Buckling and vibration of orthotropic plates with an internal line hinge

Abstract

This study presents analytical solutions for the buckling and vibration of uniaxially/biaxially loaded orthotropic thin and thick rectangular plates with an internal line hinge. The plate is taken to be flat, rectangular, with edges aligned along the material principal directions. The rectangular plate is simply supported on two parallel edges and the remaining two edges may take any combination of support conditions. The line hinge is perpendicular to the two simply supported parallel edges. The Lěvy solution method and the state-space technique are employed in connection with the classical plate theory (CPT) and first order shear deformation theory (FSDT) to study the buckling and vibration of orthotropic thin and thick rectangular plates with an internal line hinge. Numerical results are presented for all the six possible sets of boundary conditions. Exact buckling factors are obtained for rectangular plates of different modulus ratios (orthotropy), and aspect ratios corresponding to various hinge locations, and edge support conditions. In particular, buckling factors are determined for plates with modulus ratios of 1, 3, 10 and 25 using the classical plate theory and first order shear deformation theory. Vibration frequencies are obtained for the first 10 modes of vibration using both the theories. Extensive results are tabulated and complemented with figures in order to provide a vivid picture of the influence of the internal line hinge on the buckling and vibration behavior of orthotropic rectangular plates.