Modelling of the vibration of self-similar branched structures such as trees

Abstract

This report aims to provide a concise and clear study of fractal patterns using tree fractals to study the free vibrational characteristics that tree fractals exhibit. This report will provide an understanding of where and how tree fractal structures are used currently. Through the literature review, it hopes to give a clear picture on the lack of study of tree fractal structures and provide the motivation to conduct the study. The study depicted in this report uses both manual calculations and MATLAB software to generate the tree models to be used in the study. Furthermore, with the usage of ANSYS APDL, the tree models will be analysed through three main studies. The first study is based on each fractal iteration, this is followed by changes to branch lengths over a constant ratio. The last portion of the study is based on element divisions across each fractal iteration, these studies will provide an understanding of the natural frequency characteristics exhibited by the tree models. After conducting the studies on tree fractals, the report will review the observations and findings that can be seen from the results of the study. In addition, the report will attempt to explain why certain patterns are present. The report will then conclude with what could be further done to provide a better understanding on the subject of tree fractals.