School of Engineering Department of Civil and Environmental Engineering 89 Department of Civil and Environmental Engineering Biomimicry: Structural Design Lessons from Trees Supervisor: Ilias DIMITRAKOPOULOS / CIVL Student: PENG Yongxi / CIVL Course: UROP 1100, Fall UROP 2100, Spring The rapid urbanization and increasing demand for housing have led to the proliferation of high-rise buildings characterized by high slenderness ratios, making them susceptible to structural instability under lateral vibrations from extreme weather events like hurricanes and typhoons. To address this, engineers have explored innovative structural systems for vibration mitigation, with biomimicry emerging as a promising approach. Specifically, the study of tree architecture, particularly sympodial trees, has revealed vibration mitigation mechanisms that could inform the design of resilient high-rise structures. Sympodial trees, with their fractal, hierarchical branching patterns, exhibit a unique ability to localize vibrations to smaller branches, stabilizing the slender trunk during strong winds. This phenomenon, known as self-similar modal behavior, was analytically demonstrated by Loong and Dimitrakopoulos (Loong et al. 2023, 2024) for both symmetrical and non-symmetrical sympodial trees, highlighting the critical role of their recursive branching structure in achieving these modal properties. Continuing on the previsous progress report with the aim of verifying the existence of self-similar modes through experiments. This study recorded relevant detail and results of the shake table tests, conducted on 3D-printed second- and thrid-order sympodial tree models designed. The setup of LiDAR and camera (used to record motion of tree models), frequences and amplitudes of shake table tests as well as observed selfsimilar frequences and mode shapes are included in the later sections. While the models demonstrated high accuracy in replicating structural parameters, significant discrepancies were observed between theoretical and actual vibration frequencies, suggesting areas for further investigation. Biomimicry: Structural Design Lessons from Trees Supervisor: Ilias DIMITRAKOPOULOS / CIVL Student: WONG Hok Kam / CIVL Course: UROP 1100, Fall UROP 2100, Spring Building on the previous UROP 1100 progress report, this report continues to analytically solve the modal frequencies and mode shapes of the shear-beam lumped mass structures using graphical solutions introduced in. Using the results from the previous UROP 1100 progress report, this report proves the recursive formation of the auxiliary P-functions of the shear-beam lumped mass structure. Moreover, it demonstrates that the mode shapes of the shear-beam lumped mass structure can be expressed in terms of the auxiliary P-functions.
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