Boundary Element Method For Nonlinear Modal Analysis Of Systems Undergoing Unilateral Contact

Download Boundary Element Method For Nonlinear Modal Analysis Of Systems Undergoing Unilateral Contact full books in PDF, epub, and Kindle. Read online Boundary Element Method For Nonlinear Modal Analysis Of Systems Undergoing Unilateral Contact ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Boundary Element Method for Nonlinear Modal Analysis of Systems Undergoing Unilateral Contact

Author : Jayantheeswar Venkatesh
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (11 download)

DOWNLOAD NOW!

Book Synopsis Boundary Element Method for Nonlinear Modal Analysis of Systems Undergoing Unilateral Contact by : Jayantheeswar Venkatesh

Download or read book Boundary Element Method for Nonlinear Modal Analysis of Systems Undergoing Unilateral Contact written by Jayantheeswar Venkatesh and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "In structural dynamics, autonomous conservative systems commonly exhibit continuous families of periodic orbits in the phase space, usually known as modes of vibration. The main task of modal analysis is to accurately compute natural frequencies and corresponding mode shapes of vibratory mechanical systems as they are known, at least in a linear context, to properly predict the conditions under which the associated periodically forced and slightly damped systems will resonate.Characterizing the modes of vibration of nonlinear yet smooth mechanical systems (systems governed by ordinary or partial differential equations that are smooth with respect to the unknown displacement and velocity) is a current topic of interest in the industrial and academic spheres. Many useful tools, such as the Finite Element Method (FEM), the Harmonic Balance Method (HBM), the continuation techniques and the Frequency--Energy Plots (FEP) provide great assistance in understanding the modal dynamics. Theoretical as well as numerical issues arise when extending these tools to nonsmooth problems such as unilateral contact formulations. The dynamics of two impacting bodies is characterized by travelling waves emanating from the contact interface. In the one-dimensional setting, chosen in this work, these waves couple time and space, in the sense that they are functions of the form f(x+ct) or f(x-ct) where c is the wave velocity. Uncoupling time t and space x leads to numerical and theoretical issues. In FEM, the displacement commonly takes the form u(x,t)= \sum_i \phi_i(x) u_i(t), where u_i(t) is the i-th displacement participation and \phi_i(x), the corresponding shape function. This leads to spurious oscillations, dispersion, and energy dissipation, for most numerical schemes dealing with unilateral contact conditions. Additionally, an impact law is required to uniquely describe the time-evolution of a space semi-discretized formulation. The impact law should be purely elastic to preserve energy, making it difficult to describe lasting contact phases which are expected in the continuous framework. Time-Domain Boundary Element Medthod (TD-BEM) which appropriately combines space and time seems promising as it uses Green's functions that are travelling waves.In this work, unilateral contact conditions are considered for a one-dimensional bar system clamped on one end and undergoing a complementarity condition on the other end. The complementarity form is dealt with as a switch between Dirichlet and Neumann boundary conditions. In dynamics, the solution can thus be retrieved through time marching using TD-BEM with a switch between fixed state when it is in contact and free when it is released. In vibration analysis of autonomous systems, periodic solutions are sought to obtain the mode shapes of the system. In this thesis, TD-BEM presumes the existence of periodic solutions and shooting is employed to find the initial conditions that lead to the assumed periodic solutions. Backbone curves in frequency-energy are constructed via continuation. Existing analytical solutions serve as references for validating the suggested scheme. TD-BEM does not numerically dissipate energy unlike FEM and properly captures wave fronts as expected. The proposed formulation is capable of capturing main, subharmonic as well as internal resonance backbone curves known to emerge in nonlinear dynamics. For the system of interest, the main and subharmonic mode shapes are piecewise-linear function in space and time, as opposed to the linear mode shapes that are half sine waves in space and full sine waves in time." --

Boundary Element Methods

Author : S. Kobayashi
Publisher : Springer Science & Business Media
ISBN 13 : 3662061538
Total Pages : 422 pages
Book Rating : 4.6/5 (62 download)

DOWNLOAD NOW!

Book Synopsis Boundary Element Methods by : S. Kobayashi

Download or read book Boundary Element Methods written by S. Kobayashi and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Boundary Element Methods (BEM) has become one of the most efficient tools for solving various kinds of problems in engineering science. The International Association for Boundary Element Methods (IABEM) was established in order to promote and facilitate the exchange of scientific ideas related to the theory and applications of boundary element methods. The aim of this symposium is to provide a forum for researchers in boundary element methods and boundary-integral formulations in general to present contemporary concepts and techniques leading to the advancement of capabilities and understanding of this com putational methodology. The topics covered in this symposium include mathematical and computational aspects, applications to solid mechanics, fluid mechanics, acoustics, electromagnetics, heat transfer, optimization, control, inverse problems and other interdisciplinary problems. Papers deal ing with the coupling of the boundary element method with other computational methods are also included. The editors hope that this volume presents some innovative techniques and useful knowl edge for the development of the boundary element methods. February, 1992 S. Kobayashi N. Nishimura Contents Abe, K.

Boundary Element Methods for Engineers and Scientists

Author : Lothar Gaul
Publisher : Springer Science & Business Media
ISBN 13 : 3662051362
Total Pages : 491 pages
Book Rating : 4.6/5 (62 download)

DOWNLOAD NOW!

Book Synopsis Boundary Element Methods for Engineers and Scientists by : Lothar Gaul

Download or read book Boundary Element Methods for Engineers and Scientists written by Lothar Gaul and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past decades, the Boundary Element Method has emerged as a ver satile and powerful tool for the solution of engineering problems, presenting in many cases an alternative to the more widely used Finite Element Method. As with any numerical method, the engineer or scientist who applies it to a practical problem needs to be acquainted with, and understand, its basic principles to be able to apply it correctly and be aware of its limitations. It is with this intention that we have endeavoured to write this book: to give the student or practitioner an easy-to-understand introductory course to the method so as to enable him or her to apply it judiciously. As the title suggests, this book not only serves as an introductory course, but also cov ers some advanced topics that we consider important for the researcher who needs to be up-to-date with new developments. This book is the result of our teaching experiences with the Boundary Element Method, along with research and consulting activities carried out in the field. Its roots lie in a graduate course on the Boundary Element Method given by the authors at the university of Stuttgart. The experiences gained from teaching and the remarks and questions of the students have contributed to shaping the 'Introductory course' (Chapters 1-8) to the needs of the stu dents without assuming a background in numerical methods in general or the Boundary Element Method in particular.

Nonsmooth Modal Analysis of a Finite Elastic Bar Subject to a Unilateral Contact Constraint

Author : Carlos Yoong Ormaza
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (111 download)

DOWNLOAD NOW!

Book Synopsis Nonsmooth Modal Analysis of a Finite Elastic Bar Subject to a Unilateral Contact Constraint by : Carlos Yoong Ormaza

Download or read book Nonsmooth Modal Analysis of a Finite Elastic Bar Subject to a Unilateral Contact Constraint written by Carlos Yoong Ormaza and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "This dissertation proposes a methodology to perform nonsmooth modal analysis of a simplified prototype system in the form of a finite elastic bar whose motion is unilaterally restricted by a rigid obstacle on the boundary. Mathematically, the problem reduces to finding periodic solutions to the well-known autonomous wave equation together with a switching mechanism between Dirichlet and Neumann boundary conditions. Closed-form expressions of such nonsmooth modes of vibration exist only under special simplifying assumptions. In a more general context, numerical techniques shall be employed to approximate them. Previous investigations have shown that the traditional Finite Element Method in conjunction with a time-stepping technique fails on approximating solutions to unilateral contact problems, for two main reasons: (1) numerical energy dissipation and dispersion are introduced, and (2) a questionable chattering phenomenon might arise at the contact interface. In the present work, the one-dimensional Wave Finite Element Method (WFEM) is instead utilized in the discretization of the governing wave equation. This approach is a shock-capturing Finite Volume Method capable of accurately simulating the propagation of discontinuous pressure waves without the above numerical issues, which is crucial for seeking unilaterally constrained periodic trajectories. Also, it should be noted that the WFEM does not require a supplementary impact law for the well-posedness of the problem. The contact constraints are enforced by switching the appropriate boundary conditions from Dirichlet (closed contact) to Neumann (open contact). A detailed study is conducted on two distinct settings: (1) an internally resonant bar and (2) a non-internally resonant bar. The internally resonant system satisfies a complete internal resonance condition, i.e. all natural frequencies are commensurate with the first one, which has drastic consequences on the nonsmooth modal analysis. Both settings are analyzed on three bar configurations: initially unstressed, initially grazing and initially prestressed. In line with shooting methods, nonsmooth modal analysis via the WFEM is expressed as a constrained power-like eigenvalue problem in terms of the initial conditions and the period of vibration. Numerical results show that the unilaterally constrained bar features sophisticated autonomous dynamics, involving main, subharmonic and internally resonant nonsmooth modes. In contrast to the linear system (without unilateral contact conditions) whose modes of vibration are standing harmonic waves, nonsmooth modes of vibration are shown to be periodic travelling shock waves generated by the unilateral contact constraints. The frequency-energy "nonlinear" spectrum reveals that the unstressed and prestressed settings undergo hardening and stiffening behaviours respectively. The initially grazing case mimics a linear spectrum exhibiting constant nonlinear natural frequencies distinct from the linear ones. A brief insight on the stability of nonsmooth modes is also provided. For the internally resonant bar, closed-form expressions are conjectured by first proving that the periodic motions that pertain to a nonsmooth mode must be piecewise linear functions of space and time. It is also shown that vibratory resonances of the periodically-driven system of interest embedding light structural damping are well predicted by nonsmooth modal analysis, as expected. " --

Nonlinear Structures and Systems, Volume 1

Author : Gaetan Kerschen
Publisher : Springer
ISBN 13 : 303012391X
Total Pages : 271 pages
Book Rating : 4.0/5 (31 download)

DOWNLOAD NOW!

Book Synopsis Nonlinear Structures and Systems, Volume 1 by : Gaetan Kerschen

Download or read book Nonlinear Structures and Systems, Volume 1 written by Gaetan Kerschen and published by Springer. This book was released on 2019-06-28 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Structures & Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics, 2019, the first volume of eight from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Nonlinear Reduced-order Modeling Jointed Structures: Identification, Mechanics, Dynamics Experimental Nonlinear Dynamics Nonlinear Model & Modal Interactions Nonlinear Damping Nonlinear Modeling & Simulation Nonlinearity & System Identification

Progress in Boundary Element Methods

Author : BREBBIA
Publisher : Springer Science & Business Media
ISBN 13 : 147576300X
Total Pages : 226 pages
Book Rating : 4.4/5 (757 download)

DOWNLOAD NOW!

Book Synopsis Progress in Boundary Element Methods by : BREBBIA

Download or read book Progress in Boundary Element Methods written by BREBBIA and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: A substantial amount of research on Boundary Elements has taken place since publication of the first Volume of this series. Most of the new work has concentrated on the solution of non-linear and time dependent problems and the development of numerical techniques to increase the efficiency of the method. Chapter 1 of this Volume deals with the solution of non-linear potential problems, for which the diffusivity coefficient is a function of the potential and the boundary conditions are also non-linear. The recent research reported here opens the way for the solution of a: large range of non-homogeneous problems by using a simple transformation which linearizes the governing equations and consequently does not require the use of internal cells. Chapter 2 summarizes the main integral equations for the solution of two-and three dimensional scalar wave propagation problems. This is a type of problem that is well suited to boundary elements but generally gives poor results when solved using finite elements. The problem of fracture mechanics is studied in Chapter 3, where the ad vantages of using boundary integral equations are demonstrated. One of the most interesting features of BEM i~ the possibility of describing the problem only as a function of the boundary unknowns, even in the presence of body, centrifugal and temperature induced forces. Chapter 4 explains how this can be done for two-and three-dimensional elastostatic problems.

Advanced Boundary Element Methods

Author : Joachim Gwinner
Publisher : Springer
ISBN 13 : 3319920014
Total Pages : 661 pages
Book Rating : 4.3/5 (199 download)

DOWNLOAD NOW!

Book Synopsis Advanced Boundary Element Methods by : Joachim Gwinner

Download or read book Advanced Boundary Element Methods written by Joachim Gwinner and published by Springer. This book was released on 2018-07-28 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic and electromagnetic scattering. It serves as the mathematical foundation of the boundary element methods (BEM) both for static and dynamic problems. The book presents a systematic approach to the variational methods for boundary integral equations including the treatment with variational inequalities for contact problems. It also features adaptive BEM, hp-version BEM, coupling of finite and boundary element methods – efficient computational tools that have become extremely popular in applications. Familiarizing readers with tools like Mellin transformation and pseudodifferential operators as well as convex and nonsmooth analysis for variational inequalities, it concisely presents efficient, state-of-the-art boundary element approximations and points to up-to-date research. The authors are well known for their fundamental work on boundary elements and related topics, and this book is a major contribution to the modern theory of the BEM (especially for error controlled adaptive methods and for unilateral contact and dynamic problems) and is a valuable resource for applied mathematicians, engineers, scientists and graduate students.

Boundary Element Methods in Nonlinear Fluid Dynamics

Author : P.K. Banerjee
Publisher : CRC Press
ISBN 13 : 1482296551
Total Pages : 368 pages
Book Rating : 4.4/5 (822 download)

DOWNLOAD NOW!

Book Synopsis Boundary Element Methods in Nonlinear Fluid Dynamics by : P.K. Banerjee

Download or read book Boundary Element Methods in Nonlinear Fluid Dynamics written by P.K. Banerjee and published by CRC Press. This book was released on 1990-05-31 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume demonstrates that boundary element methods are both elegant and efficient in their application to time dependent time harmonic problems in engineering and therefore worthy of considerable development.

The Boundary Element Method, Volume 1

Author : L. C. Wrobel
Publisher : John Wiley & Sons
ISBN 13 : 9780471720393
Total Pages : 480 pages
Book Rating : 4.7/5 (23 download)

DOWNLOAD NOW!

Book Synopsis The Boundary Element Method, Volume 1 by : L. C. Wrobel

Download or read book The Boundary Element Method, Volume 1 written by L. C. Wrobel and published by John Wiley & Sons. This book was released on 2002-04-22 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The boundary element method (BEM) is a modern numerical techniquewhich has enjoyed increasing popularity over the last two decades,and is now an established alternative to traditional computationalmethods of engineering analysis. The main advantage of the BEM isits unique ability to provide a complete solution in terms ofboundary values only, with substantial savings in modelling effort. This two-volume book set is designed to provide the readers with acomprehensive and up-to-date account of the boundary element methodand its application to solving engineering problems. Each volume isa self-contained book including a substantial amount of materialnot previously covered by other text books on the subject. Volume 1covers applications to heat transfer, acoustics, electrochemistryand fluid mechanics problems, while volume 2 concentrates on solidsand structures, describing applications to elasticity, plasticity,elastodynamics, fracture mechanics and contact analysis. The earlychapters are designed as a teaching text for final yearundergraduate courses. Both volumes reflect the experience of theauthors over a period of more than twenty years of boundary element research. This volume, Applications in Thermo-Fluids and Acoustics, provides acomprehensive presentation of the BEM from fundamentals to advancedengineering applications and encompasses: Steady and transient heat transfer Potential and viscous fluid flows Frequency and time-domain acoustics Corrosion and other electrochemical problems. A unique feature of this book is an in-depth presentation of BEMformulations in all the above fields, including detaileddiscussions of the basic theory, numerical algorithms and practicalengineering applications of the method. Written by an internationally recognised authority in the field,this is essential reading for postgraduates, researchers andpractitioners in civil, mechanical and chemical engineering andapplied mathematics.

Boundary Elements in Nonlinear Fracture Mechanics

Author : V. M. A. Leitão
Publisher : Computational Mechanics
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!

Book Synopsis Boundary Elements in Nonlinear Fracture Mechanics by : V. M. A. Leitão

Download or read book Boundary Elements in Nonlinear Fracture Mechanics written by V. M. A. Leitão and published by Computational Mechanics. This book was released on 1994 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Boundary Element Methods in Engineering

Author : Balkrishna S. Annigeri
Publisher : Springer Science & Business Media
ISBN 13 : 3642842380
Total Pages : 596 pages
Book Rating : 4.6/5 (428 download)

DOWNLOAD NOW!

Book Synopsis Boundary Element Methods in Engineering by : Balkrishna S. Annigeri

Download or read book Boundary Element Methods in Engineering written by Balkrishna S. Annigeri and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Boundary Element Method (BEM) has become established as an effective tool for the solutions of problems in engineering science. The salient features of the BEM have been well documented in the open literature and therefore will not be elaborated here. The BEM research has progressed rapidly, especially in the past decade and continues to evolve worldwide. This Symposium was organized to provide an international forum for presentation of current research in BEM for linear and nonlinear problems in solid and fluid mechanics and related areas. To this end, papers on the following topics were included: rotary wing aerodynamics, unsteady aerodynamics, design and optimization, elasticity, elasto dynamics and elastoplasticity, fracture mechanics, acoustics, diffusion and wave motion, thermal analysis, mathematical aspects and boundary/finite element coupled methods. A special session was devoted to parallel/vector supercomputing with emphasis on mas sive parallelism. This Symposium was sponsored by United Technologies Research Center (UTRC) , NASA Langley Research Center, and the International Association of Boundary Ele ment Methods (lAB EM) . We thank the UTRC management for their permission to host this Symposium. In particular, we thank Dr. Arthur S. Kesten and Mr. Robert E. Olson for their encouragement and support. We gratefully acknowledge the support of Dr. E. Carson Yates, Jr. of NASA Langley, Prof. Luigi Morino, Dr. Thomas A.

The Boundary Element Method

Author : A. Ali
Publisher : CRC Press
ISBN 13 : 9789058096579
Total Pages : 212 pages
Book Rating : 4.0/5 (965 download)

DOWNLOAD NOW!

Book Synopsis The Boundary Element Method by : A. Ali

Download or read book The Boundary Element Method written by A. Ali and published by CRC Press. This book was released on 2004-08-15 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Boundary Element Method, or BEM, is a powerful numerical analysis tool with particular advantages over other analytical methods. With research in this area increasing rapidly and more uses for the method appearing, this timely book provides a full chronological review of all techniques that have been proposed so far, covering not only the fundamentals of the BEM but also a wealth of information on related computational analysis techniques and formulations, and their applications in engineering, physics and mathematics. An indispensable handbook and source of inspiration for researchers and professionals in these fields, this book is also an ideal textbook for graduate engineering students.

Linear and Nonlinear Dynamic Analysis by Boundary Element Method

Author : Shahid Ahmad
Publisher :
ISBN 13 :
Total Pages : 229 pages
Book Rating : 4.:/5 (499 download)

DOWNLOAD NOW!

Book Synopsis Linear and Nonlinear Dynamic Analysis by Boundary Element Method by : Shahid Ahmad

Download or read book Linear and Nonlinear Dynamic Analysis by Boundary Element Method written by Shahid Ahmad and published by . This book was released on 1986 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Boundary Element Method with Programming

Author : Gernot Beer
Publisher : Springer Science & Business Media
ISBN 13 : 3211715762
Total Pages : 496 pages
Book Rating : 4.2/5 (117 download)

DOWNLOAD NOW!

Book Synopsis The Boundary Element Method with Programming by : Gernot Beer

Download or read book The Boundary Element Method with Programming written by Gernot Beer and published by Springer Science & Business Media. This book was released on 2008-09-03 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thorough yet understandable introduction to the boundary element method presents an attractive alternative to the finite element method. It not only explains the theory but also presents the implementation of the theory into computer code, the code in FORTRAN 95 can be freely downloaded. The book also addresses the issue of efficiently using parallel processing hardware in order to considerably speed up the computations for large systems. The applications range from problems of heat and fluid flow to static and dynamic elasto-plastic problems in continuum mechanics.

Boundary Element Methods

Author : Q. Du
Publisher : Elsevier
ISBN 13 : 1483297942
Total Pages : 429 pages
Book Rating : 4.4/5 (832 download)

DOWNLOAD NOW!

Book Synopsis Boundary Element Methods by : Q. Du

Download or read book Boundary Element Methods written by Q. Du and published by Elsevier. This book was released on 2014-05-23 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significant developments in the boundary element method during the last two decades have made it a powerful alternative to the domain-type numerical methods of solution such as the finite element method. The advances made in the BEM are more or less due to the innovation of efficient computational techniques by introducing boundary elements for discretization of the boundary integral equations resulting from the so-called direct formulation. BEM has therefore become an efficient tool for optimal design and other inverse problems. These proceedings include discussion of the applications of BEM in mechanical engineering and the principles that have developed to make it an increasingly useful method of problem solving.

Boundary Element Method in Geomechanics

Author : W. S. Venturini
Publisher : Springer
ISBN 13 :
Total Pages : 262 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!

Book Synopsis Boundary Element Method in Geomechanics by : W. S. Venturini

Download or read book Boundary Element Method in Geomechanics written by W. S. Venturini and published by Springer. This book was released on 1983 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical techniques for solving many problems in continuum mechanics have experienced a tremendous growth in the last twenty years due to the development of large high speed computers. In particular, geomechanical stress analysis can now be modelled within a more realistic context. In spite of the fact that many applications in geomechanics are still being carried out applying linear theories, soil and rock materials have been demonstrated experimentally to be physically nonlinear. Soils do not recover their initial state after removal of temporary loads and rock does not deform in proportion to the loads applied. The search for a unified theory to model the real response of these materials is impossible due to the complexities involved in each case. Realistic solutions in geomechanical analysis must be provided by considering that material properties vary from point to point, in addition to other significant features such as non-homogeneous media, in situ stress condition, type of loading, time effects and discontinuities. A possible alternative to tackle such a problem is to inttoduce some simplified assumptions which at least can provide an approximate solution in each case. The validity or accuracy of the final solution obtained is always dependent upon the approach adopted. As a consequence, the choice of a reliable theory for each particular problem is another difficult decision which should be 2 taken by the analyst in geomechanical stress analysis.

Advanced Topics in Nonsmooth Dynamics

Author : Remco Leine
Publisher : Springer
ISBN 13 : 3319759728
Total Pages : 462 pages
Book Rating : 4.3/5 (197 download)

DOWNLOAD NOW!

Book Synopsis Advanced Topics in Nonsmooth Dynamics by : Remco Leine

Download or read book Advanced Topics in Nonsmooth Dynamics written by Remco Leine and published by Springer. This book was released on 2018-06-07 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses emerging topics in the area of nonsmooth dynamics research, such as numerical methods for nonsmooth systems, impact laws for multi-collisions, nonlinear vibrations and control of nonsmooth systems. It documents original work of researchers at the European Network for NonSmooth Dynamics (ENNSD), which provides a cooperation platform for researchers in the field and promotes research focused on nonsmooth dynamics and its applications. Since the establishment of the network in 2012, six ENNSD symposia have been organized at different European locations. The network brings together 40 specialists from 9 different countries in and outside Europe and a wealth of scientific knowledge has been gathered and developed by this group of experts in recent years. The book is of interest to both new and experienced researchers in the field of nonsmooth dynamics. Each chapter is written in such a way as to provide an introduction to the topic for researchers from other fields.