Module information on this degree can be found below, separated by year of study.

The module information below applies for the current academic year. The academic year runs from August to July; the 'current year' switches over at the end of July.

Students select optional courses subject to rules specified in the Mechanical Engineering Student Handbook,  for example at most three Design and Business courses. Please note that numbers are limited on some optional courses and selection criteria will apply.

Applied Vibration Engineering

Module aims

To teach students how to use the theoretical principles of vibration, and vibration analysis techniques, for the practical solution of vibration problems. The course thus builds on students prior knowledge of vibration theory, and concentrates on the applications. A key feature is that students work on identifying and defining the problems to be solved, prior to solving them. This includes choices of assumptions, choices of measurements to be made and information to be investigated, and choices of analysis techniques to be employed. In keeping with the applied focus, the course includes practical analysis and measurement activities and a project in which students play the roles of clients and consultants while solving a real vibration problem.

ECTS units:  5

Learning outcomes

On successfully completing this module, students will be able to:

  • Describe the nature of real vibration problems in engineering, and their unwanted results
  • Explain the operating principles of common vibration measurement tools and of signal analysis techniques
  • Describe the principles of the advanced vibration modelling and analysis techniques, e.g. frequency response functions and Finite Element analysis
  • Analyse a vibration problem to identify and model its principal features
  • Estimate, from this analysis, a numerical solution (using simplified hand calculations where possible) and an assessment of its validity
  • Propose a strategy for the solution of a practical vibration problem
  • Take measurements using force hammers, accelerometers, noise meters and spectrum analysers
  • Prepare a Consultant-Client report and presentations, keeping a logbook of all practical work

Module syllabus

  • Illustrative examples of vibrations problems in engineering. Range of vibration problems: Nature of range of vibration phenomena and their effects on structures; Case study - worked illustration of a problem and its solution. Review of Fourier Transform and essentials of time and frequency signal processing.
  • Modal analysis I: modal analysis applied to single degree of freedom vibration, including frequency response functions (FRF), Bode and Nyquist plots, circle-fitting. Introduction to analysis of multi-degree of freedom problems.
  • Modal analysis II: models used to describe damping, modal analysis techniques used for measuring damping. Introduction to practical implications and difficulties.
  • Measurement techniques: Principles of operation of accelerometer, hammer with force gauge, shaker, use of these with spectrum analysis hardware/software. Comparison of sinusoidal and impulse excitation. Measurements on active structures, including vibrating machines, rotating shafts.
  • Noise: Nature of noise emission and propagation, noise meter and measurement, frequency band measurements, dB(A) readings.
  • Use of equipment: Practical sessions using measurement equipment (instruction, simple example measurements by groups of students).
  • Assessment of vibration problems: types of problem and governing equations - unforced, harmonic forcing, transient; simplified lumped parameter representations; simplified analysis of continuous structures; natural frequencies and mode shapes; use of handbook solutions.
  • Finite element analysis I: concept of the method, kinds of analysis possible, governing equations, nature of solutions. Example of application of Finite Elements to the solution of a real vibration problem.
  • Finite element analysis II: strategy for undertaking finite element analysis; selection of elements; boundary conditions; forcing; type of solution. Power of the method, dangers of misuse, checking of results. Model validation: techniques for the comparison of results from modal analysis, finite element analysis and experimental measurements. Extraction of the structural parameters, refinement of the models.
  • Analysis of transient response: solution techniques for transient forcing, including shock loading; integral and mode summation methods; measurement of transients.
  • Practical approaches to solving vibration problems: solutions involving changing mass, stiffness or forcing, vibration absorbers; solutions involving damping; solutions involving the reduction of the symptoms of vibration.


ME2-hDYN  Dynamics, or equivalent course elsewhere.

Teaching methods

  • Duration: Autumn and Spring terms (21 weeks)
  • Lecture/tutorials: 1 x 1h/week lectures on theory and analytical methods. Several lectures include practical demonstrations. The lectures follow a developing sequence, covering the key aspects of problem identification, theoretical and experimental tools for understanding the problems, and strategies for solutions. During the Spring term two of these lecture slots will be used to provide assistance with group projects and tutorial sheets.
  • Projects: Consultant-Client project. Student groups (3-4) tackle a real vibration problem, playing the roles of consultant and client. This is done in some of the lecture periods, plus some extra periods (about 5-8 hours) scheduled to fit with student's other timetable commitments, and also in students' own time. A consultant group investigates a vibration problem, identifies possible solutions, and then reports back to the client group. The exercise is repeated concurrently on another vibration problem with the consultant and client groups reversed. The projects are initiated by problem definition statements which are issued to the consultants, and provision of the actual structures/machines in the laboratory. The consultants then perform any measurements and analyses of their choice. The results are reported by:
    • a written report which is passed to the clients, followed by
    • a 25 minute meeting between the consultants and the clients in which the consultants make a presentation of their work and the clients present a constructive criticism of it.

Summary of student timetabled hours







Other (design, lab, computing etc.)





Expected private study time

4-5 h per week, plus exam revision


Written examinations:

Date (approx.)

Max. mark

Pass mark

Advanced Vibration Engineering (3h)


A Data and Formulae book and a course-specific information document are provided.


This is an CLOSED BOOK Examination.

April/ May




Coursework (including progress tests, oral presentations etc.)

Submission date

Max. mark

Pass mark



Consultant-Client reports and presentations; logbook of all practical work

Oral comments given during class







Module leaders

Dr Christoph Schwingshackl