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UCL Mechanical Engineering
Faculty of Engineering Sciences


MECHGM04 Vibrations, Acoustic & Control

MECHGM04 Vibrations, Acoustic & Control

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.

Alt. Codes(s) MECHM008; very similar to MECHGR04
Title Vibrations, Acoustic & Control
Level MSc, MEng
UCL Credits/ECTS 15 / 6
Start September
End March
Taught by Dr Paul Fromme (33%) Module Coordinator
Prof Nader Saffari (33%)
Dr D. Western (33%)


  • Vibrations and Control knowledge equivalent to undergraduate degree in Mechanical Engineering.
  • UG level Solid/Fluid Mechanics.
  • UG level Engineering Mathematics


The course has the following assessment components:

  • Written Examination (2 hours, 100%) answer 3 mandatory questions (one each from Vibrations, Control and Acoustics).

To pass this course, students must:

  • Obtain an overall pass mark of 50% for all sections combined


[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



  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

  1. 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

  1. 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

  1. 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

  1. 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

  1. 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



  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

  1. 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

  1. Discrete Time Systems

3.1 z Domain Transfer Function

3.2 Stability Criteria

3.3 Time Domain Response

3.4 Frequency Response

  1. 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



  • Introduction to Acoustics:

Basic nature of sound; particle displacement; particle velocity; acoustic pressure; condensation; sound velocity in gasses and fluids.

  • 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.

  • 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.

  • 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.

  • Sound in an enclosure:

The reverberant and direct fields; reverberation time; Sabine formula; sound intensity in an enclosure; room constant; the directivity factor.

Additional Information

All the material in this module is common to MECHGR04. Students on the MSc Marine Engineering take MECHGR04 instead of MECHGM04. This includes additional lectures on underwater acoustics.

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