Aim

The aim of this experiment is to: Investigate the free/Forced response of a vibrating system in the time and frequency domain

Part -1

Task description

Vibration testing and analysis

(a) Investigate the free response of a vibrating system in the time and frequency domains using experimental method (Refer to Lab 2: Vibration analysis and modelling of a cantilever beam)

i. Investigate the time and frequency domain response of the cantilever beam when perturbed (without the mass attached to the end of the beam).

ii. Attach the mass at the end of the beam and determine the damped natural frequency of the cantilever beam

(b) Analyse the response data of the vibrating systems utilising MATLAB software (Refer to Lab 1 (Part 2) - MATLAB for Modelling & Analysis)

i. Identify the dominant damped natural frequencies and plot time and frequency domain responses of cantilever beam with/without mass attached.

ii. Using the time domain response, determine the natural frequency and damping ratio using log decrement method.

(c) Investigate the forced response of a vibrating systems identifying natural frequencies and associated mode shapes (Refer to Lab 2: Vibration analysis and modelling of a cantilever beam)

i. Perform a frequency sweep using the signal generator starting from 5Hz to 300Hz. As you increase the frequency, determine the first three damped natural frequencies and their associated vibrating shapes where the amplitudes of vibration increase significantly.

ii. Develop your understanding of the concepts of magnification factor - Perform a frequency sweep from 1Hz to three times the first damped natural frequency. Take regular readings of frequency and accelerometer amplitude and try to recreate graph for magnification factor.

(d) Mathematical modelling of the cantilever beam

Theoretically model the cantilever beam, which you have used in your experiment, as one degree of freedom system. You should consult your lecture notes and tutorial examples regarding one degree of freedom modelling and utilise your critical reasoning skills for analysing how to model these systems. Calculate the natural frequency of the beam with/without mass attached.

(e) Verification and validation of the results by comparing the experimental and the analytical results.

Part -2:

Principal stress determination - Overview

NB: This task belongs to the Solid Mechanics part that will be taught in term 2.

(a) To conduct a laboratory experiment to measure strains on the surface of the cantilever subject to a lateral load using a strain rosette (see Figure 1 showing Strain rosette connected to Strain indicator)

(b) To determine the experimental principal strains by applying strain transformation methods

(c) To calculate the experimental principal stresses by applying the generalised Hooke's law

(d) To calculate the theoretical principal stresses by applying the simple bending theory

(e) To estimate the principal stresses by computer simulation using an industry standard FEA software, Solidworks Simulation

(f) To verify the principal stress results by comparing the theoretical and the simulation results

(g) To validate the principal stress results by comparing the experimental and the analytical results

(h) To demonstrate critical investigations of discrepancies in the verification and validation process.

(i) To compare the three different approaches of principal stress determination, i.e., theoretical solution, numerical solution by FEA simulation and experimental testing. Evaluate the merits and limitations of each approach and their integrated application.

Report Description

Report
An e-report is required to be submitted via Moodle. The report should be limited to within 20 pages for the main body and additional appendices, without a page limit, should be used to include computer programs, lengthy calculations and any results that have been referred to in the main text.

Report Content
You are required to submit an individual report for this assessment. All tasks in the Task Description section should be addressed.

Report Structure and Style
Follow the guidance on writing reports published in the Student Toolkit on the School of Engineering Students Moodie area.

Your report should have the following sections:

Title
Abstract
Introduction
Literature survey
Theory, method, result and discussion for each item in Task Description
Discussions on more general aspects not covered within the above section
Conclusion
Bibliography
References
Appendices

Attachment:- Lab.rar