Course code: wb1412

Course name: Non-linear Vibrations

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.Th.L.M. van

Tel.:  015 - 27 82792 /      

Catalog data:

Nonlinearities: engineering cases.

Linearization; equivalent linearization; premature linearization; descibing functions.

Phase plane analysis.

General perturbation theory: asymptotic expansions; Poincaré; Lindstedt; two-variable; Duffing; Van der Pol.

Stability theory: Routh-Hurwitz; Lyapunov; Mathieu;

time delays; bifurcation; catastrophy.

Nonlinear oscillations and chaos.

Course year:

MSc 1^st year

Semester:

2A / 2B

Hours per week:

2

Other hours:

-

Assessment:

Written report

Assessment period:

, ,

(see academic calendar)

Prerequisites (course codes):

wb1211, wb1215, wi2051wb, wi3097wb

Follow up (course codes):

Detailed description of topics:

The course focuses on nonlinear behavior in mechanical systems. Main line of presentation:

possibilities and pitfalls of quick linearization; phase plane geometrical analysis; general perturbation theory; stability theory; chaos.

Description of a selection of nonlinear phenomena involving dry friction (description, utilization, compensation); rigid body angular motion and control; galopping cables; ship roll, surge and sway in sea waves; sound production (loudspeaker) and sound perception (human hearing); beam buckling; metal cutting; PC printing; digital control; atomic force microscope operating in tapping mode.

Course material:

• Course notes

References from literature:

• Jordan, D.W. and Smith, P. Nonlinear Ordinary Differential Equations, 2nd edition. Clarendon Press, Oxford, 1995
• Thomson, J.J. Vibrations and Stability - Order and Chaos. McGraw-Hill, London, 1997.
• Moon, F.C. Chaotic Vibrations - an Introduction for Applied Scientists and Engineers. J. Wiley and Sons, Inc., N.Y., 1987.

Remarks assessment, entry requirements, etc.:

The course will be presented during alternate years; please contact the teacher to assist you in planning.

At the end of the course a take-home assignment will be issued. It may be either theoretical in nature, or display a strong numerical component. The assignment will be drafted in cooperation with the individual students or with teams of students.

Learning goals:

Provide insight in the fundamental aspects of nonlinearities in mechanical systems. Review of some mathematical tools for their analysis. Awareness of possible risks and benefits of nonlinearities in real mechanical systems.

Computer use:

MATLAB use  for final take-home assignment

Laboratory project(s):

-

Design content:

-

Percentage of design:  -%