1. 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 Mechanics FEMTO-ST UMR 6174, Besançon, France (2) LTDS, Ecole Centrale de Lyon, Ecully, France dMEMS Conf, Besançon 2012

2. université de technologie Belfort-Montbéliard dMEMS 2012 - Besançon Motivations 2 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 …. Active Control of Vibroacoustic interface by the synthesis of generalized Impedance operator

3. université de technologie Belfort-Montbéliard dMEMS 2012 - Besançon 3 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. Motivations

4. université de technologie Belfort-Montbéliard dMEMS 2012 - Besançon 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. université de technologie Belfort-Montbéliard dMEMS 2012 - Besançon 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. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 6 Part 1 - Mathematical Formulation Part 1 - Mathematical Formulation

7. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 7 Bloch Expansion Theorem ‘Generic’ Elliptic PDE : (Bloch Expansion) whereare the eigenvectors : of the shifted cell operator : Periodic System

8. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 8 Piezo-Elastodynamic Application The Piezo-Elastodynamic equilibrium : Boundary Conditions With : The weak formulation is also: QEP The shifted cell eigenvalue problem : and :

9. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 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.e K, L and H depend on  The problem is Non Linear, and non quadratic on  We prefer to solve that QEP by fixing  and  and search k :

10. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 10 Part 2 - Electric Impedance Optimization Part 2 - Electric Impedance Optimization

11. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 11 The Considered System PZT-Aluminum Composite

12. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 12 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 :

13. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 13 Transmission Optimization Induced effects on Acoustic normal wave number Acoustic coincidence

14. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 14 Reactive Circuit Quasi constant Cneg : The Optimal Impedance Transmission Optimization

15. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 15 Effect on Acoustic normal wave number Acoustic coincidence Acoustic decay rate Absorption Optimization

16. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 16 Dissipative Circuit Quasi constant Cneg : The Optimal Impedance Absorption Optimization

17. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 17 Validation on a periodically semi-distributed adaptive cells The considered System :

18. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 18 Validation on a periodically semi-distributed adaptive cells

19. dMEMS 2012, Besançon université de technologie Belfort-Montbéliard 19 Conclusions Wave Dispersion in 2D Application of the Bloch Theorem Shunted Piezoelectric System Finite Element Approach (Multiphics) Concepts Whole 2D K-space computation with electric shunt Group Velocity based Indicator Impedance optimization Vibroacoustic energy diffusion control Results Periodic smart Structures Passive, semi-active or active control Waves Diffusion at 2D Medium Interface Wave Trap Concepts Future