Don’t say “modal analysis:” A backdoor introduction to vibrations via programming and numerical methods

• Published in: The Journal of the Acoustical Society of America 2024-03, Vol.155 (3_Supplement), p.A208-A208
• Main Author: Wallen, Samuel P.
• Format: Article
• Language: English
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/10.0027326

As an undergraduate degree requirement, The Walker Department of Mechanical Engineering at the University of Texas at Austin teaches a lower-division, introductory course on computer programming and numerical methods. The enrollment consists primarily of second-year mechanical engineering (ME) students, approximately half of whom enter the course with no prior programming experience. Due to its relatively early position in the ME curriculum, the course presents the unique challenge of teaching students to apply numerical methods to ME-relevant problems, with little background about the physics involved or the contexts in which they are likely to occur in practice. This talk presents an end-of-term project in which students use two numerical methods discussed earlier in the course, singular value decomposition and Runge-Kutta methods, to construct, simulate, and benchmark a reduced-order, dynamic model of a vibrating guitar string. In addition to reinforcing course outcomes associated with programming, mathematics, and data visualization, this project provides an introduction to acoustics, vibration, and modal analysis at a level that belies its position in the overall curriculum.