MECH GR04 – Vibrations, Airborne and Underwater Acoustics & Control
Note: Whilst every effort is made to keep the syllabus and assessment records correct, the
precise details must be checked with the lecturer(s) and PORTICO.
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MECH GR04
very similar to MECH GM04, M008
Vibrations, Airborne and Underwater Acoustics & Control
M
15/6
September
March
Dr. P. Fromme (33%)
Module Coordinator
Dr. N. Saffari (33%)
Dr. D. Western (33%)
Prerequisites
Vibrations and Control knowledge equivalent to undergraduate degree in Mechanical
Engineering. UG level Solid/Fluid Mechanics. UG level Engineering Mathematics.
Course Aims
The Vibrations part of the course reinforces the modelling and vibrations knowledge from UG
level. Building on these skills and mathematical tools, vibrations in more realistic and complex
structures are investigated and analysed, increasing the understanding of vibration problems in
engineering structures.
The main aims of this course in digital control systems are:
 To give students an appreciation of the need for modern control systems
 To explain and discuss the systems that make up modern control systems
 To provide students with mathematical tools needed in the design and performance
analysis of digital control systems
In the Acoustics part of the course, the aim is to impart knowledge of the sources and nature of
acoustic noise in an engineering environment. The coverage starts with basic physical concepts
and leads on to the treatment of vibrating structure/fluid interactions for a number of simple
examples of practical interest.
Method of Instruction
Assessment
The course has the following assessment components:
 Written Examination (2 hours, 100%) answer 3 mandatory questions (one each from
Vibrations, Control, Acoustics)
To pass this course, students must:
 Obtain an overall pass mark of 50%
Resources
[1] Digital Control Systems
B.C. Kuo
Saunders College Publishing
[2] Design of Feedback Control Systems
R.T. Stefani, B. Shahian, C.J. Savant Jr., and G.H. Hostetter
Oxford University Press
[3] Digital Control of Dynamic Systems
G.F. Franklin and J.D. Powell
Addison-Wesley Publishing
[4] Real-Time Computer Control: An Introduction
S. Bennett
Prentice Hall International
[5] Control Systems Theory
O.I. Elgerd
McGraw-Hill
[6] The Art of Control Engineering
K. Dutton, S. Thompson, B. Barraclough
Addison-Wesley
[7] Control System Design and Simulation
J. Golten, A. Verwer
McGraw-Hill
[8] ‘Fundamentals of Acoustics’ Fourth Edition (2000).
L.E. Kinsler, A.R Frey, A.B. Coppens and J.V. Sanders.
John Wiley & Sons, ISBN 0-471-84789-5.
[9] ‘Sound and Structural Vibration’ (1985).
F. Fahy,
Academic Press, ISBN 0-12-247671-9.
[10] Theory of Vibration with Applications
W. T. Thomson and M. D. Dahleh
Chapman & Hall
Additional Information
none
Content:
Vibrations
1. Introduction – Free response of SDOF systems
1.1 Terminology
1.2 Equation of motion
1.3 Unforced response of SDOF system with no damping
1.4 Free vibration of a SDOF system with damping
1.5 Energy method for equation of motion
2. Forced vibration of SDOF systems
2.1 General solution
2.2 Dynamic magnification
2.3 Resonance frequency
2.4 Q factor
2.5 Vibration isolation
2.6 Support motion
3. Transient response of SDOF systems
3.1 Impulse function
3.2 Impulse response of SDOF systems
3.3 Convolution integral
3.4 Vibration instrumentation: accelerometer and vibrometer
4. Unforced MDOF systems
4.1 Example of MDOF system with 2 DOF
4.2 Natural frequencies
4.3 Modeshapes
4.4 Undamped free vibration of an N-degree of freedom system
4.5 Orthogonality of modeshape vectors
4.6 Diagonalisation of MDOF system and principal coordinates
4.7 Lagrange’s equations
5. Harmonic force applied to a MDOF system
5.1 Forced vibration of an undamped MDOF system
5.2 Receptance and mobility
5.3 Viscous damping
6. Vibration in continuous systems
6.1 Longitudinal (axial) vibration of a rod
6.2 Lateral vibration on a string in tension
6.3 Bending waves on a thin beam
6.4 Unforced flexural vibration of a thin beam
Control
1. Introduction to Digital Control Systems
1.1 Review and Classification of Control Systems
1.2 Analogue and Digital Control Systems
1.3 Components of a Control System
1.4 Sampling Theorem
2. Mathematics of Digital Control Engineering
2.1 Continuous Systems and Transfer Function Revision
2.2 Discrete Time Systems and Linear Difference Equations
2.3 z Transform
2.4 Transfer Function
2.5 Inverse z Transform
3. Discrete Time Systems
3.1 z Domain Transfer Function
3.2 Stability Criteria
3.3 Time Domain Response
3.4 Frequency Response
4. Discrete Control Systems
4.1 Equivalent Continuous Time Design
4.2 Realization and Implementation
4.3 Discrete PID Controller Design
4.4 Digital Control Applications
Acoustics
1- Introduction to Acoustics:
Basic nature of sound; particle displacement; particle velocity; acoustic pressure; condensation;
sound velocity in gasses and fluids.
2- Propagation of sound waves in solids and fluids:
Derivation of the wave equation for a homogeneous, infinite medium in Cartesian co-ordinates;
simple solution to the wave equation; the acoustic energy of plane waves; longitudinal and shear
waves in infinite solids; torsional waves; quasi-longitudinal and flexural waves in bars and plates;
dispersion curves.
3- Interaction between vibrating structures and sound:
The wave equation in spherical co-ordinates; general solution to the spherical wave equation; the
monopole; source strength; the radiating dipole; vibrating piston in an infinite baffle; far-field directivity
patterns; radiation from an arbitrary vibrating body; the Kirchoff-Helmholtz equation; radiation from
an infinite plate; radiation efficiency; sound radiation from a finite plate; edge modes and corner
modes; fluid loading of vibrating structures; radiation resistance and reactance.
4- Propagation through partitions:
Transmission and reflection coefficients for pressure, intensity and power; rigid and pressure
release boundaries; normal transmission through two boundaries; transmission loss for a
bounded, homogeneous, single panel; the field-incidence mass law.
5- Sound in an enclosure:
The reverberant and direct fields; reverberation time; Sabine formula; sound intensity in an
enclosure; room constant; the directivity factor.
Underwater Acoustics (MECHGR04 only)

Introduction to underwater acoustics.
o Acoustic wave propagation in the sea:
o Sound velocity profile in the sea, Ray theory,
o Sound channelling.

Transmission and absorption losses.

Volume and surface scattering. Target strength.

The active and passive sonar equations.

The detection threshold in a sonar system. Receiver Operating Curves (ROC).

Coherent and incoherent detection
Additional Information
All the material in this module is common to MECHGM04. Students on the MSc Marine Engineering take
MECHGR04 instead of MECHGM04. This includes additional lectures on underwater acoustics.