Etienne Balmès - SDTools · stiffness dynamic stiffness equal at resonance ⇒ Response is the same Devices Mechanisms Problems Characteristics Models Meshes Design Different local

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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


Design

Dampers with fluid cavities•Dampers or shock absorbers

•Automotive, aerospace, …



Design

Friction dampers•Traditional vehicle suspension

•Custom high-tech applications (Ariane SARO from Jarret)

•Aircraft engine



Design

2

Viscoelastic point to point connections

+ Rugged, efficient, fairly simple design

- Operating temperature

www.artec-spadd.com



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



Design

Viscoelastic layer treatments•Traditional free and constrained layer viscoelastic treatments

•Constrained layer more efficient for relatively soft damping materials



Design

Viscoelastic rib designs•Mechanical amplification can be used to enhance constrained layer treatment effectiveness

www.artec-spadd.com



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



Design

Viscoelastic materials

ε

σΕsη

−Εsη

−1 1ElasticViscoelastic



Design

3

Non linear devices/connections•Non linear point to point connection : force-state mapF = f(q,t)

•Friction model



Design

Fluid / structure coupling•Classical fluid/structure coupling

Damped if fluid is moving or dissipative

•Damping in coupling : surface impedance, porous media (Biot model), …



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



Design

Viscoelastic constitutive relations

• Stress is a function of strain history • Complex modulus in Laplace domain



Design

Reduced frequency nomogramsDevicesMechanismsProblems


Design

Viscoelastic constitutive laws

Viscous Hysteretic Standard viscoelastic

Alternatives : • More relaxation constants• Fractional derivatives• Direct use of experimental master curve

K



Design

4

Material damping models

Stress/strain curveSimple models

K+iB



Design

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



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)



Design

Initial stress, friction coefficient, …

Friction depends on

•Contact stress

•Friction coefficient

Z.Abbadi ISMA 04Session 18 (structural joints)



Design


•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




Design

• Nominal model (elastic + viscous damping)

• Conservative eigenvalue problem

• M>0 & K≥0 ⇒ φ real

Normal modes of elastic structureDevicesMechanismsProblems


Design

5

Normal modes of elastic structure

• Orthogonality• Scaling conditions

• Unit mass• Unit amplitude

• Principal coordinates



Design

Modal damping assumption• Assume Γ diagonal

• Leads to second order spectral decomposition

Mode shape Participation factor Residue



Design

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



Design

Small damping ⇒small error on system behavior

System vs. local

• System models (dynamic behaviour)

• FEM models (geometry/material knowlege)

• Each objective requires different assumptions



Design

System damping. 1 DOF example.

a) Bodeb) Nyquistc) 1DOF modeld) Dynamic stiffness

dynamic stiffness equal at resonance ⇒Response is the same



Design

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



Design

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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



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



Design



Design

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



Design

Non proportional damping model

• Modal & MSE loose localization of damping• Good for system, not local analysis

•Forced response around a resonance



Design

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



Design

7

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



Design


•Dominant software implements simple methods







Design

Frequency dependent modelsProblem : dynamic stiffness linear

combination of fixed matrices

Target predictions

• Frequency response• Poles• Complex modes



Design

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



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



Design

Parametric studies = similar challenge

•Squeal can be studies as a parametric problem with non-symmetric dissipative coupling

Theory : F. Moirot PhD 98Model : BOSCH



Design

8

Spectral decompositions

For frequency dependent moduli E(s)• Solve non-linear eigenvalue • Identify from computed transfers



Design

Frequency independent models

• Material formulation with internal fields (rational and fractional derivates)

Trick increase model orderto gain frequency independence



Design

☺ 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


Design









Design

Meshing detail•Classical result : layer cutsinfluence damping and there are optimal solutions

•They need to be modeled in detail



Design

Meshing detailsExample: shell/rigid/ volume/rigid/shell

+ General- normals and thickness ?



Design

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Non conform meshes•Variable refinement•Non coincident nodes•Offset from mid-plane



Design

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



Design



•Numerical design methods still needed• Choose device type, optimize placement and functional characteristics

• Define design details (material selection, …)

• Do validation and robustness studies



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


Design

Functional models of SPADD devices

• Struts (point to point connections)

• Lines (multi-device placed on a support surface)

• Patches (constrained layer variation)



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



Design

10

Step 1 : automated placement• Base criterion : surface elongation

with an offset• Target mode selection or multi-mode

averaging



Design

Step 2 : model optimizationFunctional model stiffness

Initial designfind an optimal kv

What does optimal mean ?



Design

Step 2 : optimal pole

• Efficient for a few target modes

• Not appropriate at higher frequencies



Design



Design

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



Design



Design

Approximation validity• Flexion, torsion modes• Damped struts

Undamped modal

Damped modal

1st orderMSE

Damped modal : very narrow validity range

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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, …



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 ?

[email protected]

Documents

Etienne Balmès - SDTools · stiffness dynamic stiffness equal at resonance ⇒ Response is the same Devices Mechanisms Problems Characteristics Models Meshes Design Different local