Engineers & Differential Equations: Modeling Tuned Mass Dampers - Part I

I am happy to announce another publication in SIMIODE with my mentor, colleague and friend, Dr Brian Winkel, titled  “Tuned Mass Dampers – Part I,”  This paper is the first in a two-part series which utilizes principles and concepts we introduced in earlier papers to engage students in the mathematical modeling of structural response to oscillatory, dynamic loading. There is also a Teacher Version of the same work available exclusively to our teacher colleagues in SIMIODE.

In this paper, we provide a short history of how tuned mass dampers have been used to reduce displacements in infrastructure to illustrate common applications and hopefully catch students' interest. Through a series of scaffolded activities, students are introduced to the concepts of resonance and near-resonance in forced, undamped systems to establish a foundation for later exploring the effect of adding damping to the model. Some fun is had with the idea of "tuning" the natural frequency of the system to the forcing function then to the TMD and observing the results. This piece is offered as an introduction to a significant area of interest in structural engineering for teachers and students who use SIMIODE for teaching and learning differential equations in a modeling first approach. 

Note from the publisher: "SIMIODE offers materials to students and teachers (FREE) using a peer review, double blind referee system and full editorial engagement. We are very pleased that you are a contributor to that effort with this material. Thank you very much for your effort on behalf of our community and on behalf of the broader mathematics community. Your exposition and your helpful comments (based on your own experiences with this material) to fellow teachers who might elect to use this material in their classes is a great contribution as well."