ENGINEERING TRIPOS PART IIA - 2012/2013

Project SC3 - Vibration Modelling

Leader: Prof D. Cebon email: dc

Project Type: Standard
Project Category: Design
Prerequisites: 3C5 & 3C6 essential
Timing: Thursdays 11-1pm, Mondays 9-11am, plus afternoons

SUMMARY

This project will involve modelling the vibration response of a mechanical system employing different levels of approximation, ranging from simple analytical calculations and one-degree-of-freedom models to comprehensive finite element descriptions of the response. Students will measure the response of various vibrating systems in the laboratory and will compare the experimental measurements with predicted responses.

AIMS

• To introduce four techniques of modelling the vibration of continuous systems.
• To investigate various analytical and numerical methods for predicting vibration response, and to study their fitness for solving the problem, their accuracy and computational effort.

FORMAT 

Students work individually, but coordinate results within groups of three.

ACTIVITIES

Week 1: Collect experimental data and do simple hand-calculations of natural frequencies. Introduction to Matlab. Write first interim report.

Week 2: Preliminary exercises. All students do two 'guided' exercises individually, to calculate vibration frequencies and mode shapes of a simple beam, using: (i) the dynamic stiffness method and (ii) the FE method with Patran. Write second interim report.

Weeks 3 & 4: Develop and implement detailed models. Each student will implement a detailed model of the laboratory component, using either: (i) lumped parameter model (Matlab), (ii) dynamic stiffness method (Matlab), (iii) FE method. Final report comparing the results of all three methods with experimental results.

MINI-LECTURES

Three mini-lectures will be presented, covering:

1. Summary of calculation methods;
2. Modelling issues: mass, stiffness, damping;
3. The dynamic stiffness method;
4. The finite element method.
5. The lumped-parameter method.

Calculation Methods to be Employed

1. Analytical: beam solutions, single DOF, Rayleigh's method.
2. Lumped-parameter models (Matlab).
3. Dynamic stiffness method (Matlab).
4. Finite element method.

ASSESSMENT

Format: Submission Date - Marks

Interim report 1: Thursday 16 May 2013 - 15 marks

Interim report 2: Thursday 23 May 2013 - 15 marks

Final report: 4pm Thursday 6 June 2013 - 50 marks

Last updated: November 2012