Formulation of Statistical Model to Determine Natural Frequencies of the Cantilever Beam for Linear Variation of Circular Perforation Along the Length
Main Article Content
In the present work effect of circular perforation on free vibrations of a cantilever beam is studied. The arrangement considered in this study is the linear variation of single circular cut-out starting from the support end of the cantilever. This study focuses on the dependence of the natural frequency of beam on various perforation parameters. Perforation parameters considered are the diameter of perforation and distance of perforation from the support end and geometry parameters of the beam like length, breadth, and thickness. An expression for natural frequency relating to above parameters was found out and formulated into a polynomial equation of 4th order using curve fitting techniques. The main aim of this research is to non-dimensionalize the dependency relation so that the results are valid for a broad range of dimensions of cantilever without the need for modal analysis to find natural frequencies of perforated cantilever beams. These non-dimensionalized expressions are further validated by predicting frequencies of test cases and gave error percentages in the range of 1% - 3%. The natural frequencies of perforated beams were predicted as the effective resonant frequency which is the ratio of the natural frequency of perforated beam to that of the solid beam.
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