Dynamic Stability of Plates by Finite Elements

The parametric resonance (dynamic stability) of flat plates under the action of pulsating inplane normal and shear loads is investigated using finite element techniques. Included in the investigation are rectangular, homogeneous and isotropic flat plates of constant thickness. Plates, with and without damping, and plates on an elastic foundation, with and without damping, are considered. The governing matrix equations for an idealized system of rectangular plate elements are developed using the Lagrangian equation. This is equivalent to the direct stiffness approach. Several examples are solved and the results are illustrated on a series of charts and figures. No presupposition of similarity between vibration and static buckling modes is made. Accordingly, it is possible to define the regions of dynamic instability in relation to any of the frequencies of transverse free vibration. In the special cases of similar vibration and static buckling modes, the results obtained check favorably with the previous work.