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ENGG952 Assignment
Engineering and Information Sciences Assignment
Rules: 1. The assignment may be completed individually or by a group of up to 3 students. The group formation is your own responsibility. Members may be from the same or different tutorial groups. 2. Any case of plagiarism including copying, sharing works/results between groups, will be penalized. Students should make themselves aware of the university policies regarding plagiarism (see Subject Outline under University and Faculty Policies). 3. The assignment is due Friday 15th October by 5pm and to be submitted to Moodle as a report PDF and associated MATLAB codes. Strictly follow the report structure and page length instructions (see Report Guidelines and template on Moodle). Late submission will incur penalties as described in the Subject Outline. 4. If the assignment is completed by a group, a statement indicating the effort or contribution to the assignment by each member must be included in the report. Alternatively, all group members agree that they have contributed equally to the report and a statement to this effect is added to the report. ENGG952 Engineering Computing Spring Session 2021 ENGG952 Spring 2021 – Assignment 2 University of Wollongong Problem Statement A tuned mass damper (TMD) is a critical piece of equipment that is used to minimize vibrations in structures and machines, by using a smaller mass and the properties of resonance. TMDs find wide application in stabilizing buildings, bridges, machines and power transmission structures. As a design engineer, the ability to model and simulate the behavior of the TMD is a vital first step. In this assignment, you will use a model of the TMD shown below and simulate its dynamic behaviour in MATLAB. You will then perform an optimization to find the optimal characteristics of the TMD to fit a certain engineering criteria. Figure 1: Tuned mass damper (TMD) fitted to a single degree of freedom oscillating mass 1. A disturbance force is applied to the mass 1. ENGG952 Spring 2021 – Assignment 3 University of Wollongong Model The equations describing the dynamics of the oscillating mass and the TMD are, 1̈1 + 2(̇1 − ̇2) + (1 + 2)1 − 22 = ….. (1) 2̈2 + 2(̇2 − ̇1) + 2(2 − 1) = 0 ….. (2) where, 1 is the oscillating mass (kg), 2 is the mass of the TMD (kg), 1 is the spring coefficient (N/m) of the spring attaching 1 to the ground, 2 is the spring coefficient (N/m) of the spring attaching 2 to 1, and 2 is the damping coefficient (Ns/m) of the damper attaching 2 to 1. The displacement of mass 1 is denoted by 1, and that of mass 2 is denoted by 2. The disturbance force acts on the oscillating mass 1. ASSIGNMENT TASKS (60%) 1. Reduce the 2nd order equations (1) and (2) to a system to 1st order equations. Use the Week 8 lecture and tutorial notes for guidance. (5% Marks) 2. Input these reduced 1st order equations into MATLAB such that they can be used in the RK45 method. You are provided with a template for this in the code “Handout_ModelDynamics.m”. (5% Marks) 3. Set 1 = 50000 kg and 1 = 500 N/m. Your engineering brief requires the TMD mass 2 to be between 1-3% of the oscillating mass, 1. Choose a ratio within this range and set your mass 2. The oscillating mass 1 has a disturbance force of = 1000 N applied for the first 100ms. At initial time, the springs are at rest length (i.e. the position of 1 and 2 can be assumed to be zero) and the system is at standstill. Set all these conditions into the MATLAB code. (5% Marks) 4. Choose reasonable values for 2 and 2 and simulate the behaviour of the system for the first 400s using the RK45 routine. You may use the ode45 function in MATLAB, or use the function provided in “Handout_ModelDynamics.m”. Try to manually choose 2 and 2 such that the oscillation of 1 is minimized within 300s. (15% Marks) 5. Setup up an optimization problem using MATLAB’s fminsearch to find optimal values of 2 and 2. The objective is to have the lowest absolute amplitude of the oscillating mass 1 after 300s. Compare these values of 2 and 2 to those chosen manually.(30% Marks) ENGG952 Spring 2021 – Assignment 4 University of Wollongong Report (40 %) Follow the structure below strictly, including page length restrictions (max. 6 pages for Sections 1-4). There will be negative marking for each missing section. Cover page (Title of report, Author list, Abstract (max. 150 words)) 1) Introduction a. Explain the problem in your own words. b. Briefly describe any background that will be used to solve the problem 2) Methods a. Derive the model equations into the form required for the solution. b. Explain the methodology that will be used to solve the problem c. Explain the parameters that you will be using and why 3) Results a. State the main model results b. Explain your result figures (don’t add figures without explanation) 4) Discussion/Conclusion a. Provide a brief but concise discussion/conclusion based on your results Author contribution statement References M A X IM U M 6 P A G ES