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# MEng Mechanical Engineering with Industrial Experience

Year of entry: 2021

## Course unit details:Acoustics & Advanced Vibrations

Unit code MACE40442 15 Level 6 Semester 2 Mechanical and Aeronautical Engineering Division (L5) No

### Overview

The unit helps prepare students to tackle and solve a substantial range of engineering problems, some of them complex and/or novel.

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  Please see Blackboard / course unit related emails for any further updates

### Aims

Introduce students to waves in fluids
Introduce students to the importance of noise in Engineering Systems
Introduce students to advance analytical methods in acoustics
Introduce students to advance analytical methods in vibrations

### Syllabus

• The relevance of sound - 1 lecture
• The 1D wave equation - 4 lectures
¿ The 1D wave equation in solids and fluids - 1 lecture
¿ 1D wave propagation - 1 lecture
¿ 1D waves in pipes - 1 lecture
¿ 1D wave propagation across impedance changes
¿ 2 tutorial classes
• The 3D wave equation - 5 lectures
¿ 3D waves in cartesian co-ordinates - 1 lecture
¿ Snell’s Law - 1 lecture
¿ Ray theory - 1 lecture
¿ Cylindrical polar waves - 1 lecture
¿ Spherical waves - 1 lecture
¿ 2 tutorial classes
• Sources of sound - 3 lectures
¿ Lighthill’s acoustic analogy - 1 lecture
¿ General sources of sound - 1 lecture
¿ Sound sources and sinks - 1 lecture
¿ 1 tutorial class
• The relevance of advanced vibration - 1 lecture
• Revision of basic vibration - 1 lecture
• Multiple degrees of freedom for discrete systems - 7 lectures
• Equations of motion: Newton's law, D'Alembert's Principle, Lagrange's Equation;
• Eigenvalue problem: natural frequencies and mode shapes, eigenvalue approach to normal mode solution;
• Orthogonality of modes, transformation from physical to modal space/co-ordinates;
• Proportional and non-proportional damping, static and dynamic coupling;
• Modal analysis: solving for free and forced vibration via modal co-ordinates, FRF for multiple degree of freedom systems, modal participation factor.
• Multiple degrees of freedom for continuous systems - 6 lectures
• Wave theory: Derivations and solutions of 2nd order wave equations (PDEs) for longitudinal and torsional vibrations of rods and shafts; Exact frequency equations; Free and forced vibration using closed form solutions;
• Wave theory: Derivations and solutions of 4th order wave equations (PDEs) for flexural vibrations of beams using Bernoulli-Euler theory; Exact frequency equations; Free and forced vibration using closed form solutions;
• Rayleigh-Ritz approach: Derivations of equations of motion for flexural vibrations of beams using Rayleigh-Ritz approach; Free and forced vibration via assumed modes;
• Vibration and Shock Control using Viscoelastic and Smart Materials - 3 lectures
• Viscoelasticity: complex modulus of viscoelastic materials, anti-vibration mounts;
• Smart materials: electrorheological and magnetorheological fluids, piezoelectric materials, shape memory alloys;
• Smart structures: collocated sensors and actuators, PZT shunts, active vibration control, semi-active vibration dampers

### Assessment methods

Method Weight
Other 20%
Written exam 80%

Other - assessed tutorial work

### Feedback methods

Assessed tutorial work - 3 hours support and 11 hours self study

### Study hours

Scheduled activity hours
eAssessment 14
Lectures 26
Tutorials 10
Independent study hours
Independent study 100

### Teaching staff

Staff member Role