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

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

(1) Dept Applied MechanicsFEMTO-ST UMR 6174, Besançon, France (2) LTDS, Ecole Centrale de Lyon, Ecully, France

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université de technologieBelfort-Montbéliard dMEMS 2012 - Besançon

Motivations

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Classical approaches of ANC or AVC is difficult to apply into real fully distributed applications :

Technological and Numerical complexity

Difficulties for integrating such technology into the Design Process (Robustness/Performances)

Energy Cost

Necessity to propose a new approach ….

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Active Control of Vibroacoustic interface by the synthesis of generalized Impedance operator

université de technologieBelfort-Montbéliard dMEMS 2012 - Besançon3

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 Synthetize and integrate dedicated programmable vibroacoustic functionnalities inside structures for realizing adaptive interfaces.

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Motivations

université de technologieBelfort-Montbéliard dMEMS 2012 - Besançon4

The Targeted Application

Let us consider the elasto-dynamical wave control by means of shunted piezoelectric periodic patches :

The shunt impedance is complex Damped SystemWe 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

université de technologieBelfort-Montbéliard dMEMS 2012 - Besançon5

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.

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Part 1-

Mathematical Formulation

Part 1-

Mathematical Formulation

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Bloch Expansion Theorem

‘Generic’ Elliptic PDE :

(Bloch Expansion)

where are the eigenvectors :

of the shifted cell operator :

Periodic System

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Piezo-Elastodynamic Application

The Piezo-Elastodynamic equilibrium :

Boundary Conditions

With :

The weak formulation is also:

QEP

The shifted cell eigenvalue problem :

and :

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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.e K, 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 :

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Part 2-

Electric Impedance Optimization

Part 2-

Electric Impedance Optimization

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The Considered System

PZT-Aluminum Composite

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Optimization of the shunted electric impedance

The Critera for Optimizing the Flexural Wave Propagation:Based on computing the Group Velocity :

Two vibroacoustic functions to minimize is (Nelder Mead algorithm):

(Transmission)

(Absorption)

The normal acoustic wave number is given by :

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Transmission Optimization

Induced effects on Acoustic normal wave number Acoustic coincidence

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Reactive Circuit

Quasi constant Cneg :

The Optimal Impedance

Transmission Optimization

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Effect on Acoustic normal wave number Acoustic coincidence

Acoustic decay rate

Absorption Optimization

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Dissipative Circuit

Quasi constant Cneg :

The Optimal Impedance

Absorption Optimization

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Validation on a periodically semi-distributed adaptive cells

The considered System :

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Validation on a periodically semi-distributed adaptive cells

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Conclusions

Wave Dispersion in 2DWave Dispersion in 2D

Application of the Bloch TheoremApplication of the Bloch Theorem

Shunted Piezoelectric SystemShunted Piezoelectric System

Finite Element Approach (Multiphics)Finite Element Approach (Multiphics)

ConceptsConcepts

Whole 2D K-space computation with electric shuntWhole 2D K-space computation with electric shunt

Group Velocity based IndicatorGroup Velocity based Indicator

Impedance optimizationImpedance optimization

Vibroacoustic energy diffusion controlVibroacoustic energy diffusion control

ResultsResults

Periodic smart StructuresPeriodic smart Structures

Passive, semi-active or active controlPassive, semi-active or active control

Waves Diffusion at 2D Medium InterfaceWaves Diffusion at 2D Medium Interface

Wave Trap ConceptsWave Trap Concepts

FutureFuture