Vibration and Dynamic Stability of Stiffened Plates with Cutout

Abstract

Stiffened plates are structural components consisting of plates reinforced by a system of ribs to enhance their load carrying capacities. The stiffened plates are often subjected to dynamic in-plane loads of varying magnitude and complexity. Cutouts in aerospace, civil, mechanical and marine structures are inevitable mainly for practical and design considerations. The applied load is seldom uniform and the boundary conditions may be completely arbitrary in practice. Stiffened plates subjected to dynamic in-plane loading may undergo unstable transverse vibrations for certain combinations of the values of the load parameters. The present paper deals with the dynamic instability analysis of eccentrically stiffened plates with cutout subjected to harmonic in-plane partial edge load using Bolotin’s method and Hill’s infinite determinants. Finite element formulation is applied to study the effects of different boundary conditions, aspect ratios, various parameters of stiffened plates, cutout size, various partial edge loading position and extent on excitation frequency parameters and principal instability regions. In the present analysis, the plate is modeled with the nine nodded isoparametric quadratic element with five degrees of freedom, where the contributions of bending and membrane actions are taken into account. Stiffened plates with cutout are more pronounced in comparison to the unstiffened plates. The onset of instability occurs with lower excitation frequencies for small cutout. The width of instability region increases with the increase of cutout size for both simply supported and clamped edge conditions.