Browsing by Author "Ndukwu, Micheal Uchenna"

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    Free vibration analysis of rectangular thin plate using finite element method
    (Federal University of Technology, Owerri, 2021-09) Ndukwu, Micheal Uchenna
    This research work presents Free Vibration Analysis of Rectangular Thin Plate Using Finite Element Method. The analysis is limited to five boundary conditions. These boundary conditions are plates clamped on four edges (CCCC), plates clamped and simply supported on adjacent edges (CCSS), plates clamped on two opposite edges and simply supported on the other two opposite edges (CSCS), plates clamped on one edge and simply supported on three edges (CSSS) and plates clamped on three edges and simply supported on one edge (CCCS). A shape function which satisfies the twelve degrees of freedom of plate was assembled from the Pascal triangle to formulate a stiffness matrix which is refered to as the general flexural element stiffness matrix of thin rectangular plate. The fourth order differential equation of plate in vibration was analized with the shape function to derive the general stiffness (K) of the plate and inertia stiffness (Ki) subject to vibration. Analysis with the finite element method, the individual stiffness for CCCC, CCSS, CSCS, CSSS, CCCS was obtained. A grid size discretization, one of the major importance of finite element method; was applied to determine the approximate values of the fundamental natural frequencies of the rectangular thin plates in vibration. A MATLAB program was generated to compute the fundamental natural frequencies  for plates of various aspect ratios (from 1.0 to 2.0 at an increment of 0.1) and grid size (n) (from 3 to 21 etc. at odd number increment) and the results were tabulated. The odd number increment for the grid size is to make the central deflection of the plate concide with the central node of the plate for easy calculation. The maximum percentage difference of the natural frequencies obtained between this study and previous research works done by Onwuka et al., Njoku, Leissa et al., Sakata et al., Chakraverty and Gorman are 0.4060%, 0.4070% and 3.1600% for CCCC boundary condition, 0.5503%, 0.5675% and 0.1283% for CCSS boundary condition, 0.4025%, 0.1629% and 0.1208% for CSCS boundary condition, 3.6188%, 1.4968% and 0.1034% for CSSS boundary condition and 0.4394% and 0.1461% for CCCS boundary condition. The natural frequency values obtained by the present study are close when compared with other approximate methods of Onwuka et al., Njoku, Leissa et al., Sakata et al., Chakraverty and Gorman which are clearly shown on the line graph.