Dynamic Stability

Dynamic instability or dynamic buckling as applied to structures is a term that has been used to describe many classes of problems and many physical phenomena. It is not surprising, then, that the term finds several uses and interpretations among structural mechanicians. Problems of parametric resonance, follower-force, whirling of rotating shafts, fluid-solid interaction, general response of structures to dynamic loads, and several others are all classified under dynamic instability. Many analytical and experimental studies of such problems can be found in several books as either specialized topics or the main theme. Two such classes, parametric resonance and stability of nonconservative systems under static loads (follower-force problems), form the main theme of two books by V. V. Bolotin, which have been translated from Russian. Moreover, treatment of aero elastic instabilities can be found in several textbooks. Finally, analytical and experimental studies of structural elements and systems subjected to intense loads (of very short duration) are the focus of the recent monograph by Lindberg and Florence. The first chapter attempts to classify the various "dynamic instability" phenomena by taking into consideration the nature of the cause, the character of the response, and the history of the problem. Moreover, the various concepts and methodologies as developed and used by the various investigators for estimating critical conditions for suddenly loaded elastic systems are fully described. Chapter 2 demonstrates the concepts and criteria for dynamic stability through simple mechanical models with one and two degrees of freedom.

The dynamics of bodies containing fluids is a subject of long-standing im portance in many technical applications. The stability of motion of such bodies, in particular, has been the subject of study by Soviet engineers and applied mathematicians who have brought their fuH powers of analysis to bear on the problem, and have succeeded in developing a very weH-founded body of theory. It is difficult to find a more striking example anywhere of the application of the classical methods of analytical mechanics, together with more modern concepts of stability analysis, in such a comprehensive and elegent form as that presented by Profs. Moiseyev and Rumyantsev. Therefore, it is highly significant that this recent monograph has been trans lated and made available to the English-speaking community. H. NORMAN ABRAMSON San Antonio July, 1967 v Foreword During the last 15-20 years, problems of dynamics of rigid bodies with fluid-filled cavities have increasingly attracted the attention of scientists.

Aircraft Dynamic Stability and Response deals with the fundamentals of dynamic stability in aircraft. Topics covered include flight dynamics, equations of motion, and lateral and longitudinal aerodynamic derivatives. Basic lateral and longitudinal motions are also considered. A non-dimensional system of notation is used, and problems are included at the end of chapters. This book is comprised of 13 chapters and begins with an introduction to aircraft static stability and maneuverability, with emphasis on the theoretical basis of flight dynamics and the technical terms used. The physical background for the estimation of aerodynamic derivatives is discussed. Subsequent chapters focus on the longitudinal and lateral motion of aircraft, including the effect of automatic control; modern developments such as the effects of aeroelasticity, dynamic coupling, and high incidence; and aircraft response to gusts. The final chapter demonstrates how to estimate the aerodynamic derivatives, and hence the dynamic stability characteristics, of a typical fighter aircraft. Throughout the text, the aircraft and its behavior are kept well to the fore. This monograph is intended for undergraduate students of aeronautical engineering and for newcomers to the aircraft industry.

This report deals primarily with extension of the energy-based concepts of dynamic stability, developed earlier for finite-degree-of-freedom systems, to continuous systems. Moreover, the related criteria for dynamic stability are demonstrated through several structural configurations, such as eccentrically loaded simple two-bar frames, geometrically imperfect, thin, cylindrical shells (of stiffened and unstiffened construction) and subjected to uniform axial compression and lateral pressure, and a pinnted, half-sine, shallow arch loaded transversely. All of these systems are subject to violent buckling under static application of the loads. Moreover, the developed concepts are extended, so as to apply to structural systems, which are either subject to smooth buckling or are not subject to buckling at all under static loading.

Dynamic Stability of Structures covers the proceedings of an International Conference on Dynamic Stability of Structures, held in Northwestern University, Evanston, Illinois on October 18-20, 1965, jointly sponsored by the Air Force of Scientific Research and Northwestern University. The conference aims to delineate the various categories of dynamic stability phenomena. This book is organized into six sections encompassing 20 chapters that tackle general topics such as mathematical methods of analysis, physical phenomena, design applications in engineering, and reports of field research. The first two sections deal with the fundamentals, principles, and concept of dynamic stability, as well as an introduction to the use of computing machines as an aid in studying the motions of complicated dynamical systems. The succeeding two sections highlight the statistical aspects in the structural stability theory and certain problems of structural dynamic. These sections also look into the dynamic buckling of elastic structures and the buckling of long slender ships due to wave-induced whipping. The last two sections explore the stability and vibration problems of mechanical systems under harmonic excitation and the dynamic buckling under step loading. These sections also include discussions on the nonlinear dynamic response of shell-type structures and of a column under random loading, as well as Italian research in the field. Structural and mechanical engineers will find this book invaluable.

This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”Mathematical analysis on time scales accomplishes exactly this. This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.

Based on a 15-year successful approach to teaching aircraft flight mechanics at the US Air Force Academy, this text explains the concepts and derivations of equations for aircraft flight mechanics. It covers aircraft performance, static stability, aircraft dynamics stability and feedback control.

The second edition of Flight Stability and Automatic Control presents an organized introduction to the useful and relevant topics necessary for a flight stability and controls course. Not only is this text presented at the appropriate mathematical level, it also features standard terminology and nomenclature, along with expanded coverage of classical control theory, autopilot designs, and modern control theory. Through the use of extensive examples, problems, and historical notes, author Robert Nelson develops a concise and vital text for aircraft flight stability and control or flight dynamics courses.

Anyone who has experience with a car, bicycle, motorcycle, or train knows that the dynamic behavior of different types of vehicles and even different vehicles of the same class varies significantly. For example, stability (or instability) is one of the most intriguing and mysterious aspects of vehicle dynamics. Why do some motorcycles sometimes exh