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

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

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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.

  6. Part 1 - Mathematical Formulation

  7. Bloch Expansion Theorem ‘Generic’ Elliptic PDE : (Bloch Expansion) Periodic System where are the eigenvectors : of the shifted cell operator :

  8. Piezo-Elastodynamic Application • The Piezo-Elastodynamic equilibrium : The shifted cell eigenvalue problem : Boundary Conditions and : With : The weak formulation is also: QEP

  9. 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 :

  10. Part 2 - Electric Impedance Optimization

  11. The Considered System PZT-Aluminum Composite

  12. 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 :

  13. TransmissionOptimization • Induced effects on Acoustic normal wave number Acoustic coincidence

  14. Transmission Optimization The Optimal Impedance Quasi constant Cneg : Reactive Circuit

  15. Absorption Optimization • Effect on Acoustic normal wave number Acoustic coincidence Acoustic decay rate

  16. Absorption Optimization The Optimal Impedance Quasi constant Cneg : Dissipative Circuit

  17. Validation on a periodically semi-distributed adaptive cells • The considered System :

  18. Validation on a periodically semi-distributed adaptive cells

  19. 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

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