Abstract: In this study, integral calculus has been applied to the beam analogy method for the evaluation of the non-dimensional frequency parameters of isotropic functionally graded (FG) rectangular plates resting on Winkler elastic foundation. The fundamental assumptions of linear, elastic, small-deflection theory of bending for thin plates due to Kirchhoff are taken into consideration. Using direct integration, characteristic orthogonal polynomials (COPs) shape function for all-round clamped (CCCC) plate is formulated. The effect of aspect ratios on the natural frequency of the plate is examined. It is evident that adding an elastic foundation increases the non-dimensional frequency parameter of the plates. Furthermore, like plates resting on Winkler foundation, an increase in aspect ratio, causes a corresponding increase in frequency for plates not subjected to the effect of Winkler elastic foundation regardless of the boundary configuration. Hence, fixity of supports increases the fundamental natural frequency of the plate, and so increases the resistance of the plate to higher forcing frequencies before resonance can occur. It is also observed that an increase in power law index decreases the frequency parameters of the plate. The validity of the present theory is investigated by comparing some of the present results with those reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of FG plates.
Keywords: Winkler foundation, vibration, functionally graded plate, rectangular plat, characteristic orthogonal polynomials.
Title: Vibration Characteristics of Functionally Graded Fixed Thin Rectangular Plate on Winkler Elastic Foundation Using Beam Analogy Method
Author: Ohia, C. A, Onwuka, D. O, Okere, C. E, Onwuka, S. U
International Journal of Civil and Structural Engineering Research
ISSN 2348-7607 (Online)
Vol. 12, Issue 1, April 2024 - September 2024
Page No: 10-28
Research Publish Journals
Website: www.researchpublish.com
Published Date: 09-April-2024
