Module overview
The module aims to provide a detailed understanding of the representation and analysis of dynamic systems, and their solution. It goes on to apply this to simple circuit problems as well as to mechanical systems. Vibration problems in mechanical systems are further studied using frequency response and energy approximation methods, and modelling and analysis is then extended to continuous mechanical systems, including beams and shafts. Application to circuit theory is used to develop a good understanding of the fundamental theory of three phase circuits.
Linked modules
Pre-requisites: ELEC1200 AND MATH1055
Aims and Objectives
Learning Outcomes
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Methods of analysis, measurement and control of vibration
- The causes and effects of vibration within various mechanical systems
- Balanced and unbalanced three phase circuit theory
- Power in AC circuits, and conservation of power
- State-space method applied to circuit problems and mechanical systems
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Make engineering judgement on the problem or reducing vibration when required
- Translate a physical problem in mechanical vibration to an appropriate dynamic model
- Analyse and solve simple electrical circuit and mechanical system problems
- Calculate electrical power in single and three-phase circuits
- Apply circuit theorems for the solution of unbalanced three-phase circuits
Transferable and Generic Skills
Having successfully completed this module you will be able to:
- Record and report laboratory work
- Undertake laboratory experiment as part of a small team
Subject Specific Practical Skills
Having successfully completed this module you will be able to:
- Undertake measurements to estimate dynamic parameters of mechanical beams
- Perform range of electrical measurements on three-phase circuits
Syllabus
Mechanical Systems:
- One Degree of Freedom Systems Application of Laplace transform and state space methods to mechanical systems. Analysis of dynamic response and role of Damping (Viscous and
Coulomb) Base Excitation, Displacement Transmissibility Vibration Isolation.
- Two Degree of Freedom Systems Modelling of two degree of freedom systems in state space form. Physical interpretation of solutions. Free Vibration and Normal Modes, Co-ordinate
Coupling and Principal Co-ordinates, Forced Vibration, Damping, Impedance Matrix, Vibration Absorber. Decoupling using Modal Matrix.
- Multi Degree of Freedom Systems Orthogonality, Modal Space Matrix Methods, Approximate Frequency Analysis, e.g. Rayleigh’s, Dunkerley’s Methods Lagrange’s Equations
- Continuous Systems Vibration of Strings, Rods, Beams and derivation of equations of motion.
- Application of Rayleigh’s method to approximate natural frequencies. Vibration and Instrumentation, Transmissibility.
Three-phase:
- Unbalanced mesh and four-wire star circuits; unbalanced three-wire star circuits; solution by Millman's theorem, star-delta transform and graphical methods; symmetrical components and
use in solving unbalanced systems; positive, negative and zero sequence networks; use of two-wattmeter method on balanced and unbalanced systems for kW and kVAr measurement.
State Space:
- Application of circuit and mechanical analogies.
- Need for state space method; definition of terms: state-variable, state-matrices, etc.; consideration of the elements that store energy; formation of equations, in particular the formation of matrix equation in the form of X = A.X + B.E, nature of these terms.
- Solution of state space equations by Laplace transform methods; solution of simple circuit network problems.
- Solution of state equations in the time domain (linear-time invariant case): solution of the state differential equation (exponential of a matrix, its computation, forced- and free response in the state-space setting).
Laboratory Coursework:
- 3-phase Star and Mesh circuit relationships; Cantilever vibration experiment
Learning and Teaching
Type | Hours |
---|---|
Lecture | 24 |
Preparation for scheduled sessions | 12 |
Follow-up work | 12 |
Revision | 10 |
Wider reading or practice | 72 |
Tutorial | 12 |
Completion of assessment task | 8 |
Total study time | 150 |
Resources & Reading list
Textbooks
Rao. Mechanical Vibrations. Addison Wesley.
Morrison J L M & Crossland B. Introduction to the Mechanics of Machines.
Dorf and Svoboda (2006). Electric Circuits. Wiley.
Thomson W T. Theory of Vibration with Applications. Chapman & Hall.
Rogers (1965). Topology and Matrices in Solution of Networks.
Tse, Morse & Hinkle. Mechanical Vibrations. Allyn & Bacon.
Thomas R E and Rosa A J (2000). The Analysis and Design of Linear Circuits. Wiley.
Van Valkenburg M E (1974). Network Analysis. Prentice Hall.
William J. Palm III (2007). Mechanical Vibration. John Wiley & Sons.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
Method | Percentage contribution |
---|---|
Final Assessment | 90% |
Continuous Assessment | 10% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Method | Percentage contribution |
---|---|
Set Task | 100% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
Method | Percentage contribution |
---|---|
Set Task | 100% |
Repeat Information
Repeat type: Internal & External