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

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 t...

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Bibliographic Details
Published in2017 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
LanguageEnglish
Published IEEE 01.08.2017
Subjects
continuum mechanics
Euler-Bernoulli beam
Finite element analysis
Fractals
Mathematical model
Numerical models
Strain
tessellated
vibration
Vibrations
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DOI10.1109/MCSI.2017.21

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Summary: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.
DOI:10.1109/MCSI.2017.21