP
~1000sFirst orderError small
Ψ,λ(500*T)reduced
~ 12 daysSOL107Ψ,λ(500*T)
490s First orderError <4%
Ψ,λReduced
300sSOL103Φ,ω
2200sSOL107Ψ,λ
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
A major computational challengeMulti-material. Frequency & temperature dependent.Design and robustness are needed
• AMLS (U. Texas, …) : piece-wise solutions (domain decomposition) • Krylov solvers ( www.fft.be ) : narrow frequency full model
subspace approximation• Residue Iterations ( www.sdtools.com ) similar to Krylov with
error control• Pade Approximants ( www.cadoe.com ) rational fraction
approximant
DevicesMechanismsProblems
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Parametric studies = similar challenge
•Squeal can be studies as a parametric problem with non-symmetric dissipative coupling
Theory : F. Moirot PhD 98Model : BOSCH
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Spectral decompositions
For frequency dependent moduli E(s)• Solve non-linear eigenvalue • Identify from computed transfers
DevicesMechanismsProblems
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Frequency independent models
• Material formulation with internal fields (rational and fractional derivates)
Trick increase model orderto gain frequency independence
DevicesMechanismsProblems
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☺ Proved methodologies ADF (Lesieutre), GHM (Gola, …) , Prony series (Abaqus)
☺ Integrates into standard solvers
- High order for good material– solvers need to account for block structure
time domain ☺ frequency domain
determination of parameters is still problematic
Frequency independent modelsDevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Where are the problems ?•Physical characteristics
•Dominant software implements simple methods
• Modal damping : widespread but insufficient when you are really interested in damping
• New solvers needed for frequency dependent and independent models
• Utilities are needed to handle the modeling detail
•Numerical design methods still needed
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Meshing detail•Classical result : layer cutsinfluence damping and there are optimal solutions
•They need to be modeled in detail
DevicesMechanismsProblems
CharacteristicsModelsMeshes
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Meshing detailsExample: shell/rigid/ volume/rigid/shell
+ General- normals and thickness ?
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Non conform meshes•Variable refinement•Non coincident nodes•Offset from mid-plane
DevicesMechanismsProblems
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Modeling tools needed
•1D : Detailed joint model generation
•2D : Layered model generation including : cuts & layer connections
•3D : Volume filling tools (foam, rubber)
•Remeshing for during layer thickness optimization
•Curved surfaces, non conform meshes
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Where are the problems ?•Physical characteristics
•Dominant software implements simple methods
•Numerical design methods still needed• Choose device type, optimize placement and functional characteristics
• Define design details (material selection, …)
• Do validation and robustness studies
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
In most applications efficient damping is only found for optimized treatment properties
Optimization of the behavior of a loudspeaker(Kergourlay PhD at ECP 04)
A key feature : there is an optimumDevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Functional models of SPADD devices
• Struts (point to point connections)
• Lines (multi-device placed on a support surface)
• Patches (constrained layer variation)
DevicesMechanismsProblems
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Design
Step 1 : manual placementPoint to point struts : give extremities.
Possibly select in a list of possibilities
Patches specify directions and stepsNon conform mesh support
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Step 1 : automated placement• Base criterion : surface elongation
with an offset• Target mode selection or multi-mode
averaging
DevicesMechanismsProblems
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Step 2 : model optimizationFunctional model stiffness
Initial designfind an optimal kv
What does optimal mean ?
DevicesMechanismsProblems
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Step 2 : optimal pole
• Efficient for a few target modes
• Not appropriate at higher frequencies
DevicesMechanismsProblems
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DevicesMechanismsProblems
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Step 2 : optimal transfer• Input (location, content)• Output (location,
vibration/pressure, …)• Data aggregation : RMS,
MIF
Step 2 : cost and accuracy• Exact complex mode solution impractical :
often days, convergence is not robust• Reanalysis
a) T = untreated structure real modesb) T = optimal treated structure real modesc) T = first order correction
DevicesMechanismsProblems
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DevicesMechanismsProblems
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Approximation validity• Flexion, torsion modes• Damped struts
Undamped modal
Damped modal
1st orderMSE
Damped modal : very narrow validity range
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DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Approximation validity• Patch, driving point
Undamped modal, good trends, difficulties when too much deviation from origin
Undamped modal 1st order
Then finalize, validate, …• Select material• Finalize geometry,
fabrication process, price, …
• Evaluate environmental factors
• Validate vibroacousticperformance, resistance, durability, …
Lots of workBut you know it is worth
the try
Material Selection1. Select
frequency range2. Select temp
range3. Validate
relevance on nomogram
Other considerations : Manufacturing, price, outgazing, aging, oil, …
DevicesMechanismsProblems
CharacteristicsModelsMeshes
Design
Temperature robustness validation
For a selected design performance is judged byFRFs and Poles
Sensitivity to temperature must be evaluated
B1/TaB1/SM50e
Conclusion• Damping modeling can be achieved with
– Detailed physical characteristics– Appropriate software / solvers
• Damping treatments add value to many products– Damping prediction should be integrated in the
design process– Optimization is needed most of the time
• Good applications involve redesign for damping to get energy in the damping material. Many of these designs lead to patents.
www.sdtools.com/Publications.html
Perspectives
Are some of you interested in aSEM Working Group ?
First step :a session next year ?
balmes@sdtools.com
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