Vibration, Data Analysis and Data Decomposition
Overview
This unit of study aims to introduce students to the underlying fundamentals of mechanical vibrations, and the analysis of data that is obtained from the measurement of these systems. Students will be able to recognize the fundamental components required for vibration to occur, and produce mathematical models of vibrating systems.
Students will be able to analyse the dynamics of these systems using Fourier analysis techniques, as well as emerging techniques in data-driven decomposition. The presentation of the material focuses on the practical application and analysis of vibrations using examples and virtual experiments.
Requisites
MTH10012 Calculus and Applications
AND
MTH10013 Linear Algebra and Applications
OR for PDE
MTH10007 Engineering Mathematics 2 *
OR
MTH10003 Engineering Mathematics 2P *
01-June-2025
Learning outcomes
Students who successfully complete this unit will be able to:
- Understand and implement the mathematical modelling of mechanically vibrating systems and analyze the solutions of these systems (K1, K2, K3, S1)
- Apply signal sampling and Nyquist theory to design acquisition systems (K2, K3, S1, S2, S3)
- Apply digital filters, time and frequency domain analysis techniques to signal processing (K2, K3, S1, S2, S3)
- Apply Fourier series and the Fast Fourier Transform to analysing sound and vibration signals (K2, K3, S1)
- Apply data-driven computation techniques and regression methods to decompose and interpret empirical data (K2, K3, K4, S1, S2)
Teaching methods
Hawthorn
| Type | Hours per week | Number of weeks | Total (number of hours) |
|---|---|---|---|
| Online Lecture |
2.00 | 12 weeks | 24 |
| On-campus Class |
2.00 | 3 weeks | 6 |
| On-campus Class |
2.00 | 9 weeks | 18 |
| On-campus Lecture |
1.00 | 12 weeks | 12 |
| Unspecified Activities Independent Learning |
4.00 | 12 weeks | 48 |
| Unspecified Activities Assessment Preparation |
3.50 | 12 weeks | 42 |
| TOTAL | 150 |
Assessment
| Type | Task | Weighting | ULO's |
|---|---|---|---|
| Take home assessment | Individual | 40 - 60% | 1,2,3,4,5 |
| Online Quizzes | Individual | 10 - 20% | 1,2,3,4,5 |
| Test 2 | Individual | 10 - 20% | 2,3,4,5 |
| Mid-Semester Test | Individual | 10 - 20% | 1 |
Content
- Fundamentals of free mechanical vibration in one degree of freedom
- Forced or driven vibration in one degree of freedom
- Free and forced vibration in multiple degrees of freedom
- Vibration control and nonlinear vibration
- Fourier series and Fourier transforms
- Sampling, aliasing and filtering
- Fourier analysis extensions to multiple dimensions
- Data-driven decomposition in one dimension using Empirical Mode Decomposition
- Data-driven decomposition in multiple dimensions using Proper Orthogonal Decomposition
- GA 5 - Digital Literacies 1 - Information literacy
- GA 6 - Digital Literacies 2 - Technical literacy
Study resources
Reading materials
A list of reading materials and/or required textbooks will be available in the Unit Outline on Canvas.