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Table of contents
1 Introduction
1.1 Background and Motivations
1.2 Literature Review
1.3 Ideas and Research Objectives
1.4 Outline
2 Preliminaries
2.1 Continuum Kinematics
2.1.1 Body, References, Coordinates
2.1.2 Deformations of Continuum Bodies
2.1.3 Beam Kinematics
2.2 Virtual Power Principle
2.2.1 Introduction
2.2.2 De…nitions
2.2.3 Statement
2.2.4 Considerations
2.3 Piezoelectric Materials
2.3.1 Linear Constitutive Relations
2.3.2 Voigt Notation
2.3.3 Uniaxial States
2.3.4 PZT Transducers
3 Electrical Systems
3.1 Discrete Systems
3.2 Electromechanical Analogies
3.3 Periodic Systems and Homogenized Models
3.3.1 Lumped Transmission Line
3.3.2 Homogenized Model
4 Layered Composite PEM Beam
4.1 Continuous Layered Composite PEM Beam
4.1.1 System Description
4.1.2 Kinematics
4.1.3 Constitutive Relations
4.1.4 Power Balance
4.1.5 Balance Equations
4.1.6 Weak Formulation
4.2 Elastic Beam
4.2.1 Equilibrium Equations
4.2.2 Weak Formulation
4.2.3 Dimensional Analysis and Approximations
4.3 Beam with PZT Transducers
4.3.1 Internal Powers
4.3.2 External Powers
4.3.3 Power Balance
4.4 Results Review
5 Periodic PEM Structures and Homogenized Models
5.1 Bending Coupling
5.1.1 Re…ned Model of the Basic Cell
5.1.2 Homogenized Continuous Model
5.2 Extensional Coupling
5.2.1 Re…ned Model of the Basic Cell
5.2.2 Homogenized Continuous Model
6 Comparison of Optimal Network Con…gurations
6.1 Wave Form Solutions
6.2 Waves in PiezoElectroMechanical Beams
6.2.1 Transversal-Electric Coupling
6.2.2 Longitudinal-Electric Coupling
6.3 Optimization for Vibrations Suppression
6.3.1 Performance Index
6.3.2 Optimization Method
6.4 Transversal-Electric Waves
6.4.1 Isolated Resonant Shunts (IRS)
6.4.2 Transmission Line with Line Resistance and Inductance(TL-Rl-Ll)
6.4.3 Transmission Line with Line Inductance and Ground Resistance(TL-Rg-Ll) .
6.4.4 Comparison of Network Con…gurations
6.5 Longitudinal-Electric Waves
6.5.1 Isolated Resonant Shunts (IRS)
6.5.2 Transmission Line with Line Resistance and Inductance(TL-Rl-Ll)
6.5.3 Transmission Line with Line Inductance and Ground Resistance(TL-Rg-Ll) .
6.5.4 Comparison of Network Con…gurations
7 Experiments
7.1 Goals
7.2 System Design and Realization
7.2.1 Beam with PZT Transducers
7.2.2 Electric Networks
7.3 Experimental Modal Analysis
7.3.1 Instrumentation
7.3.2 Experimental Setup for Mechanical and Electrical FRF Measures
7.3.3 Identi…cation Procedure
7.4 Results
7.4.1 Beam Modal Parameters
7.4.2 Synthetic Inductors Characterization
7.4.3 Beam with Resonant Shunted PZT
7.5 Next Steps
7.6 Conclusions
Appendix A – Physical Dimensions
Appendix B – Ma terial Properties and External Actions
B.1 Materi al Properties
B.2 Extern al Actions
B.3 Physical Dimensions
Appendix C – Numerical Values
C.1 Geometric and Local Material Characteristics
C.2 Sectional Material Characteristics
C.3 Homogenized Material Characteristics
C.4 Dimensionless Parameters
C.4.1 Bending Coupling
C.4.2 Longitudinal Coupling
