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Table of contents
1 Introduction
1.1 Overview of flow energy harvesting
1.2 Flutter instability
1.2.1 Stability and dynamics of a single flag placed in a uniform flow 3
1.2.2 Stability and dynamics of several flags placed in uniform flow 6
1.2.3 Concluding remarks: why we choose piezoelectric flags
1.3 A brief introduction to piezoelectricity
1.4 Energy harvesting using piezoelectric materials
1.5 Introduction of numerical models used in the present work
1.5.2 Piezoelectric effects
1.5.3 Dimensionless equations
1.6 Energy harvesting
1.7 Energy harvesting using piezoelectric flag connected to resistive circuits
1.8 Outline of manuscript
2 Single Piezoelectric Coverage
2.1 Experimental set-up
2.2 Comparison between PVDF and MFC
2.3 Modelling of a flag covered by one piezoelectric pair
2.3.1 Simple current source model neglecting piezoelectric feedback
2.3.2 Nonlinear numerical model
2.4 Characterisation of the coupling coefficient
2.4.1 Measurement of B
2.4.2 Measurement of
2.5 Experimental and numerical results
2.5.1 PVDF flag in Tunnel A
2.5.2 PVDF flag in Tunnel B
2.5.3 MFC flag and feedback of piezoelectric effect
2.6 Summary and conclusion
3 Fluid-solid-electric lock-in
3.1 Modelling of a flag continuously covered by pairs of piezoelectric patches
3.2 Linear stability
3.3 Nonlinear dynamics and energy harvesting
3.4 Impact of the coupling factor
3.5 Perspective: lock-in with one single piezoelectric pair
3.6 Conclusion
4 Non-local electric network
4.1 Equations of non-local electric network
4.1.1 Flag covered by a finite number of piezoelectric pairs
4.1.2 Periodic networks and continuous limit
4.1.3 Boundary conditions and energy balance
4.1.4 Dimensionless Equations
4.2 Purely resistive circuits
4.3 Purely inductive circuits
4.3.1 Frequency lock-in
4.3.2 Energy harvesting at ext!0 1
4.4 Electrical energy flux
4.5 Conclusion and perspectives
5 Coupled flutter
5.1 Two piezoelectric flags connected in one circuit
5.1.1 Electrical circuits
5.1.2 Harvesting efficiency
5.2 Fluid forcing: vortex sheet model
5.3 Side-by-side flags
5.3.1 Influence of in-phase and out-of-phase flapping
5.3.2 Influence of separation distance d
5.3.3 Resistive-inductive circuits
5.4 Flags in tandem
5.4.1 Resistive circuit
5.4.2 Resistive-inductive circuit
5.5 Conclusion and perspectives
6 Conclusion and perspectives
6.1 Conclusion
6.1.1 Frequency lock-in
6.1.2 Two flags’ synchronisation through the fluid-solid-electric resonance
6.2 Perspectives
6.2.1 External forcing-induced vibration of piezoelectric flag
6.2.2 Flags placed in other types of flows
6.2.3 Flags positioned in alternative configurations
Appendices
