Undergraduate Teaching 2024-25

Engineering Tripos Part IIB, 4C6: Advanced Linear Vibrations, 2024-25

Engineering Tripos Part IIB, 4C6: Advanced Linear Vibrations, 2024-25

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Module Leader

Dr JP Talbot

Lecturers

Dr JP Talbot, Dr Tore Butlin

Lab Leader

Dr JP Talbot

Timing and Structure

Michaelmas term. 13 lectures + 2 examples classes + coursework. Assessment: 75% exam/25% coursework. This course will be delivered in-person in 2021-22.

Prerequisites

3C6 assumed.

Aims

The aims of the course are to:

  • teach some essential tools for the understanding, analysis and measurement of vibration in engineering structures.

Objectives

As specific objectives, by the end of the course students should be able to:

  • be familiar with the theory and practice of modal analysis and its application to engineering structures.
  • 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.
  • analyse simple damped vibrating systems.

Content

Introduction (1L, Dr JP Tabot)

Outline of course and introduction to the laboratory experiment.

Measurement methods and modal analysis (4L, Dr JP Talbot)

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

Analysis of damped systems (4L, Dr Tore Butlin)

  • 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 Dr Tore Butlin)

  • 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.

Further notes


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 experiment plus FTR.

 

Coursework Format

Due date

& marks

Lab experiment: modal analysis

Measure vibration transfer functions over a grid of points covering a simple structure, then use modal analysis techniques explained in the lectures to infer the first few mode shapes.

Learning objective:

  • Revise measurement procedures for transfer functions
  • Consolidate and apply material from lectures on modal fitting
  • Develop critical skills in interpreting modal data
  • Undertake a small-scale industrial-style application of the method, to modify a structure to meet vibration targets

Individual/pair

Report

Anonymously marked

Completed reports should be submitted via Moodle as a PDF file by 4pm on Mon 2 Dec

[15/15]

 

Booklists

Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 30/10/2024 08:34

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