Problems such as jumps in elastic systems, problems of aeroelasticity, problems of frictional self-oscillations, and self-synchronization are discussed. The stability of equilibrium shapes of elastic systems is examined. Problems of oscillations of linear systems are discussed, including systems with a fractional number of degrees of freedom as well as free oscillations of a cantilever in the field of centrifugal forces.

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.

The motion of mechanical systems undergoing rotation about a fixed axis has been the subject of extensive studies over a few centuries. These systems are generally subject to gyroscopic forces which are associated with coriolis accelerations or mass transport and render complex dynamics.The unifying theme among topics presented in this book is the gyroscopic nature of the system equations of motion. The book represents comprehensive and detailed reviews of the state of art in four diverse application areas: flow-induced oscillations in structures, oscillations in rotating systems or rotor dynamics, dynamics of axially moving material systems, and dynamics of gyroelastic systems. The book also includes a chapter on dynamics of repetitive structures. These systems feature spatial periodicity and are generally subject to considerable gyroscopic forces. “Gyroelastic systems” and “repetitive structures” are the topics with very recent origins and are still in their infancies compared to the other examples represented in this book. Thus, the contributions on gyroelastic systems and repetitive structures are limited to only modeling, localization and linear stability analysis results.This book covers many important aspects of recent developments in various types of gyroscopic systems. Thus, at last, a comprehensive book is made available to serve as a supplement and resource for any graduate level course on elastic gyroscopic systems, as well as for a course covering the stability of mechanical systems. Moreover, the inclusion of an up-to-date bibliography attached to each chapter will make this book an invaluable text for professional reference.

This revised and significantly expanded edition contains a rigorous examination of key concepts, new chapters and discussions within existing chapters, and added reference materials in the appendix, while retaining its classroom-tested approach to helping readers navigate through the deep ideas, vast collection of the fundamental methods of structural analysis. The authors show how to undertake the numerous analytical methods used in structural analysis by focusing on the principal concepts, detailed procedures and results, as well as taking into account the advantages and disadvantages of each method and sphere of their effective application. The end result is a guide to mastering the many intricacies of the range of methods of structural analysis. The book differentiates itself by focusing on extended analysis of beams, plane and spatial trusses, frames, arches, cables and combined structures; extensive application of influence lines for analysis of structures; simple and effective procedures for computation of deflections; introduction to plastic analysis, stability, and free and forced vibration analysis, as well as some special topics. Ten years ago, Professor Igor A. Karnovsky and Olga Lebed crafted a must-read book. Now fully updated, expanded, and titled Advanced Methods of Structural Analysis (Strength, Stability, Vibration), the book is ideal for instructors, civil and structural engineers, as well as researches and graduate and post graduate students with an interest in perfecting structural analysis.

"Stability Problems in Applied Mechanics starts with the stability problems in statics. The example of buckling of columns is studed through Euler method followed by the Energy method, based on Lagrange-Dirichlet theorem. Snap buckling, instability of shape, buckling due to follower load are also discussed. Insufficiency of static analysis for instability is clearly brought out and buckling problems are revisited from the point of view of dynamics. The theory of Dynamical System and the foundations of bifurcation theory and Floquet theory are developed and used to revisit the stability problems in the light of these unified mathematical concepts. This mathematical basis is then applied to investigate the stability problems encountered in dynamics of particle, rigid and flexible bodies. Finally the emergence of length scale and pattern formation as a consequence of instability in fluid, thermal and diffusion systems are discussed through a number of real-life problems. Different notions of stability and the analysis of nonlinear states are briefly included in two appendices."--BOOK JACKET.