טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentShufrin Igor
SubjectStability and Vibration of Thick Plates with Variable
Thickness
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Professor Moshe Eisenberger


Abstract

This work presents the exact numeric calculation of the natural frequencies and buckling loads for thick elastic rectangular plates tapered in one or two directions with various combinations of boundary conditions. The thickness variation of the plate is taken in a polynomial form. A wide range of plates can be described by this way to any desired accuracy. The First Order Shear Deformation Plate Theory of Mindlin and the Higher Order Shear Deformation Plate Theory of Reddy have been applied to the plate’s analysis. The governing equations and the boundary conditions are derived using the dynamic version of the principle of minimum of total energy. The solution is obtained by the extended Kantorovich method, which assumes the solution as fully separable to the directions of plate’s dimensions. This approach is combined with the exact element method for the vibration and stability analysis of compressed members, which provides for the derivation of the exact stiffness matrix of tapered strips including the effect of in-plane and inertia forces. This matrix is exact (depending only on accuracy of the computations on the digital computer), since its terms derivation is based on the exact shape functions, which are obtained by solving the set of the differential equations of motion. The critical value of the in-plane load or frequency is found such that the determinant of the corresponding stiffness matrix becomes zero. The large number of numerical examples demonstrates the applicability and versatility of the present method. Plates with linear and parabolic thickness variations for different taper ratios, length-width ratios, thickness-width ratios and various combinations of boundary conditions have been considered. The results obtained by both shear deformation theories are compared with those obtained by the classical thin plate’s theory and with published results. Many new results are given too.