ISSN PRINT 2345-0533, ISSN ONLINE 2538-8479, KAUNAS, LITHUANIA 63
Free vibrational characteristics determination of plates
with various cutouts
M. L. Pavan Kishore
1
, Ch. Rajesh
2
, Ram Komawar
3
Department of Mechanical engineering, Faculty of Science and Technology, ICFAI Foundation for Higher
Education, Hyderabad, India
1
Corresponding author
E-mail:
1
kishoreml@ifheindia.org,
2
chrajesh@ifheindia.org,
3
ram.komawar017@gmail.com
Received 5 October 2018; accepted 18 October 2018
DOI https://doi.org/10.21595/vp.2018.20286
Copyright © 2019 M. L. Pavan Kishore, et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract. This paper presents a numerical study on the analysis of plates made of different shapes
aimed at the prediction of free vibration analysis in terms of natural frequencies and mode shapes.
The free vibration analysis provides the basis for designing and modeling of plates employed for
structural applications. The baseline design uses two different shapes of plates (rectangular and
square) experimented with various central holes. A symmetrical approach has been adopted in the
present investigation to find out the mode shapes and natural frequencies. The computational
efficiency in predicting the Eigenvalues by using finite element method is determined through a
number of case studies. The effect of boundary conditions (clamped free and simply supported)
in determining Eigen frequencies applied to the plate and are studied in detail. From the results, it
may be observed that the cutout has a significant effect on modal frequencies. The numerical study
carried out provides a good insight for predicting the modal behaviour characteristics of plates.
Keywords: cutouts, eigen frequencies, free vibration analysis, mode number, plates.
1. Introduction
Numerous methods have been developed for performing structural analysis of plate-like
structures. Theoretical methods give a solution to such structures which are of uniform in nature
in case of complexity it may become difficult to obtain a solution which may contain various
boundary conditions, geometry, material properties. Consequently, one may confine to
approximate numerical methods for obtaining a solution to dynamic problems. Most of the
researchers have done extreme work on the free vibration analysis of plates considering various
geometries of plates, cut-outs, bluntness, material properties, cut-out orientation, stress
concentration factors, aspect ratios etc.
2. Literature survey
The free vibration analysis of elastic plate structures using an integral approach studied by
Tanaka [1] et al. In their approach, they used the boundary integral equation method for finding
out the Eigen frequency. For zero determinant value of the system matrix. This new integral
equation approach resulted in the determination of the fundamental solution to the static problem.
For determining the free vibration analysis of an arbitrary shaped thick plate Liu [2] used a
differential cubature method a numerical technique in their analysis a linear differential operator
as a continuous function having a linear sum of discrete function values are chosen for the overall
domain. The free vibration analysis for frame type structures was carried by Moon and Choi [3],
they developed transfer dynamic stiffness coefficient method, based on the concept of transfer of
dynamic stiffness coefficient which relates to force and displacement vector at each node.
For plate type structures Myung [4] developed a finite element transfer stiffness coefficient
method for free vibration analysis using a set of different boundary conditions for Kirchhoff
rectangular plates, Lu [5] et al. used differential quadrature method for analyzing the vibrations.
A shear deformable triangular plate element was used by Karunasena and Killipornchai [6] for