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ENGINEERING TRIPOS PART IIB - 2012/2013

Module 4C6 - Advanced Linear Vibration

Leader:	Prof. J. woodhpouse
Timing:	Michaelmas Term
Prerequisites:	3C6 assumed
Structure:	13 lectures + 2 examples classes + coursework
Assessment:	*Material / Format / Timing / Marks* Lecture Syllabus / Written exam (1.5 hours) / Start of Easter Term / 75 % Coursework / Report / Start of Lent Term / 25 %

AIMS

This module aims to teach some essential tools for the understanding, analysis and measurement of vibration in engineering structures.

LECTURE SYLLABUS

Introduction (1L, Prof J. Woodhouse)

Outline of course and introduction to the laboratory experiment.

Measurement methods and modal analysis (4L, Dr H.E.M. Hunt)

Instrumentation for vibration measurement;
Review of modal analysis; General properties of vibration response;
Introduction to experimental modal analysis; Modelling the bounce of a hammer.

Analysis of damped systems (4L, Prof J. Woodhouse)

Mechanisms of damping: complex modulus, boundary dissipation, lumped dissipative elements;
Adding damping to structures, constrained and unconstrained layers;
Viscous damping, complex modes.

System components and coupling (4L Prof J. Woodhouse)

The Helmholtz resonator and its uses;
Review of beam, membrane and plate governing equations;
The circular membrane, Bessel functions, mode shapes and frequencies;
Coupling of subsystems, constraints and the interlacing theorem.

COURSEWORK

One laboratory experiment on experimental modal analysis, to be performed in pairs, essentially unsupervised. A booking sheet will offer a wide range of possible times at which the experiment may be performed. A normal laboratory write-up is to be prepared, which will be assessed for the coursework credit. Total time commitment will be comparable to a Part IIA major experiment.

OBJECTIVES

On completion of the module students should:

Be familiar with the theory and practice of modal analysis and its application to engineering structures;
Be able to apply experimental modal techniques;
Understand the vibration behaviour of idealised system components, and be able to draw implications from this for complex coupled systems;
Appreciate the physical principles of vibration damping;
Be able to analyse simple damped vibrating systems.

REFERENCES

Please see the Booklist for Group C Courses for references for this module.

Last updated: May 2012

teaching-office@eng.cam.ac.uk