# Formulation of Statistical Model to Determine Natural Frequencies of the Cantilever Beam for Linear Variation of Circular Perforation Along the Length

## Abstract

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.

## Article Details

How to Cite
[1]
EAGA, A., BHOSALE, S. and MALI, K. 2020. Formulation of Statistical Model to Determine Natural Frequencies of the Cantilever Beam for Linear Variation of Circular Perforation Along the Length. Romanian Journal of Acoustics and Vibration. 16, 2 (Apr. 2020), 106-112.
Section
Articles

## References

[1] Burgemeister, K. A., and C. H. Hansen., Calculating resonance frequencies of perforated panels, Journal of Sound and Vibration, 196.4, 387-399, 1996.
[2] Torabi, K., and A. R. Azadi., Vibration analysis for rectangular plate having a circular central hole with point support by Rayleigh-Ritz method, Journal of Solid Mechanics, 6.1, 28-42, 2014.
[3] Mali, Kiran D., and Pravin M. Singru., Determination of the fundamental frequency of perforated rectangular plates: Concentrated negative mass approach for the perforation, Advances in Acoustics and Vibration, 2013.
[4] Ghonasgi, Keya, Kalpit Bakal, and Kiran D. Mali., A Parametric Study on Free Vibration of Multi-Perforated Rectangular Plates, Procedia Engineering, 144, 60-67, 2016.
[5] Mali, Kiran D., and Pravin M. Singru., Determination of modal constant for fundamental frequency of perforated plate by Rayleighâ€™s method using experimental values of natural frequency, International Journal of Acoustics and Vibrations, 20.3, 177-184, 2015.
[6] Gilbert-Rainer Gillich, Emilian Stanciu, Zoltan Iosif Korka, Zeno-Iosif Praisach, Codruta Hamat, Assessing Corrosion Damage from the Natural Frequency Changes, Romanian Journal of Acoustics and Vibration, vol. 14, no. 2, 2017, pag. 63-68.
[7] Cristian Tufisi, Gilbert-Rainer Gillich, Codruta Oana Hamat, Nicoleta Gillich and Zeno-losif Praisach, 2018. Numerical Study of the Stiffness Degradation Caused by Branched Cracks and its Influence on the Natural Frequency Drop. Romanian Journal of Acoustics and Vibration. 15, 1 (Aug. 2018), 53-57.
[8] Amit Sharma, Ashish Kumar Sharma, Mathematical Modeling of Vibration on Parallelogram Plate with Non Homogeneity Effect, Romanian Journal of Acoustics and Vibration, vol. 13, no. 1, 2016, pag. 53-57.
[9] Kanak Kalita, Ishwer Shivakoti, Ranjan Kumar Ghadai, Salil Haldar, Rotary Inertia Effect in Isotropic Plates Part I: Uniform Thickness, Romanian Journal of Acoustics and Vibration, vol. 13, no. 2, 2016, pag. 68-74.
[10] Kanak Kalita, Ishwer Shivakoti, Ranjan Kumar Ghadai, Salil Haldar, Rotary Inertia Effect in Isotropic Plates Part II: Tapper Thickness, Romanian Journal of Acoustics and Vibration, vol. 13, no. 2, 2016, pag. 75-80.