3rd TAGRA

This study focuses on the development and MATLAB implementation of a four-node quadrilateral (Q4) finite element for the free bending vibration analysis of isotropic plates. A Mindlin–Reissner plate formulation is adopted so that transverse displacement and two independent rotations are considered at each node. The element formulation includes bending and transverse shear deformation, and a consistent mass formulation is used for dynamic analysis. The element equations are formulated in natural coordinates using bilinear Q4 shape functions, Jacobian transformation, numerical integration, and global finite element assembly. The transverse free vibration behavior of a uniform rectangular-cross-section structure fixed at its left edge is investigated. The natural frequencies are calculated by solving the generalized eigenvalue problem obtained for the global system. The results are also validated using ANSYS software. To further validate the numerical model, experimental modal testing was conducted on polyester specimens with three different thicknesses: 8 mm, 12 mm, and 16 mm. The experimental results exhibit good agreement with the numerical predictions across all three specimen thicknesses.