Download Free Nonlinear Deformable Body Dynamics Book in PDF and EPUB Free Download. You can read online Nonlinear Deformable Body Dynamics and write the review.

"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of nonlinear dynamics in dynamical systems and deformable solids.
This book offers a recipe for constructing the numerical models for representing the complex nonlinear behavior of structures and their components, represented as deformable solid bodies. Its appeal extends to those interested in linear problems of mechanics.
This book presents theories of deformable elastic strings and rods and their application to broad classes of problems. Readers will gain insights into the formulation and analysis of models for mechanical and biological systems. Emphasis is placed on how the balance laws interplay with constitutive relations to form a set of governing equations. For certain classes of problems, it is shown how a balance of material momentum can play a key role in forming the equations of motion. The first half of the book is devoted to the purely mechanical theory of a string and its applications. The second half of the book is devoted to rod theories, including Euler’s theory of the elastica, Kirchhoff ’s theory of an elastic rod, and a range of Cosserat rod theories. A variety of classic and recent applications of these rod theories are examined. Two supplemental chapters, the first on continuum mechanics of three-dimensional continua and the second on methods from variational calculus, are included to provide relevant background for students. This book is suited for graduate-level courses on the dynamics of nonlinearly elastic rods and strings.
The book focuses on the nonlinear dynamics based on the vector fields with bivariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems based on bivariate vector fields. Such a book provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems on linear and nonlinear bivariate manifolds. Possible singular dynamics of the two-dimensional quadratic systems is discussed in detail. The dynamics of equilibriums and one-dimensional flows on bivariate manifolds are presented. Saddle-focus bifurcations are discussed, and switching bifurcations based on infinite-equilibriums are presented. Saddle-focus networks on bivariate manifolds are demonstrated. This book will serve as a reference book on dynamical systems and control for researchers, students and engineering in mathematics, mechanical and electrical engineering.
This book contains an edited versIOn of lectures presented at the NATO ADVANCED STUDY INSTITUTE on VIRTUAL NONLINEAR MUL TIBODY SYSTEMS which was held in Prague, Czech Republic, from 23 June to 3 July 2002. It was organized by the Department of Mechanics, Faculty of Mechanical Engineering, Czech Technical University in Prague, in cooperation with the Institute B of Mechanics, University of Stuttgart, Germany. The ADVANCED STUDY INSTITUTE addressed the state of the art in multibody dynamics placing special emphasis on nonlinear systems, virtual reality, and control design as required in mechatronics and its corresponding applications. Eighty-six participants from twenty-two countries representing academia, industry, government and research institutions attended the meeting. The high qualification of the participants contributed greatly to the success of the ADVANCED STUDY INSTITUTE in that it promoted the exchange of experience between leading scientists and young scholars, and encouraged discussions to generate new ideas and to define directions of research and future developments. The full program of the ADVANCED STUDY INSTITUTE included also contributed presentations made by participants where different topics were explored, among them: Such topics include: nonholonomic systems; flexible multibody systems; contact, impact and collision; numerical methods of differential-algebraical equations; simulation approaches; virtual modelling; mechatronic design; control; biomechanics; space structures and vehicle dynamics. These presentations have been reviewed and a selection will be published in this volume, and in special issues of the journals Multibody System Dynamics and Mechanics of Structures and Machines.
This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics, control systems, and engineering.
This book focuses on the nonlinear dynamics based on the vector fields with univariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems. It provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems. Such a two-dimensional dynamical system is one of simplest dynamical systems in nonlinear dynamics, but the local and global structures of equilibriums and flows in such two-dimensional quadratic systems help us understand other nonlinear dynamical systems, which is also a crucial step toward solving the Hilbert’s sixteenth problem. Possible singular dynamics of the two-dimensional quadratic systems are discussed in detail. The dynamics of equilibriums and one-dimensional flows in two-dimensional systems are presented. Saddle-sink and saddle-source bifurcations are discussed, and saddle-center bifurcations are presented. The infinite-equilibrium states are switching bifurcations for nonlinear systems. From the first integral manifolds, the saddle-center networks are developed, and the networks of saddles, source, and sink are also presented. This book serves as a reference book on dynamical systems and control for researchers, students, and engineering in mathematics, mechanical, and electrical engineering.
A method of the spatial kinematic and dynamic analysis of deformable multibody systems subject to topology changes and impacts is presented. A pieced interval analysis scheme that accounts for the change in the spatial system topology due to the changes on the connectivity between bodies is developed. Deformable bodies in the system are discretized using the finite element method and accordingly a finite set of deformation modes is employed to characterize the system vibration. Even though there are infinitely many arrangements for deformable body axes, computational difficulties may be encountered due to the use of a limited number of deformation modes. Therefore, the deformable body references have to be carefully selected, and accordingly as the system topology changes, new bases for the configuration space to another, a set of spatial interface conditions or compatibility conditions that are formulated using a set of nonlinear algebraic equations are developed. The solution of these equations uniquely define the spatial configuration of the deformable multibody system after the change in the system kinematic structure. The techniques proposed in this research are applied to several technological system such as robotic manipulators and weapon systems. Keywords: Spatial kinematics; Dynamic analysis; Deformable multibody systems; Interval analysis scheme; Nonlinear algebraic equations.
A unique approach to teaching particle and rigid body dynamics using solved illustrative examples and exercises to encourage self-learning The study of particle and rigid body dynamics is a fundamental part of curricula for students pursuing graduate degrees in areas involving dynamics and control of systems. These include physics, robotics, nonlinear dynamics, aerospace, celestial mechanics and automotive engineering, among others. While the field of particle and rigid body dynamics has not evolved significantly over the past seven decades, neither have approaches to teaching this complex subject. This book fills the void in the academic literature by providing a uniquely stimulating, “flipped classroom” approach to teaching particle and rigid body dynamics which was developed, tested and refined by the author and his colleagues over the course of many years of instruction at both the graduate and undergraduate levels. Complete with numerous solved illustrative examples and exercises to encourage self-learning in a flipped-classroom environment, Dynamics of Particles and Rigid Bodies: A Self-Learning Approach: Provides detailed, easy-to-understand explanations of concepts and mathematical derivations Includes numerous flipped-classroom exercises carefully designed to help students comprehend the material covered without actually solving the problem for them Features an extensive chapter on electromechanical modelling of systems involving particle and rigid body motion Provides examples from the state-of-the-art research on sensing, actuation, and energy harvesting mechanisms Offers access to a companion website featuring additional exercises, worked problems, diagrams and a solutions manual Ideal as a textbook for classes in dynamics and controls courses, Dynamics of Particles and Rigid Bodies: A Self-Learning Approach is a godsend for students pursuing advanced engineering degrees who need to master this complex subject. It will also serve as a handy reference for professional engineers across an array of industrial domains.
Dynamics of Multibody Systems, 3rd Edition, first published in 2005, introduces multibody dynamics, with an emphasis on flexible body dynamics. Many common mechanisms such as automobiles, space structures, robots and micromachines have mechanical and structural systems that consist of interconnected rigid and deformable components. The dynamics of these large-scale, multibody systems are highly nonlinear, presenting complex problems that in most cases can only be solved with computer-based techniques. The book begins with a review of the basic ideas of kinematics and the dynamics of rigid and deformable bodies before moving on to more advanced topics and computer implementation. This revised third edition now includes important developments relating to the problem of large deformations and numerical algorithms as applied to flexible multibody systems. The book's wealth of examples and practical applications will be useful to graduate students, researchers, and practising engineers working on a wide variety of flexible multibody systems.