The University of Southampton

# FPProvisional000009 ELEC3 - USMC3214 Circuits and Mechatronic Systems

## 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. It will also provide an introduction to vibration measurments and testing as well as distributed systems that cannot be approximated by lumped parameters.

### Aims & Objectives

#### Knowledge and Understanding

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

• Students will be able to demonstrate knowledge and understanding of: 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

Having successfully completed this module, you will be able to:

• Students will be able to: Analyse and solve simple electrical circuit and mechanical system problems. Translate a physical problem in mechanical vibration to an appropriate dynamic model. Make engineering judgement on the problem or reducing vibration when required. Analyze the step and frequency response of a system to identify the form and paremeter values of a model.

#### Transferable and Generic

Having successfully completed this module, you will be able to:

• Students will be able to: Undertake laboratory experiment as part of a small team. Record and report laboratory work.

#### Subject Specific Practical

Having successfully completed this module, you will be able to:

• Students will be able to: Undertake measurements to estimate dynamic parameters of mechanical beams. Describe the commonly used equipment for stimulating a vibratory response and for collecting response data. Perform a transform analyis of signal data to estimate natural frequencies.

### 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.
• Vibration measurement and testing - system identification, transform analysis of signals, random processes, data aquisition and signal processing
• Distributed systems - solution of wave equation, sepration of variables, transverse vibration of beams.

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).

### Learning & Teaching

#### Learning & teaching methods

• Lecture - 24 hours per semester
• Tutorial - 12 hours per semester
• Specialist Lab - 6 hours per semester

### Assessment

#### Assessment methods

MethodHoursPercentage contribution
Cantilever vibration experiment-5%%
System identification experiment.-5%%
Exam2 hours90%

Referral Method: By examination