Description
SPRINGER Theory Of Adaptive Fiber Composites 2009 Edition by BROCKMANN TOBIAS H.
Adaptive structural systems in conjunction with multifunctional materials facilitate technical solutions with a wide spectrum of applications and a high degree of integration. By virtue of combining the actuation and sensing capabilities of piezoelectric materials with the advantages of fiber composites, the anisotropic constitutive properties may be tailored according to requirements and the failure behavior can be improved. Such adaptive fiber composites are very well-suited for the task of noise and vibration reduction. In this respect the helicopter rotor system represents a very interesting and widely perceptible field of application. The occurring oscillations can be reduced with aid of aerodynamic couplings via fast manipulation of the angle of attack, being induced by twist actuation of the rotor blade. On the one hand the sensing properties may be used to determine the current state of deformation, while on the other hand the actuation properties may be used to attain the required state of deformation. The implementation of such concepts requires comprehensive knowledge of the theoretical context, which shall be illuminated in the work at hand from the examination of the material behavior to the simulation of the rotating structure. 1 Introduction ; 1.1 Adaptive Structural Systems ; 1.2 Objective and Scope ; 1.3 Outline and Overview ; 2 Helicopter Applications ; 2.1 Noise and Vibration ; 2.1.1 Generation ; 2.1.2 Areas of Relevance ; 2.2 Main Rotor ; 2.2.1 Rotational Sources ; 2.2.2 Impulsive Sources ; 2.2.3 Broadband Sources ; 2.3 Passive Concepts ; 2.3.1 External Devices ; 2.3.2 Aeroelastic Conformability; 2.4 Active and Adaptive Concepts ; 2.4.1 Pitch Control at the Blade Root ; 2.4.2 Discrete Flap Actuation ; 2.4.3 Integral Blade Actuation ; 2.5 Adaptive Beam Aspects ; 2.5.1 Beam Actuation Concepts ; 2.5.2 Adaptive System Concepts ; 2.5.3 Development Status; 3 Fundament a1 Considerations; 3.1 Mathematical Preliminaries; 3.1.1 Euclidean Vectors; 3.1.2 Tensor Representation ; 3.1.3 Matrix Representation ; 3.2 Deformable Structures . Mechanical Fields; 3.2.1 Loads ; 3.2.2 Stresses; 3.2.3 Mechanical Equilibrium; 3.2.4 Strains; 3.2.5 Transformations ; 3.3 Dielectric Domains - Electrostatic Fields; 3.3.1 Electric Charge; 3.3.2 Electric Flux Density; 3.3.3 Electrostatic Equilibrium; 3.3.4 Electric Field Strengths; 3.4 Principle of Viual Work; 3.4.1 General Principle of Virtual Work; 3.4.2 Principle of Virtual Displacements ; 3.4.3 Principle of Virtual Loads ; 3.4.4 Principle of Virtual Electric Potential; 3.4.5 D'Alembert's Principle in the Lagrangian Version; 3.4.6 Summation of Virtual Work Contributions ; 3.5 Other Variational Principles ; 3.5.1 Extended Dirichlet's Principle of Minimum Potential Energy ; 3.5.2 Extended General Hamilton's Principle; 4 Piezoelectric Materials; 4.1 Piezoelectric Effect ; 4.1.1 Historical Development; 4.1.2 Crystal Structures; 4.2 Constitutive Formulation ; 4.2.1 Mechanical Fields; 4.2.2 Electrostatic Fields; 4.2.3 Electromechanical Coupling ; 4.2.4 Spatial Rotation; 4.2.5 Analogy of Electrically and Thermally Induced Deformations; 4.3 Constitutive Examination ; 4.3.1 Constitutive Relation ; 4.3.2 Converse Piezoelectric Effect; 4.3.3 Direct Piezoelectric Effect;4.4 Constitutive Reduction; 4.4.1 Unidirectional Electrostatic Fields; 4.4.2 Planar Mechanical Fields; 4.4.3 Planar Rotation ; 4.4.4 Negated Electric Field Strength; 4.5 Actuator and Sensor Conditions; 4.5.1 Actuator Application with Voltage and Current Source ; 4.5.2 Sensor Application with Voltage and Current Measurement; 5 Piezoelectric Composites; 5.1 Classification of General Composites ; 5.1.1 Topology of the Inclusion Phase; 5.1.2 Laminated Composites and Laminated Fiber Composites; 5.2 Conception of Piezoelectric Composites ; 5.2.1 Interdigitated Electrodes and Piezoelectric Fibers ; 5.2.2 Electroding Implications ; 5.2.3 Development Status ; 5.2.4 Representative Volume Element and Fiber Geometry ; 5.2.5 Modeling Preliminaries; 5.3 Micro-Electromechanics with Equivalent Inclusions; 5.3.1 Mean Fields and Concentration Matrices; 5.3.2 Elementary Rules of Mixture ; 5.3.3 Equivalence of Inclusion and Inhomogenity'5.3.4 Non-Dilute Concentrations ; 5.4 Micro-Electromechanics with Sequential Stacking ; 5.4.1 Stacking of Constituents with Uniform Fields; 5.4.2 Normal Mode Stacking Coefficients; 5.4.3 Shear Mode Stacking Coefficients; 5.4.4 Stacking Sequences; 5.4.5 Non-Homogeneous Electrostatic Fields; 5.4.6 Stacking Sequences for Non-Homogeneous Electrostatic Fields; 5.5 Validation of the Micro-Electromechanics; 5.5.1 Experiments and Finite Element Models; 5.5.2 Dielectric, Piezoelectric, and Mechanical Properties ; 6 Adaptive Laminated Composite Shells; 6.1 Macro-Electromechanics; 6.1.1 Lamination Theory; 6.1.2 Laminates with Groups of Electrically Paralleled Laminae ; 6.2 Kinematics and Equilibrium; 6.2.1 General Thin Shell Kinematics; 6.2.2 Cylindrical Thin Shell Kinematics; 6.2.3 Cylindrical Thin Shell Equilibrium ; 6.3 Constitutive Reduction ; 6.3.1 Negligence of Strain and Stress Components ; 6.3.2 Potential Energy Considerations; 7 Adaptive Thin-Walled Beams; 7.1 General Beam Kinematics; 7.1.1 Positions and Displacements; 7.1.2 Rotations; 7.1.3