Equivalent property between the one-half order and first-order shear deformation theories under the simply supported boundary conditions. (October 2017) - Endo, Mitsuru
Highlights: Relations between the one-half and first order shear deformation theories were investigated. Equivalent properties were verified for plates and beams with all edges simply supported. Frequency relationships between the classical and shear deformable theories were obtained. Series-type synthetic-frequency method was applied to obtain a frequency relationship. Abstract: It was verified that if the boundary conditions for all edges of a plate or both ends of a beam are assumed to be simply supported the theoretical framework of the one-half order shear deformation plate or beam theory with total deflection w being assumed as the sum of the bending and shearing deflections wb and ws results in being equivalent to that of the Mindlin plate theory or the Timoshenko beam theory. Based on its equivalent property, exact frequency relationships between the classical Kirchhoff plate and the above two equivalent shear deformable plate theories were deduced for general polygonal plates with all edges simply supported, and in addition an approximate frequency relationship which has a very simple form and almost enough accuracy for practical use was obtained based on the series-type synthetic-frequency method.