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.
Highlights
Many vibrating airframe structural components could be modelled as thin plates
10 more different sets of boundary conditions were considered, where the Dynamic Coefficient Matrix (DCM) results were validated against only exact results from reference [13]
As explained before, the DCM formulation can be applied to any thin rectangular plate configuration with any aspect ratio
Summary
Many vibrating airframe structural components could be modelled as thin plates. that do these structural elements transmit various internal and external loads that may affect their stiffness but they are frequently in close proximity to vibrating components such as engines. It is of utmost importance to device and develop solution techniques to study the vibrational characteristics of these structures during preliminary design stages Such vibrational analyses would allow the designers to investigate the effects of various boundary conditions the structural elements would be subjected to during its operation and the vibrational characteristics of the component before progressing to advanced stages of design. Among the many methods available for vibration analysis, the analytical and semianalytical methods yield the highest accuracy but one major hurdle in using these methods is that they require the closed form solution to the governing partial differential equation This can be a very tedious process if at all a tractable one. These exact methods are only applicable to specific plate shapes, geometries, and those subjected to certain boundary conditions
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