Dynamic Stability Of Structures

This book explores the theory of parametric stability of structures under deterministic and stochastic loadings.

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.

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.

Structural configurations subjected to loads that fall under the category of an ideal impulse are considered. Emphasis is placed on systems that exhibit either limit point instability or an unstable bifurcational branch in the post-buckling region. The purpose of the present work is to investigate the concept of dynamic stability of structural elements subjected to step-loads and develop the related criteria and estimates for finding critical conditions. The step load consists of a suddenly applied load of constant magnitude and finite duration t sub o, and the investigation will include the two extreme cases of t sub o approaches infinity and t sub o approaches 0 (ideal impulse). Moreover, the effect of various parameters (small damping and preloading) on the critical conditions is studied. The developed solution methodology is demonstrated through a geometrically imperfect model and a load eccentricity model of one degree of freedom and a snap-through model of two degrees of freedom. (Author).

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.

A crucial element of structural and continuum mechanics, stability theory has limitless applications in civil, mechanical, aerospace, naval and nuclear engineering. This text of unparalleled scope presents a comprehensive exposition of the principles and applications of stability analysis. It has been proven as a text for introductory courses and various advanced courses for graduate students. It is also prized as an exhaustive reference for engineers and researchers. The authors' focus on understanding of the basic principles rather than excessive detailed solutions, and their treatment of each subject proceed from simple examples to general concepts and rigorous formulations. All the results are derived using as simple mathematics as possible. Numerous examples are given and 700 exercise problems help in attaining a firm grasp of this central aspect of solid mechanics. The book is an unabridged republication of the 1991 edition by Oxford University Press and the 2003 edition by Dover, updated with 18 pages of end notes.