Abstract
The free flexural vibration of thin rectangular plates is revisited. A new, quasi‐exact solution to the governing differential equation is formed by following a unique method of decomposing the governing equation into two beam‐like expressions. Using the proposed quasi‐exact solution, a Dynamic Coefficient Matrix (DCM) method is formed and used to investigate the free lateral vibration of a rectangular thin plate, subjected to various boundary conditions. Exploiting a special code written on MATLAB®, the flexural natural frequencies of the plate are found by sweeping the frequency domain in search of specific frequencies that yield a zero determinant. Results are validated extensively both by the limited exact results available in the open literature and by numerical studies using ANSYS® and in‐house conventional FEM programs using both 12‐ and 16‐DOF plate elements. The accuracy of all methods for lateral free vibration analysis is assessed and critically examined through benchmark solutions. It is envisioned that the proposed quasi‐exact solution and the DCM method will allow engineers to more conveniently investigate the vibration behaviour of two‐dimensional structural components during the preliminary design stages, before a detailed design begins.
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