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.
The great bulk of the literature on aeroelasticity is devoted to linear models. The oretical work relies heavily on linear mathematical concepts, and experimental results are commonly interpreted by assuming that the physical model behaves in a linear manner. Nevertheless, significant work has been done in nonlinear aero elasticity, and one may expect this trend to accelerate for several reasons: our ability to compute has increased at an astonishing rate; as linear concepts have been assimilated widely, there is a natural increase in interest in the foundations of nonlinear modeling; and, finally, some phenomena long recognized to be of interest, but beyond the effective range of linear models, are now known to be essentially nonlinear in nature. In this volume, an exhaustive review of the literature is not attempted. Rather the emphasis is on fundamental ideas and a representative selection of problems. Despite obvious successes in research on problems of aeroelasticity and the existence of a broad literature, including a number of excellent monographs, up to now little attention has been devoted to a general nonlinear theory of interac tion. For the most part nonlinearity has been considered either solely in the description of the behavior of a shell or in the description of the motion of a gas.
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