Engineering Science - MECH 226 - Mechanics Coursework


1. Introduction
This course work, which carries 50% of the module marks, consists of the following parts:
Each student must write up a report which briefly describes the equipment and the procedures followed. The bulk of the marks are for the discussion of the results:
i) The results from (i) should be compared with 'standard' curves and you should comment on how accurately your results follow the expected trends.
ii) As well as the measurements, theoretical values for stress and strain should be calculated for your apparatus.
The results from (ii) and (iii) should be compared and reasons for the differences discussed.
For all three parts explain how the accuracy of the results might be improved.

2. Equipment and Outline Procedures
More detailed information will be available when the experiment is carried out.
i) The vibration experiment uses a pivoted beam fitted with an electro-magnetic exciter, an eddy current damper and an LDV to measure the beam motion. The procedure involves the following:


a) Investigating the response of the beam under free vibration with differing amounts of damping. The log decrement is calculated from the plotted curves then the damping ratio (zeta) can be determined from the logarithmic decrement.
The damped frequency can be calculated (omegad) and then using the corresponding values of zeta, the natural frequency of the system can be calculated (omegan)
b) Investigating the response of the beam under forced vibration with different amounts of damping. This involves:
a) setting a damping current;
b) setting a frequency, using the frequency analyser to measure the amplitude of the output (in volts or milli volts) and the phase angle of the output (in degrees) with respect to the input;
c) the next frequency is set and the measurements in (b) repeated;
d) a different damping current is set and (b) and (c) are repeated;
e) plot graphs of the amplitude against frequency and phase angle against frequency. Omegad values can be obtained from these curves.
ii) The equipment used for the two dimensional stress investigation will depend upon the location, but will either be a thin flat diaphragm restrained at the edge (which can be pressurised on one side) or a thin wall cylinder which can:
a) be internally pressurised;
b) have a torque applied about its axis.
These components are fitted with strain gauges in a variety of orientations. The procedure involves increasing the pressure in stages and measuring the strain on all the gauges at each pressure step. The stresses in the components can then be found by:
a) formulae for determining hoop and longitudinal stresses in thin wall cylinders when the pressure is known;
b) formulae for determining 2D stress from 2D strain measurements

iii) The finite element modelling and analysis will be carried out either with Pro/Mechanica Structure 'full version' or with the 'student edition'. If the student edition is used a full model of the component will have to be made, however in the full version, by working in the independent mode, an axisymmetric model could be used.

3. Hints on Report Writing
The text should be word processed, equations and sketches should be added by hand.
Make full use of carefully labelled sketches / digital photos to aid explanations.
Put XYZ axes on ALL DIAGRAMS to avoid confusion about directions.
Include all calculations in full - with introduction, explanation and conclusion (many of these can be put in appendices).
Either carefully read your completed report or get some one else to - to avoid careless mistakes.

4. Marking Scheme


The discussion of results should pay particular attention to comparisons between results for the same quantity obtained by different methods. Why they are different, what errors may have caused these differences and suggestions to reduce these errors.

5. Date Due
Wednesday 21st May 2003.

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David J Grieve, 3rd April 2003.