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Adaptive shunted piezoelectric metacomposite: a new integrated technology for vibroacoustic control. dMEMS Conf, Besançon 2012. Dr M. Collet(1), Dr M. Ouisse (1), F. Tatéo , Pr M. Ichchou (2), T. Huang(2) Dept Applied Mechanics FEMTO-ST UMR 6174, Besançon, France

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adaptive shunted piezoelectric metacomposite a new integrated technology for vibroacoustic control

Adaptive shunted piezoelectric metacomposite: a new integrated technology for vibroacoustic control

dMEMS Conf,

Besançon 2012

Dr M. Collet(1), Dr M. Ouisse(1), F. Tatéo, Pr M. Ichchou(2), T. Huang(2)

DeptAppliedMechanics

FEMTO-ST UMR 6174, Besançon, France

(2) LTDS, Ecole Centrale de Lyon, Ecully, France

motivations
Motivations
  • Classicalapproaches of ANC or AVC isdifficult to applyinto real fullydistributed applications :
    • Technological and Numericalcomplexity
    • Difficulties for integratingsuchtechnologyinto the Design Process (Robustness/Performances)
    • EnergyCost
    • Necessity to propose a new approach….

Active Control of Vibroacoustic interface by the synthesis of generalizedImpedanceoperator

slide3

Motivations

To Program the behavior relationship inside hybrid composite material by using a distributed set of smart cells including transducers, Computing capabilities and smart materials.

  • We have to Synthetizeand integrate dedicated programmable vibroacoustic functionnalitiesinside structures for realizing adaptive interfaces.

10

001100100110

01

the targeted application
The Targeted Application
  • Let us consider the elasto-dynamical wave control by means of shunted piezoelectric periodic patches :

The shunt impedance is complex

Damped System

We obtain evanescent Bloch wave and damped scattering

By using WFE techniques => Optimization of the energy diffusion* for wave trap

* M. Collet, K.A. Cunefare, N.M. Ichchou,

Wave Motion Optimization in Periodically Distributed Shunted Piezocomposite Beam Structures

Journal of Intelligent Material Systems and Structures, 20(7), 787-808, 2009

challenges and contents
Challenges and Contents
  • Fields of interest
    • Wave propagation in multiphysics and periodic systems : Smart Wave Guides
    • Structural Health Monitoring (Faults detection…)
    • Noise & Vibration Reduction in Complex Structures (Optimization of passive or active systems)
  • Available Techniques
    • Floquet theorem in 1D waveguide (SAFE, WFE, TL techniques …)
    • Bloch theorem in 2D for undamped or weakly damped systems (WFE)
  • Challenges
    • To predict and analyze complex waves vectors of damped mechanical systems with multiphysics coupling introduced by shunted piezoelectric patches
  • Approach
    • Formulate Bloch Expansion theorem for damped piezo-elastodynamic problems
    • Introduce a suitable criterion based on Waves Intensity vector
  • Contents - Outline
    • Mathematical methodology
    • Optimization of the shunted electric impedance
    • Acoustic induced control and 3D validations.
slide6

Part 1

-

Mathematical Formulation

bloch expansion theorem
Bloch Expansion Theorem

‘Generic’ Elliptic PDE :

(Bloch Expansion)

Periodic System

where

are the eigenvectors :

of the shifted cell operator :

piezo elastodynamic application
Piezo-Elastodynamic Application
  • The Piezo-Elastodynamic equilibrium :

The shifted cell eigenvalue problem :

Boundary Conditions

and :

With :

The weak formulation is also:

QEP

numerical implementation
Numerical Implementation
  • The proposed Weak formulation leads to a QEP:

When visco-elastic materials and adaptive metamaterials (shunted piezoelectric) are considered, we introduce frequency dependent piezo-elastodynamic operator i.eK, L and H depend on w : The problem is Non Linear, and non quadratic on w

We prefer to solve that QEP by fixing w and f and search k :

slide10

Part 2

-

Electric Impedance Optimization

the considered system
The Considered System

PZT-Aluminum Composite

optimization of the shunted electric impedance
Optimization of the shunted electric impedance
  • The Critera for Optimizing the FlexuralWave Propagation:
  • Based on computing the Group Velocity :
  • Two vibroacoustic functions to minimizeis (Nelder Mead algorithm):
  • (Transmission)
  • (Absorption)
  • The normal acousticwavenumberisgiven by :
transmission optimization
TransmissionOptimization
  • Induced effects on Acoustic normal wave number

Acoustic coincidence

slide14

Transmission Optimization

The Optimal Impedance

Quasi constant Cneg :

Reactive Circuit

slide15

Absorption Optimization

  • Effect on Acoustic normal wave number

Acoustic coincidence

Acoustic decay rate

slide16

Absorption Optimization

The Optimal Impedance

Quasi constant Cneg :

Dissipative Circuit

conclusions

Wave Dispersionin 2D

Whole 2D K-space computation with electric shunt

Periodic smart Structures

Application of the Bloch Theorem

Group Velocity based Indicator

Passive, semi-active or active control

Shunted Piezoelectric System

Impedance optimization

Waves Diffusion at 2D Medium Interface

Finite Element Approach (Multiphics)

Vibroacoustic energy diffusion control

Wave Trap Concepts

Conclusions

Concepts

Results

Future