Course code: wb1412

Course name: Linear and nonlinear vibrations in mechanical systems

This concerns a Course

ECTS credit points: 3

Faculty of Mechanical Engineering and Marine Technology

Section of Engineering Mechanics

Lecturer(s): Woerkom, dr. ir. P.T.L.M. van

Tel.:  015 - 27 82792 /      

Catalog data:

- Introduction and review of linear vibration theory.

- Occurrence and types of linear and nonlinear mechanical vibrations.

- Analysis of linear and nonlinear vibrations in discrete mechanical systems.

- Suppression of vibrations.

- Introduction of nonlinear vibrations in continuum systems.

Course year:

MSc 1^st year

Course language:

English

In case of Dutch: Please contact the lecturer about an English alternative, whenever needed.

Semester:

2A / 2B

Hours per week:

2

Other hours:

Assessment:

Written report

Assessment period:

 /  /

(see academic calendar)

Prerequisites (course codes):

wb1216, wi2051wb, wi3097wb

Follow up (course codes):

Detailed description of topics:

- Introduction: review of linear vibration theory, sources of excitation, nonlinear vibrations in mechanical systems.

- Occurrence and types of mechanical vibrations: forced vibrations, self-excited vibrations, stick-slip vibrations, limit cycles, jump resonance, transient response due to impulse excitation, effect of impact, effect of vibrations on humans (hearing, comfort), machine vibrations, machine-tool chatter, vibration of structures to due fluid-structure interaction, intended vibrations in micro-electro-mechanical systems (MEMS), dynamics of buckling.

- Analysis of linear and nonlinear vibrations in discrete systems: phase plane analysis, stability of equilibrium, stability of motion, stability criteria (Routh-Hurwitz, Sylvester, Lyapunov, Mathieu), Duffing's method, method of averaging (Krylov-Bogoliubov, Van der Pol), Poincaré perturbation method, Poincaré-Lindstedt perturbation method, two-time-variable perturbation method, bifurcations.

- Suppression of vibrations: isolation, damping, properties of metal and rubber springs, and composites, passive dynamic damping, passive configuration damping, active damping.

- Introduction of nonlinear vibrations in continuum systems: nonlinear sound wave propagation, nonlinear vibration of a string.

Course material:

• Course notes, on Blackboard (in preparation).

References from literature:

- Dimarogonas, A. Vibration for Engineers. Second edition. Prentice-Hall, 1996.

- Harris, C.M. and Piersol, A.G. Harris's Shock and Vibration Handbook. Fifth edition. McGraw-Hill, 2002.

- Inman, D.J. Engineering Vibration. Prentice-Hall, 1996. See especially chapter 10 on nonlinear vibrations (only in this first edition!)

- Jordan, D.W. and Smith, P. Nonlinear Ordinary Differential Equations - an Introduction to Dynamical Systems. Third edition. Oxford University Press, 1999.

- Kelly, S.G. Fundamentals of Mechanical Vibrations. Second edition. McGraw-Hill International Editions, 2000.

- Rao, S.S. Mechanical Vibrations. Fourth edition. Prentice-Hall, 2004.

- Thomson, J.J. Vibrations and Stability - Order and Chaos. McGraw-Hill, London, 1997.    

Remarks assessment, entry requirements, etc.:

The course consists of two parts:

- presentation of a number of topics selected from the above outline, by the lecturer;

- investigation of a specific topic, by the participant. The topic for the assignment will be selected in consultation between participant and lecturer. The participant will carry out an exploratory study and document his findings in the form of a written progress report and a written final report.

The assessment (grading) will be based on the quality of the investigation as documented in the report.

Learning goals:

Be able to develop insight in the fundamental aspects of linear and nonlinear mechanical vibrations. Review and understand mathematical tools for vibration analysis. Be familiar with practical examples of vibration in mechanical systems. Be familiar with concepts and design for passive and for active vibration damping.

Computer use:

Matlab, if desired as part of take-home assignment.

Laboratory project(s):

Take-home assignment (see above).

Design content:

Percentage of design:     %