Dynamics And Stability Of Motion Of Shock And Hybrid Systems

Buy this book on degruyter.com“A href="https://www.degruyter.com/viewbooktoc/product/538686">https://www.degruyter.com/viewbooktoc/product/538686

Publisher Description

This self-contained book provides systematic instructive analysis of uncertain systems of the following types: ordinary differential equations, impulsive equations, equations on time scales, singularly perturbed differential equations, and set differential equations. Each chapter contains new conditions of stability of unperturbed motion of the abo

Thank you for opening the second edition of this monograph, which is devoted to the study of a class of nonsmooth dynamical systems of the general form: ::i; = g(x,u) (0. 1) f(x, t) 2: 0 where x E JRn is the system's state vector, u E JRm is the vector of inputs, and the function f (-, . ) represents a unilateral constraint that is imposed on the state. More precisely, we shall restrict ourselves to a subclass of such systems, namely mechanical systems subject to unilateral constraints on the position, whose dynamical equations may be in a first instance written as: ii= g(q,q,u) (0. 2) f(q, t) 2: 0 where q E JRn is the vector of generalized coordinates of the system and u is an in put (or controller) that generally involves a state feedback loop, i. e. u= u(q, q, t, z), with z= Z(z, q, q, t) when the controller is a dynamic state feedback. Mechanical systems composed of rigid bodies interacting fall into this subclass. A general prop erty of systems as in (0. 1) and (0. 2) is that their solutions are nonsmooth (with respect to time): Nonsmoothness arises primarily from the occurence of impacts (or collisions, or percussions) in the dynamical behaviour, when the trajectories attain the surface f(x, t) = O. They are necessary to keep the trajectories within the subspace = {x : f(x, t) 2: O} of the system's state space.

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. Contents:Nonlinear Flow-Induced Vibration of Structures (C Folley & A Bajaj)Nonlinear Oscillations of Rotors (Y Ishida)Dynamics of High-Speed Axially Moving Material Systems (N Perkins & S-J Hwang)Gyroelastic Dynamics (G D'Eleuterio)Fluid Conveying Pipe with Shear and Compressibility (A Guran & T Atanackovic)Localization Phenomena in Structural Dynamics (C Pierre) Readership: Civil, mechanical and aerospace engineers. keywords: “… is a very useful book for students, lecturers, scientists, and engineers dealing with the stability of mechanical systems in general, and can be recommended for their libraries.” Appl. Mech. Rev. “The book certainly demonstrates the importance of the mentioned fields, and is a valuable contribution to the literature both in the presentation of the subject and in the explanation of occurring phenomena.” Mathematics Abstracts “… The authors succeed in covering a range of important problems in Stability Theory and Nonlinear Mechanics that should appeal to all who are interested in understanding Gyroscopic Systems. Besides the general principles of the motion of systems undergoing rotation about a fixed axis, the book treats applications in Nonlinear Flow-Induced Vibration of Structures, Nonlinear Rotor Dynamics, Dynamics of High-Speed Axially Moving Material Systems, Large Space Vehicles, Repetitive Structures , etc. The authors are experts in these areas and elucidate many important facets of nuclear engineering structures, aerospace structures, turbomachinery, magnetic tape recording devices, belt and chain drives, paper and web handling machinery, bandsaws, robotics, automative and automation industry. Of special interest are two chapters devoted to study the effects of shear deformation and compressibility and to analyse the phenomenon of mode localization in repetitive structures.” Professor F P J Rimrott University of Toronto, Canada