Machine System Dynamics

Module aims

This course is split in three parts. The first part (Control) will introduce an overall description of mechanical and electrical systems and their partial differential equation based transfer functions into simple block diagrams. By analysing the block diagrams and using Laplace transform theory the overall transfer function of the systems will be derived. Following this frequency response analysis, stability analysis and PID control of the systems will be applied to the whole systems and their building blocks.

The second part of the course (Vibrations) will focus on dynamic analysis of mechanical structures, the systems that you would want to control with the approach described in the first part of the course. The course will explore the dynamic response of multi-degree of freedom lumped parameter and continuous systems. It will enable you to modify spring/mass systems to adjust natural frequencies and related mode shapes, design shaft systems to avoid torsional and flexural vibration (whirl) problems and to incorporate vibration stresses into fatigue calculations. In the third part of the course (Signal Processing) you will then go on to analyse and interpret measured data using Fourier frequency analysis.

The course will build on the second year Mechatronics and Solid Mechanics courses, introducing a greater range of examples where the dynamic response of a machine must be controlled. This will involve new subject matter in the vibration of continuous systems, rotor dynamics, signal processing and control analysis. A key aspect of the course will be solving realistic problems by hand and with the use of a computer program such as MATLAB. You are encouraged to use MATLAB to explore what happens if ?  type problems and to solve the tutorial sheets. In addition to the tutorial sheets that ask you to apply your knowledge to particular problems, for the first time this year there will be online quizzes that allow you to test some of the knowledge that you gathered in each lecture and by reading the lecture notes. This is a feedback tool to give you the chance to practice your understanding and what you have taken away from reading the lecture notes. It is also a tool to made sure that you have regular involvement with the course material. However, it is key that you still attempt all tutorial sheets, they will give you the required practice without which you will not be able to pass the examination.

ECTS units:    6   
Contributing to Course Elements: 6 to ME3-mCORE (MEng) or ME3-hCORE (BEng)

Learning outcomes

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

  • Describe simple mechanical and electrical systems in form of a block diagram and derive their transfer function in the Laplace domain;
  • Appreciate the difference between active and passive control and the relative advantages of each;
  • Solve simple problems involving active or passive control analytically;
  • Use MATLAB to obtain solutions to more complex control and signal analysis problems.
  • Predict the vibration response of 2 DOF lumped mass systems and beams/shafts in bending and torsion;
  • Appreciate the importance of avoiding shaft whirl and be able to calculate critical speeds;
  • Appreciate the significance of vibration loading in generating high cycle fatigue;
  • Predict fatigue life of components by linking their vibration response to alternating stress and using this as input to fatigue calculations;
  • Explain the use of Fourier analysis to convert both single and dual channel time domain measurements into the frequency domain.

Module syllabus

3.1 Control (analogue)

Frequency response analysis, Bode diagrams

  • System models (time, frequency and complex frequency domains)
  • Negative feedback systems
  • Stability analysis, transient response design
  • Steady state response analysis
  • Compensation, PID controller

 3.2 Analysis of realistic signals and systems

  • Use of MATLAB for Fourier analysis and frequency response functions
  • Control system design
  • Control system optimisation

 3.3 Passive system dynamics

  • Forced response of MDOF systems; vibration absorber
  • Free and forced response of continuous systems (beams, shafts in torsion and bending)

 3.4 Rotor dynamics

  • Whirling of shafts; critical speeds

 3.5 Vibration induced fatigue

  • Calculation of stress from vibration mode shape and amplitude
  • Input to fatigue calculations; Goodman diagrams

3.6 Signal processing

  • Transducers: linear displacement, angular displacement, angular velocity,  pressure
  • Data  acquisition:  resolution, aliasing
  • Fourier Transform; FFT
  • Time Windows: rectangular, Hanning


Pre-requisites: ME2-hDYN; ME2-hSAN; ME2-hMTX; ME1-hCPT; ME2-hCPT or equivalent.

Teaching methods

  • Duration: Autumn and Spring terms
  • Lectures: 1hr each week
  • Tutorials: 1hr every other week
  • Laboratory exercises: tutorial is sometimes held in the PC suite when the main activity is MATLAB based.

Summary of student timetabled hours












Expected private study time

3-4hrs per week plus exam revision


Written examinations:

Date (approx.)

Max. mark

Pass mark

Machine System Dynamics (3hrs)


A Data and Formulae book is provided.

This is a CLOSED BOOK Examination

April/ May



*  On aggregate with ME3-mTDE


Coursework (including progress tests, oral presentations etc.)

Submission date

Max. mark

Pass mark



Weekly Quizes

Generic, in lecture following quiz.






Reading list


Module leaders

Dr Frederic Cegla