Free vibration analysis of thin plates: Bare versus Stiffened

Light weight thin alloys and composite materials have revolutionized aerospace, marine, electronics and construction industries. Based on their application and structural behaviour, plates are often designed in arbitrary shapes. This paper deals with free vibration analysis of simply supported plates with different geometries. The plates are modelled with a stiffener which is curvilinear in shape. To enable comparison of plates, three parameters viz., the area of plates, starting point of the stiffener and curvature of the stiffener were kept constant. The Finite Element model was developed for free vibration analysis using FEAST (Finite Element Analysis of Strctures). The geometries considered were circular, square, rectangular (with aspect ratio of 1.25, 1.50 and 1.75, respectively) and skew square (with 70(o), 76.67(o) and 83.33(o) skew angles, respectively). It was observed that the stiffness increased with the increase in aspect ratio of bare plates unlike the case of stiffened plates. In the case of stiffened plates, the stiffness increased with increase in aspect ratio up to 1.50 and thereafter decreased for the aspect ratio of 1.75. The bare and stiffened plates showed an increase in stiffness with increase in skewness of the geometry. Among the geometries considered, the stiffener was found to be most effective for the circular plate (110% increase in stiffness compared to bare plate) and least effective for the rectangular plate (50% increase in stiffness compared to bare plate) with 1.75 aspect ratio. The rectangular plate with aspect ratio 1.75 had the maximum overall stiffness and the circular plate had the minimum overall stiffness in the case of bare plates. In the case of stiffened plates, skew plates with 70(o) skew angle had the maximum overall stiffness and the circular plate had the minimum overall stiffness.