Studies in Nonlinear Aeroelasticity

0 Nonlinear Aeroelasticity: An Overview.- Summary.- 0.1 Introduction.- 0.2 Categorization of Generic Nonlinear Effects.- 0.3 The Earlier Literature.- References.- I Some Background from Continuum Mechanics.- 1.1 Methods of Describing Motion and Fluid-Structure Interaction.- 1.2 Fundamental Relations of the Nonlinear Theory of Thin Elastic Shells.- 1.3 Fundamental Equations of Hydromechanics.- 1.4 Conditions on the Surfaces of Large Discontinuities.- References.- II General Formulation and Classification of Interaction Problems of a Shell with a Fluid Flow.- 2.1 Kinematic and Dynamic Conditions at a Contact Surface.- 2.2 Reduction of Contact Conditions to the Original Surface.- 2.3 Classification of Aeroelasticity Problems.- 2.4 Interaction for Large Bending of the Shell.- 2.5 Interaction for Medium Bending of the Shell.- 2.6 Interaction for Small Bending of the Shell.- 2.7 Interaction Between a Plate and a Viscous Fluid.- References.- III Bending of a Cylindrical Shell with a Transverse Flow Around It.- 3.1 Small Bending of a Cylindrical Shell with an Unseparated Transverse Flow Around It.- 3.2 Influence of Distinction Between Deformed and Undeformed Surfaces in Contact Conditions.- 3.3 Dynamical Behavior of a Shell in a Flow.- 3.4 Bending of a Shallow Cylindrical Curved Plate in a Flow.- 3.5 Research Results: Comparison with Experiment.- 3.6 Large Bending of a Cylindrical Shell in a Flow.- 3.7 Dynamical Behavior of a System: Taking into Account Initial Bending of the Shell.- 3.8 Influence of Flow Separation from the Shell Surface.- References.- IV Interaction of a Permeable Shell with a Fluid Flow.- 4.1 Conditions on the Contact Surfaces.- 4.2 Representation of the Flow Velocity Through the Shell and the Shell Rigidity.- 4.3 Particular Cases.- 4.4 Bending of a Cylindrical Shell in an Incompressible Liquid.- References.- V Self-Excited Nonlinear Oscillations of Elastic Bodies in a Flow: An Introduction.- Summary.- 5.1 Flutter of a Buckled Plate as an Example of Chaotic Motion of a Deterministic Autonomous System.- 5.2 Nonlinear Oscillator Models in Bluff Body Aeroelasticity.- 5.3 Flutter of Airfoils at Transonic Mach Numbers.- References.- VI Unsteady Transonic Aerodynamics and Aeroelasticity.- Abstract.- Nomenclature.- 6.1 Introduction.- 6.2 Linear/Nonlinear Behavior in Unsteady Transonic Aerodynamics.- 6.3 Viable Alternative Solution Procedures to Finite Difference Methods.- 6.4 Nonuniqueness, Transient Decay Times, and Mean Values for Unsteady Oscillations in Transonic Flow.- 6.5 Effective, Efficient Computational Approaches for Determining Aeroelastic Response Using Unsteady Transonic Aerodynamic Codes.- 6.6 Nonlinear Flutter Analysis in the Frequency Domain and Comparison with Time Marching Solutions.- 6.7 Concluding Remarks.- References.- VII Chaotic Oscillations in Mechanical Systems.- Summary.- 7.1 On the Understanding of Chaos in Duffings’ Equation Including a Comparison with Experiment.- 7.2 Self-Excited, Chaotic Oscillations of an Autonomous System: Lorenz Equations.- References.- VIII The Effects of Compliant Walls on Transition and Turbulence.- Summary.- 8.1 A Brief, Historical Review.- 8.2 The Total Model and Various Component Models.- 8.3 Proposed Methods for Addressing the Total Model.- 8.4 Concluding Remarks.- References.- Appendix A: Correlation Between Theory and Experiment for Aerodynamic and Flutter Characteristics of Wavy Walls.- Appendix B: Elastic Compliant Walls for Drag Reduction using Statically and Dynamically Unstable Structures.- Appendix A Observation and Evolution of Chaos for an Autonomous System.-Summary.- Observation of Chaos.- Concluding Remarks.- References.- Appendix B An Approximate Method for Calculating the Vortex-Induced Oscillation of Bluff Bodies in Air and Water.- References.- Appendix C Unsteady Separated Flow Models.- Key Ideas.- References.