Frequency Plots for Base Excitation
Initial Publication Date: October 10, 2024
Summary
Students generate transmissibility vs. frequency ratio plots for a spring-mass-damper system with base excitation with contours for five different damping ratios.
CollapseLearning Goals
The intent of the assignment is for students to deepen their understanding of transmissibility by creating a plot they would see in a textbook but not fully comprehend.
By generating points for the plot, students connect with the equation of motion and its solution.
By plotting transmissibility vs. frequency ratio, they note key features of the relationship. For example, they will observe peak transmission near but not exactly at a frequency ratio of 1, lower transmissibility and shifting peaks for higher damping ratios, a transmission ratio of 1.0 for static loading, and transmissibility that approaches zero for very high frequency ratios.
Context for Use
This assignment is for homework in a combined senior- and graduate-level introduction to Vibrations class. Most students have basic programming experience, but their Matlab skills vary widely. However, this is the 3rd Matlab grader assignment they will have seen for the course. Students will have seen a derivation of the governing equation for a vibrating system with a periodic forcing function from textbook readings and course lectures.
Description and Teaching Materials
Students complete the activity within Matlab Grader. Once on the course site within the Matlab Grader platform, they see the problem statement and a Matlab code template. The template includes major elements of syntax needed including sample code for generating vectors within a nested loop and plotting. Both of these are included in the supporting file, along with the plots that will be generated by a functioning code.
Problem Description, Matlab Template, and Expected Output (Acrobat (PDF) 192kB Oct10 24)
Problem Description, Matlab Template, and Expected Output (Acrobat (PDF) 192kB Oct10 24)
Teaching Notes and Tips
Most student errors for the assignment are related to indexing the vectors within a nested loop. Providing sample syntax in a comment line within the template helped reduce these errors.
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Assessment
The Matlab Grader assessments are made from generating the correct Transmissibility and phase angle vectors.
References and Resources
Textbook: Mechanical Vibrations. Sixth Edition. Singiresu Rao. Published by Pearson. https://www.pearson.com/en-us/subject-catalog/p/mechanical-vibrations/P200000003425/9780137515288