MENG 470: Mechanical Vibrations
Term Project
Project weight: 10% of the final grade
This is an open-ended project, where each group designs their own project according to some restrictions and requirements. The project includes:
Written report.
Poster.
Oral Presentation.
Physical model to validate the mathematical model.
Each group should work independently, but can share their experience by teaching their colleagues some of their useful skills. Groups should NOT have similar designs, even if the parameters are different.
1- Design a vibration system that includes the following:
a. At least 2 independent DOFs.
b. At least 2 spring components.
c. At least one damping component.
d. At least one harmonic force component with changing amplitude and velocity.
e. The system should be underdamped.
2- Draw your design using a drawing program (Pro/E, SolidWorks, etc.) or clean and professional hand drawing. Write down all the dimensions and parameters of the designed system on the drawing.
3- (10 points) On Sunday Oct. 23: Final design drawings are due. Show Eng. Essam a clear drawing of your design before this date, and get the approval by this date.
4- Once approved, use the general system parameters [which are: the spring constants (K1, K2, etc.), the damping coefficients (C1, etc.), the masses (M1, M2, etc.), the force amplitude (F0) and the force frequency (ω)] to find the following: (use a word processor, no hand writing)
a. The differential equations of motion.
b. The transient and steady state responses.
c. The natural frequencies and mode shapes
d. Check if the system can be decoupled or not (only check!).
5- Build your designed system in such a way that the force amplitude can be changed within a reasonable range, and the force frequency (speed) can be changed within a range that covers at least the first two mode natural frequencies. You should also measure the actual parameters of the system (K1, K2, C1, M1, M2, etc.) and test the actual model using reasonable values for F0 and ω.
6- Write the differential equations of motion, the transient and steady state responses, the natural frequencies, and the mode shapes (from part “4a, 4b, 4c” above) by substitute with the actual values of the parameters K1, K2, C1, M1, M2, etc. and reasonable values for F0 and ω.
7- Design a vibration absorber to reduce the vibration of the primary system at a specific excitation frequency by adding a proper secondary system.
8- Validate your vibration absorber design experimentally to show that the vibration of the primary system has been reduced.
9- Write a report that includes the following:
a. Introduction and presentation of the problem.
b. Your design drawings (from “2”).
c. How the model is built, material used, challenges faced, final model and parameter values, pictures of your model throughout building it, etc.
d. Your vibration problem and solution (from “4” and “6”).
e. Your results from testing the actual model (from “5”) with some explanations.
f. The theoretical results and experimental validation of the vibration absorber (from "7" and "8")
g. Discussion and conclusions (how your results can vary if the model parameters vary, how your model might be improved, etc.).
10- Prepare a poster that includes brief summary of all of the items presented in step “9”.
11- On Sunday Nov. 13: Do the following:
a. (30 points) Prepare and present a 10-minute presentation to show your design steps, all of the items presented in step “9”, and some videos of building and testing your model
b. (40 points) Demonstrate the model motion and response at resonance using at least the first two natural frequencies so that the two mode shapes can be identified clearly from the motion. Each group member will be asked thorough details about the project, and the grade will vary from one member to member based on their participation.
c. (40 points) Submit: (1) The project model; (2) A printed copy of the report; (3) The poster; (4) A soft copy of the report and the presentation. Clarity, proficiency and organization in your work will carry points towards your grade.