Free Vibration Analysis of Thick Rectangular and Elliptical Plates with Concentric Cut-Out

This research paper deals with a numerical method which is modified and applied, by the authors to derive an eigenvalue of a thick plate having cut-out in which geometries of plate and cut-outs are different, through a deflection matching condition by including shear deformation and rotary inertia e...

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Bibliographic Details
Published in:Advances in materials science and engineering 2021, Vol.2021 (1)
Main Authors: Merneedi, Anjibabu, Mohan Rao, Nalluri, Natrayan, L., Yuvaraj, L., Paramasivam, Prabhu
Format: Article
Language:English
Subjects:
Aspect ratio
Boundary conditions
Deflection
Deformation effects
Domains
Eigenvalues
Elliptical plates
Energy
Finite element method
Free vibration
Kinematics
Matching
Numerical methods
Rotary inertia
Scientific papers
Shear deformation
Thick plates
Trigonometric functions
Vibration analysis
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Summary:This research paper deals with a numerical method which is modified and applied, by the authors to derive an eigenvalue of a thick plate having cut-out in which geometries of plate and cut-outs are different, through a deflection matching condition by including shear deformation and rotary inertia effects, with less computational efforts and high accuracy. The modified Independent Coordinate Coupling Method (ICCM) is validated with FEM package (ANSYS) and applied to know the change in eigenvalues for a plate with cut-out by varying various parameters like aspect ratios, cut-out size, and thickness ratios. Trigonometric functions considered at the boundary level conditions of a simply supported plate should be satisfied. Free vibrational exploration on a thick isotropic plate with various aspect ratios and an elliptical plate with various sizes is carried out through the modified ICCM. Independent coordinates are applied for a plate domain and for a hole domain individually followed by equating the deflection condition of hole and plate, a reduced mass to express with cut-out from which eigenvalues can be obtained. The deflection matching condition facilitates the analysis even though the geometries of plate and cut-outs are different.
ISSN:1687-8434
1687-8442
DOI:10.1155/2021/7212075