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MECH481 Wind Energy

tag 0 Download 4 Pages / 785 Words tag 20-11-2020
  • Course Code: MECH481
  • University: Queens University
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  • Country: Canada


Assignment Title: Structural Response to Unsteady Loads

The goal of this assignment is to explore some of the concepts that we learned in the lectures in more depth. There are two parts to the assignment. The first is fairly simple: you will add the mass element matrices to the bar code and analyze the natural frequencies. In the second part, you will do several more simulations of the cantilever-beam airfoil to better understand how the aerodynamic loads affect the structural dynamics of the beam.

Problem 1: Calculate natural frequencies of a 2-bar linkage

Objective: Implement the theory presented in the “Modeling Structures” lecture

What to hand in:

  • A write-up summarizing your resulting natural frequencies and the requested observations. Thiswrite-up must be sufficient resolution/font size that we can read all relevant text (including figure labels).
  • The Matlab code you wrote to generate the solutions.


Part 1. In the problem_1.m file provided with the assignment, add in the mass matrices. The body/element mass matrix can be found in the lecture slides.

Part 2. Calculate the natural frequencies (in Hz) of a 2-bar linkage with the following structural properties:


E [Pa]

A [m2]

L [m]

rho [kg/m3]

Bar 1





Bar 2






Part 3. If you double the stiffness of Bar 1, how do you expect the natural frequencies to change and why? Verify your hypothesis using the code.

Part 4. If you were instead to take the parameters in Part 2 and then double the density of Bar 2, how would you expect the natural frequencies to change? Verify your hypothesis using the code.

Problem 2: Exploration of aeroelastic responses

Objective: A deeper understanding of the cantilever-beam airfoil problem


Description of the beam-airfoil:

  • Same as in “Simulating Unsteady Aerodynamic Loads” lecture
  • Cantilever, Euler-Bernoulli beam with two degrees of freedom: deflection and rotation at tip of blade
  • FFA-W3-241 airfoil with optional S. Øye dynamic stall model
  • Aerodynamic force applied as a tip load (very simplistic assumption)

What to hand in:

  • A write-up with pictures and words that answers the questions in the text below. Someone who is not familiar with the question should be able to follow your analysis/observations purely from your writing. This write-up must be sufficient resolution/font size that we can read allrelevant text (including figure labels).
  • Any code you modified for this assignment.


Part 1. Changing the angle at which the beam is mounted to the wall (Sims. A and B)

The airfoil beam is mounted to the wall with a certain angle ????geom, which is not shown in the diagram above. Using problem_2.m, simulate two different mounting angles (????geom = 20 degrees and ????geom = 5 degrees) with the following options: steady wind at 2 m/s, an initial tip displacement/angle of 0.06 m/0 degrees, and no dynamic stall. Describe the difference in simulated tip deflections for the two mounting angles. Can you explain why? Provide plots to support your explanations.

Part 2. Comparing no dynamic stall with dynamic stall (Sims. A and C)

Set ????geom to 20 degrees, but now turn on dynamic stall. Simulate the response to steady wind with 2 m/s and plot the tip deflection. Extract CL(t ) and ???? (t ) for [0.2 s, 2 s]. Plot versus for that range and compare to Simulation A. Describe the plot. Whatcharacteristics of this plot explain the differences in time-domain behavior? (Think in terms of what we learned in the previous part.)

Part 3. Dynamic stall (and none) in unsteady wind (Sims. D, E, F, G, H, and I)

Using the parameters for Simulations D through G, simulate the system behaviour for 15 seconds, then throw out the first 5 seconds to get rid of transience.

Plot the time traces of the tip displacements with and without dynamic stall on top of one another, and then plot the time traces of CLversus ???? with and without dynamic stall. What do you see? How different are the time traces with and without dynamic stall? Give your theories on why the differences are so little.

Propose a new set of simulation parameters that should result in a more significant difference between simulations with and without dynamic stall. Run these simulations and verify your hypothesis.

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My Assignment Help (2020) Wind Energy [Online]. Available from:
[Accessed 11 August 2022].

My Assignment Help. 'Wind Energy' (My Assignment Help, 2020) <> accessed 11 August 2022.

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