Semi-Analytical Solutions for Free Vibration and Flutter of Stiffened Plates

This work presents a semi-analytical solution method for free vibration and supersonic flutter of rectangular stiffened thin plates. In this semi-analytical method, the displacements of stiffened plates are expressed as the superposition of the closed-form natural modes of unstiffened plates; the Kirchhoff plate theory and the linear piston theory are employed; and the stiffeners are modeled using a curvilinear beam theory. The present method can deal with rectangular stiffened thin plates with arbitrary homogenous boundary conditions. Numerical results demonstrate that the present semi-analytical solutions using fewer base functions can yield more accurate higher modes, which is a key advantage compared to other superposition methods. In addition, considering a rectangular plate with two opposite edges simply supported and stiffened by a single straight stiffener, exact solutions are achieved by an analytical method, where the governing differential equations of the stiffened plate are derived according to the generalized Hamilton variational principle and solved by the semi-inverse method. The present results are validated by detailed comparisons with those of the MSC/NASTRAN Software System and available literature.