Analytical modelling of flexural vibration of arbitrary flat plates by the boundary forming approach
Résumé
The approach described in this paper provides the flexural vibration response of a finite plate of arbitrary shape and arbitrary boundary conditions in terms of the known analytical response of an infinite plate. The solution is obtained by superposing to the infinite plate two excitations: an original and a secondary excitation. The latter, which is continuously distributed outside the contour line bounding the original plate, has the role of creating at this line the boundary conditions proper to the targeted original plate. The plate displacement is obtained in terms of continuous analytical functions which in turn enable comprehensive analysis of the dynamic variables such as stress, energy density and energy flow. The key advantage of the approach is the possibility to assess the computation error. The accuracy of the method has been analysed indirectly, by comparison with known modal solutions of rectangular plates, and directly, by assessing the boundary error. The potential of the method is demonstrated using an example of a plate of complex shape and non-homogeneous boundary conditions.