Remco I. Leine

Bio: Remco I. Leine is an academic researcher from University of Stuttgart. The author has contributed to research in topics: Differential inclusion & Nonlinear system. The author has an hindex of 31, co-authored 105 publications receiving 3933 citations. Previous affiliations of Remco I. Leine include Mechanics' Institute & ETH Zurich.

Dynamics and Bifurcations of Non-Smooth Mechanical Systems

Abstract: 1 Introduction.- 2 Preliminaries on Non-smooth Analysis.- 3 Differential Inclusions.- 4 Modelling of Dry Friction.- 5 Mechanical Systems with Set-valued Force-laws.- 6 Numerical Integration Methods.- 7 Fundamental Solution Matrix.- 8 Bifurcations of Equilibria in Non-smooth Continuous Systems.- 9 Bifurcations of Periodic Solutions.- 10 Concluding Remarks.- References.

Stick-slip vibrations induced by alternate friction models

Abstract: In the present paper a simple and efficient alternate friction model is presented to simulate stick-slip vibrations. The alternate friction model consists of a set of ordinary non-stiff differential equations and has the advantage that the system can be integrated with any standard ODE-solver. Comparison with a smoothing method reveals that the alternate friction model is more efficient from a computational point of view. A shooting method for calculating limit cycles, based on the alternate friction model, is presented. Time-dependent static friction is studied as well as application in a system with 2-DOF.

Bifurcations in Nonlinear Discontinuous Systems

Abstract: This paper treats bifurcations of periodic solutions in discontinuous systems of the Filippov type. Furthermore, bifurcations of fixed points in non-smooth continuous systems are addressed. Filippov's theory for the definition of solutions of discontinuous systems is surveyed and jumps in fundamental solution matrices are discussed. It is shown how jumps in the fundamental solution matrix lead to jumps of the Floquet multipliers of periodic solutions. The Floquet multipliers can jump through the unit circle causing discontinuous bifurcations. Numerical examples are treated which show various discontinuous bifurcations. Also infinitely unstable periodic solutions are addressed.

Stability and Convergence of Mechanical Systems with Unilateral Constraints

Abstract: Stability of motion is a central theme in the dynamics of mechanical systems. While the stability theory for systems with bilateral constraints is a well-established field, this monograph represents a systematic study of mechanical systems with unilateral constraints, such as unilateral contact, impact and friction. Such unilateral constraints give rise to non-smooth dynamical models for which stability theory is developed in this work. The book starts with the treatise of the mathematical background on non-smooth analysis, measure and integration theory and an introduction to the field of non-smooth dynamical systems. The unilateral constraints are modelled in the framework of set-valued force laws developed in the field of non-smooth mechanics. The embedding of these constitutive models in the dynamics of mechanical systems gives rises to dynamical models with impulsive phenomena. This book uses the mathematical framework of measure differential inclusions to formalise such models. The book proceeds with the presentation of stability results for measure differential inclusions. These stability results are then applied to nonlinear mechanical systems with unilateral constraints. The book closes with the study of the convergence property for a class of measure differential inclusions; a stability property for systems with time-varying inputs which is shown to be highly instrumental in the context of the control of mechanical systems with unilateral constraints. While the book presents a profound stability theory for mechanical systems with unilateral constraints, it also has a tutorial value on the modelling of such systems in the framework of measure differential inclusions. The work will be of interest to engineers, scientists and students working in the field of non-smooth mechanics and dynamics.

Stick-Slip Whirl Interaction in Drillstring Dynamics

Abstract: A Stick-slip Whirl Model is presented which is a simplification of an oilwell drillstring confined in a borehole with drilling fluid. The disappearance of stick-slip vibration when whirl vibration appears is explained by bifurcation theory. The numerical results are compared with the experimental data from a full-scale drilling rig.

Solving Ordinary Differential Equations

Abstract: Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

SET-Valued Analysis

Abstract: “Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas. Multivalued analysis is a remarkable mixture of many different parts of mathematics such as point-set topology, measure theory and nonlinear functional analysis. It is also closely related to “Nonsmooth Analysis” (Chapter 5) and in fact one of the main motivations behind the development of the theory, was in order to provide necessary analytical tools for the study of problems in nonsmooth analysis. It is not a coincidence that the development of the two fields coincide chronologically and follow parallel paths. Today multivalued analysis is a mature mathematical field with its own methods, techniques and applications that range from social and economic sciences to biological sciences and engineering. There is no doubt that a modern treatise on “Nonlinear Functional Analysis” can not afford the luxury of ignoring multivalued analysis. The omission of the theory of multifunctions will drastically limit the possible applications.