ENGINEERING TRIPOS PART IIB - 2012/2013
Module 4C7 - Random and Non-linear Vibrations
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Leader:
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Prof R S Langley |
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Timing:
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Michaelmas Term
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Prerequisites:
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3C6 useful
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Structure:
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12 lectures + 2 examples classes + coursework
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| Assessment: |
Material / Format / Timing / Marks
Lecture Syllabus / Written exam (1.5 hours) / Start of Easter Term / 75 %
Coursework / Report / End of Lent Term / 25 % |
AIMS
This module aims to analyse the effects of random vibrations on machines and
structures and the effects that occur as a result of non-linearities. The
course describes the characteristics of random and non linear vibrations,
derives the effects of a system's dynamic response on the input and gives
methods of determining resulting deflections or stresses. Some of the characteristics of self excited
vibrations are described.
LECTURE SYLLABUS
Non-linear and self-excited vibration. (6L, Dr. A.A. Seshia
)
- Types of non-linearities in
engineering systems and their major qualitative effects. Method of harmonic balance, describing
functions;
- Representation of
second-order nonlinear systems in the phase plane. Stationary points and their
classification. Periodic orbits;
- Introduction to self-excited vibration. Examples of systems which are excited
by instability and dry friction. Self excited oscillations in micro electromechanical systems.
Random vibration. (6L, Professor R.S. Langely)
- Characteristics of random
vibrations and the use of probability distributions and spectral densities
to describe such vibration:
- Auto and cross spectra. Transmission
of random vibration through linear systems and derivation of output
statistics and spectral densities;
- Narrow-band processes and
determination of level-crossing frequency, distribution of peaks and
frequency of maxima;
- Spectral analysis. Fourier
transforms. Problems with sampling and relevance of aliasing. Calculation
of spectra for sampled points;
- Basic lag and use of
windows and smoothing. Coherence. Accuracy of measurements.
COURSEWORK
Experiment on non-linear vibrations. This involves about 4 hours in the laboratory
and 4 hours writing-up.
OBJECTIVES
On completion of the module students should:
Random vibration
- Be able to identify and
describe random processes;
- Be able to predict the
output from a system subjected to random forcing;
- Be able to predict how
frequently output levels will be exceeded;
- Be able to apply the
correct windows and filters for analysis;
- Be able to assess the
reliability of frequency analyses.
Non-linear and self excited vibration
- Understand the effects of
non-linearities on system response;
- Be able to calculate and
use describing functions and harmonic balance;
- Be able to predict
phase-plane behaviour of second-order systems;
- Understand some of the
common self excited vibrations and their characteristics.
REFERENCES
Please see the Booklist for Group C Courses for references for this module.
Last updated: June 2012
teaching-office@eng.cam.ac.uk
