Circuits and Systems

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• 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
• The causes and effects of vibration within various mechanical systems
• Methods of analysis, measurement and control of vibration

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Analyse and solve simple electrical circuit and mechanical system problems
• Apply circuit theorems for the solution of unbalanced three-phase circuits
• Calculate electrical power in single and three-phase circuits
• Make engineering judgement on the problem or reducing vibration when required
• Translate a physical problem in mechanical vibration to an appropriate dynamic model

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Perform range of electrical measurements on three-phase circuits
• Undertake measurements to estimate dynamic parameters of mechanical beams

Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Undertake laboratory experiment as part of a small team
• Record and report laboratory work

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

Resources & Reading list

Textbooks

Rao. Mechanical Vibrations. Addison Wesley.

Tse, Morse & Hinkle. Mechanical Vibrations. Allyn & Bacon.

Morrison J L M & Crossland B. Introduction to the Mechanics of Machines.

Van Valkenburg M E (1974). Network Analysis. Prentice Hall.

Dorf and Svoboda (2006). Electric Circuits. Wiley.

Rogers (1965). Topology and Matrices in Solution of Networks.

Thomson W T. Theory of Vibration with Applications. Chapman & Hall.

Thomas R E and Rosa A J (2000). The Analysis and Design of Linear Circuits. Wiley.

William J. Palm III (2007). Mechanical Vibration. John Wiley & Sons.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

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.

Repeat Information

Repeat type: Internal & External