Session: 15-01-01: ASME International Undergraduate Research and Design Exposition

Paper Number: 151826

151826 - Modal Analysis of a Toothpick Pattern Structure 

Previous work in the field of vibrations has extensively explored the dynamical behavior of periodic structures when subjected to vibrations. Such periodic structures have enabled new engineering applications, ranging from vibration attenuation and noise control to wave guiding and non-reciprocal wave propagation. In comparison, aperiodic structures have generally received less research attention, despite their potential to realize interesting vibration and wave phenomena, such as mode localization, topological wave pumping, edge states, and corner modes. As such, the objective of this research is to study novel aperiodic toothpick-pattern structures with varying generational progressions when subjected to vibrations. Being popular in computer science and mathematics circles, the toothpick pattern is built following a replication algorithm starting from a single slender beam (i.e., a toothpick), representing the first generation, with each subsequent generation adding new toothpicks to every free end of the structure. This process results in an aperiodic structure with unique shapes that grow in complexity with increasing number of generations.

 

In a previous work by the second author, the dynamical behavior of aperiodic structures inspired by the Ulam-Warburton cellular automaton was investigated. The dynamics of such structures revealed interesting behaviors, such as corner modes, repeated natural frequencies across different generations, and symmetry in the eigenfrequency spectrum. Although the proposed toothpick pattern follows a similar generational algorithm, its behavior under dynamic loading remains unknown, necessitating a dedicated study to uncover its dynamics. Motivated by this, numerical analyses of the toothpick patterns at varying generations will be conducted, with special emphasis on the evolution of natural frequencies as the structure grows through additional generations. Additionally, the relationship between relative density (the ratio of the mass of the toothpick-pattern structure to that of a solid plate of similar overall dimensions) and the number of generations, and how this relates to frequencies, will be examined. The effective stiffness of such aperiodic structures is also of interest, and correlations between relative density, number of generations, and effective stiffness will be investigated. Furthermore, the existence (or the lack thereof) of corner modes will be explored, as these modes are of particular interest in the literature due to their intriguing behavior, allowing the corners to be excited without affecting the rest of the structure. Once the numerical analysis is completed, future work will include experimental validation of the obtained numerical results. We envision that this research will offer new insights into the study of aperiodic structures and how algorithm-based aperiodicity affects their vibratory behavior.

Presenting Author: Spencer Walter Union College

Presenting Author Biography: Spencer Walter is a 4th year student at Union college majoring in Mechanical engineering. He is pursuing research in vibrational mechanics. He has been an active member of the Union College community as a member of the club rugby team and has been a residential advisor in the residence halls.

Authors:

Spencer Walter Union College
Hasan Al Ba'ba'a Union College