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please use any student no. in the matlab table to answer the question
48660 Dynamics and Control
Project 2 – Modelling of a 2 DOF System (Part 1), Vibration Analysis (Part 2) and Experimental Verification (Part 3)
The UTS Remote Lab Shake Table rig (Figure 1) was designed to model the behaviour of a building during an earthquake scenario. The rigs have been developed as two-storey structures that emulate vibrations in a single direction with 2 degrees of freedom. The rigs were designed to help students to break down and understand the complex dynamics of such a system.
Unfortunately, the physical rigs have suffered from a lack of maintenance and are no longer operational and available for this subject. Due to this, we will be using Simulink instead.
The rig documentation is still available on UTS Online, for your reference, which contains detailed information about the shake table rigs. However, you are not required to read the documentation (“Shake_Table_User_Guide_V2-1.pdf”) in order to complete this assignment.
Students are required to model the 2 DOF system (using the simplified diagram in Figure 2), perform a vibration analysis and verify the results experimentally both in MATLAB and Simulink (which has replaced the remote lab portion of this assignment).
Figure 1- 2 Degrees of Freedom Shake Table
Students are required to produce a report detailing the three parts to the project, along with an insightful discussion and reflection relating to the tasks completed by using the provided MATLAB Live Script Template file.
Part 1: Modelling of a 2DOF System
1. Draw the free body diagrams for the two masses in the system based on the simplified diagram in Figure 2.
2. Derive the differential equations of motion for the system. The displacements ??1(??) of ??1 and ??2(??) of ??2 are measured from the rest positions of the masses.
Figure 2 shows a shear building with base motion. This building is modelled as a 2 DOF dynamic system where the variables of ??1, ??2, ??1, ??2, ??1, ??2, ??0 are specific to your student ID number and can be found in the MATLAB variable ‘StudentListVariables’ in the file entitled ‘student_list_variables_A19.mat’. Simply enter your student ID number in the MATLAB live script and the variables will be automatically populated in your workspace.
The base movement of the structure is defined by the following equation: ??(??) =
??0 sin(????).
Part 2: Vibration Analysis – MATLAB Live Script
1. By assuming undamped free vibration, calculate the natural frequencies of the system: ??1 and ??2.
2. Calculate the normal modes of vibration corresponding to ??1 and ??2, and draw their modal shapes:
(1)
???
(1) = {??1(1)}
??2

??(2)
???(2) = { 1(2)}
??2

3. Obtain the transfer functions for each of the masses, based on the differential equations of motion:
??1(??) ??(??)

??2(??) ??(??)

4. Using the provided template in the MATLAB Live Script, analyse the responses ??1(??) and ??2(??) due to the following inputs:
Unit step base movement: ??(??) = 1
Harmonic motion of the base: ??(??) = ??0 sin(??1??) Harmonic motion of the base: ??(??) = ??0 sin(??2??)
Part 3: Experimental Verification – Simulink Model
Note: to run the above Simulink “experiment” you need to have both the Simscape and Simscape Driveline add-ons installed. You can add these through the “Add-Ons” button in the MATLAB Menu tab.
1. Simulate the responses of the Shaker Table by using the provided Simulink model (shown above) and following the instructions provided in the MATLAB Live Script file.
2. Generate the required plots as prompted in the MATLAB Live Script. These should be used to conduct a brief comparative study in the discussion and reflection section. Some points to think about:
a. Was resonance observed at the calculated natural frequencies? Why/why not?
b. How did the MATLAB simulations compare with the Simulink model simulations, in terms of vibration amplitudes, modes of vibration, etc.?
Discussion and Reflection
Provide an insightful, clear, relevant but brief discussion and reflection on the tasks performed in this report. Draw some conclusions about why modelling such a system might be useful in real life engineering practice. Also discuss how the simulated (MATLAB) results compare with the simulated (Simulink) Shaker Table results.
Additional Notes
• Students should ONLY use the MATLAB Live Script Template for their submission.
• Students must include units for all quantities measured or derived.
• Students should consult the marking guide provided within the MATLAB Live Script Template file.
• Graphs and figures should be made using the template provided and annotated appropriately (with legends, titles, captions, axis labels).
• Submission is via UTS Online under the Assignments tab; follow the instructions provided.

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