Analytical solution for sectorial plateswith simply-supported radial edges based on various plate theories
Ho Kuo Huei
|關鍵字:||解析解;極正向性材料;Mindlin扇形板;Reddy扇形板;振動;analytical solution;polarly orthotropic material;Mindlin sectorial plate;Reddy sectorial plate;vibration|
This thesis presents the first known analytical solutions for vibrations of a polarly orthotropic sectorial plate with simply-supported radial edges based on the Classical plate theory, Mindlin plate theory and Reddy plate theory. These solutions are series solutions constructed using the Frobenius method and exactly satisfy not only the boundary conditions along the radial and circular edges, but also the regularity conditions at the vertex of radial edges. The moment or shear force singularity at the vertex are exactly considered in these solutions. The correctness of these proposed solutions is confirmed by comparing nondimensional frequencies of isotropic plates obtained from the present solutions corresponding to different plate theories with published data obtained from closed form solutions. This thesis also investigates the effects of elastic and shear moduli on the vibration frequencies of the sectorial plates with free or fixed boundary condition along the circumferential edge. A study is also carried out about the influence of elastic and shear moduli on moment or shear force singularity at the plate origin (r=0) for different vertex angles.