Tessellated Continuum Mechanics: Forced Vibration of Cantor Dust-Like Structures

• Published in: 2017 Fourth International Conference on Mathematics and Computers in Sciences and in Industry (MCSI) pp. 81 - 85
• Main Authors: Davey, Keith, Darvizeh, Rooholamin, Sedqi, Zainab
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.08.2017
• Subjects: continuum mechanics; Euler-Bernoulli beam; Finite element analysis; Fractals; Mathematical model; Numerical models; Strain; tessellated; vibration; Vibrations
• DOI: 10.1109/MCSI.2017.21

This paper is concerned with testing and validating tessellated continuum mechanics (TCM) through holey-structure vibration case studies. There presently exists no means of performing vibration analysis of holey structures in the framework of classical continuum mechanics. TCM is as a new approach that introduces an equivalent continuous model on a tessellated continuum that exactly replicates the physics of a corresponding discontinuous pre-fractal holey structure. In this study pre-fractal beams from the Cantor-dust set (E^3) are considered as illustrative examples of holey pre-fractal structures. The results of the study confirm the validity of the approach for classical-beam structures subject to forced vibration under clamped-free boundary conditions.