EM Brochure Nonlinear Dynamics 2008

8/2/2019 EM Brochure Nonlinear Dynamics 2008

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Graduate Course

NONLINEAR DYNAMICS

05 - 07 November 200812 - 14 November 2008

Dr.ir. R.H.B. FeyDr.ir. P.J.M. van der Hoogt

Dr.ir. E.L. JansenDr.ir.R.I.Leine

Prof.dr. H. Nijmeijer

Prof.dr.ir. D.J. RixenDr.ir. N. van de Wouw


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General

This course is an initiative of the DutchGraduate School on Engineering Mechanics.Research groups from different universities

(TU/e, UT and TUD) are actively contributingto this course. The course is part of the 3TUEngineering Mechanics training program forPhD students. As part of this program aseries of graduate courses is organized,related to the following research themes:

Computational and ExperimentalMechanics of Materials

Structural Dynamics and Control

Reliability and Optimization

Objective

The course Nonlinear Dynamics highlightsthe fact that essentially all dynamicalsystems encountered in the real world are tosome extend nonlinear, meaning that theirdescription as differential equations containsnonlinear terms. Such nonlinearities appearin various ways, such as through frictionalterms, coriolis and centrifugal terms, large

amplitude effects, or other structuralnonlinearities. The nonlinearities make thatstandard linear dynamics not alwayssuffices for the analysis and understandingof nonlinear mechanical (or biological,economic, physical) systems. Moreover, akey feature of the course is to investigateand study parameter-dependency of asystem, i.e. to investigate thestability/instability of equilibria or periodicsolutions under the influence of certainparameters. Various examples and

laboratory illustrations will be given duringthe course, and these will also be used forhands-on exercises. Students who attendthe course will at the end have a properknowledge on (in-)stability of complexnonlinear dynamic systems.

Lecturers

Delft University of Technology Dr.ir. E.L. Jansen Prof.dr.ir. D. Rixen

Eindhoven University of Technology Dr.ir. R.H.B. Fey Prof.dr. H. Nijmeijer Dr.ir. N. van de Wouw

University of Twente Dr.ir. P.J.M. van der Hoogt

ETH Zurich Dr.ir. R.I.Leine

Lecture notes

Lecture notes will be distributed during thecourse.

Poster session

An informal poster session will be organizedon the first day of the course. This session

aims to share all challenges in NONLINEARDYNAMICS from the perspective of theparticipants, providing a clear view of thebackground of all related research projectsand individuals. All participants are invited toprepare a poster and present it on the firstday.

PrerequisitesBasic undergraduate courses in Calculus and

/ or Differential Equations, Dynamics, LinearAlgebra, Mechanical Vibration


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Contents

Part 1 of the Graduate course is located at University of Twente:

Day 1 Introduction (Lecturer: Peter van der Hoogt)

Fundamental concepts in stability. Equilibrium Points Small motions from equilibrium Conservative systems. Motions in the large Limit cycles. The van der Pol oscillator Pertubation Techniques Forced oscillations of quasi-harmonic systems (Jump phenomenon, inc. demonstration) Systems with time-dependent coefficients (Parametrically excited pendulum, incl. demonstration)

Day 2 (Lecturer: Eelco Jansen)

Elementary models for nonlinear vibration and dynamic stability analysis of structures: Governingdifferential equations for basic structural elements (beams, plates, and shells), including initialgeometric imperfections and static preload. Geometrical nonlinearity. Solution methods for spatialand temporal problem. Basic analytical and numerical methods.

Nonlinear (free and forced) vibration of structural elements: Hardening and softening behavior,modal interaction.

Dynamic stability of structural elements: Concepts of dynamic stability. Dynamic buckling under in-plane step load and impulsive load, parametric excitation by in-plane pulsating load.

Day 3 (Lecturers: Daniel Rixen and Eelco Jansen)

Time integration for nonlinear systems. Reduced basis methods in Finite Element nonlinear dynamic analysis. Nonlinear (free and forced) vibration analysis using reduced basis methods.

Nonlinear transient analysis and dynamic stability analysis using reduced basis methods.

Part 2 of the Graduate course is located at Eindhoven University ofTechnology:

Day 4, 5, 6 (Lecturers: Henk Nijmeijer, Nathan van de Wouw, Remco Leine and Rob Fey)

Nonlinear dynamic systems, fundamentals, mathematical prerequisites, and examples Phase portraits of 2-dimensional systems, Bendixons criterion

Lyapunov stability, Lyapunov functions, LaSalles invariance principle, Lyapunov equation,mechanical examples

Parameter-dependency, bifurcations, basic examples, fold-bifurcation, Hopf-bifurcation Periodic orbits, multiple equilibria, chaos, Numerical tools for computing periodic orbits Dynamic stability analysis of structures. Case studies in which semi-analytic modeling and

advanced nonlinear dynamics tools and concepts are combined. Key words: semi-analytic (multi-dof) models, modern numerical analysis, experimental verification (lab demo), imperfections,parametric and direct harmonic excitation, nonlinear resonances, bifurcations, chaos (beating),multiple solutions, snap-through behaviour, structural optimization for shock excitation.

Nonsmooth dynamical systems


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Locations and dates

The course will take place in two modules ofthree days each.

The first module will take place at theUniversity of Twente (Faculty ofEngineering Technology) on 5-7

November 2008.

The second module at the EindhovenUniversity of Technology, Department ofMechanical Engineering, on 12-14November 2008.

The course language is English.

Hotel accommodation

For hotel accommodation on the UT

Campus visit www.drienerburght.nl

For hotel accommodation in the vicinity ofthe TU/e:

A reasonably priced hotel is Hotel vanNeer Kronehoefstraat 10, Eindhoven(phone: 040-2433436) and

Training hotel De Rooi Pannen,Kaakstraat 1, Eindhoven (phone 013-8506555); http://www.derooipannen.nl .

Participants are required to contact the

hotels directly.

Further information

On the contents of the course:Prof. Dr. H. NijmeijerPhone: +31- (0)40- 2473203Email: [email protected]

On the organization of the course:

Mrs. W. van den Oever, TU/e,Phone: +31-(0)40-2474696Email: [email protected]

Registration andCourse fee

Participants need to register by completingthe enclosed registration form and returningit before October 15th, 2008 to:

Graduate School on EngineeringMechanicsc/o Eindhoven University of Technology,Mrs. W. van den Oever,P.O. Box 513, W-hoog 2.113,5600 MB Eindhoven NL,Fax: +31-(0)40-2437175.

Members of the Graduate School onEngineering Mechanics receive priority in

case of over-subscription.

The course is free for registeredmembers of the Graduate School onEngineering Mechanics.

For registered members of GrasMechthe course fee is 200.

For other participants the course fee is 1000.

Participants will receive an invoice afteraccepted registration.

Upcoming courses

For further information on graduate coursesand other activities of the Graduate Schoolon Engineering Mechanics please visit ourwebsite at:

http://www.em.tue.nl
http://www.drienerburght.nl/http://www.derooipannen.nl/mailto:[email protected]:[email protected]://www.em.tue.nl/http://www.em.tue.nl/mailto:[email protected]:[email protected]://www.derooipannen.nl/http://www.drienerburght.nl/

EM Brochure Nonlinear Dynamics 2008

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