Free vibration analysis of initially deflected stiffened plates for various boundary conditions

Abstract

Free vibration analysis of initially deflected stiffened plates subjected to uniformly distributed loading with different flexural boundary conditions involving simply supported and clamped ends and zero displacement in-plane boundary conditions has been presented. A domain decomposition technique depending on the number, orientation and location of the stiffeners is employed to ensure sufficient number of computation points around the stiffeners. Geometric non-linearity arising out of large deflection is accounted for by consideration of non-linear strain-displacement relations. Mathematical formulation is based on a variational form of energy principle, and a solution technique, where static analysis serves as the basis for the subsequent dynamic study, is followed. The results are validated with the published results of other researchers. The dynamic behavior has been presented in the form of backbone curves in a dimensionless frequency-amplitude plane. Vibration mode shapes along with contour plots are provided in a few cases.