טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentEfraim Elia
SubjectFree Vibrations of Thick Segmented Shells of Revolution
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Professor Moshe Eisenberger


Abstract

            The present research deals with the natural vibration frequencies and modes of axisymmetric shells that are combined from different shell segments which may have an arbitrarily shaped meridian, general type of material properties, and any kind of boundary condition. For this purpose different types of axisymmetric shell segments with variable thickness and curvature was derived.  The variation of geometric and material parameters is taken in a polynomial form. A wide range of shells can be described in this way, to any desired accuracy. The primary objective of this study is to present a simple yet accurate procedure for obtaining modal characteristics of a combined shell structure by using an exact approach.

            In this work the two-dimensional shell theory presented by Reissner for the analysis of thin shells, and the first order shear deformation shell theory, in which the effects of both transverse shear stresses and rotary inertia are accounted, were applied to the analysis of thick isotropic shells, composite shells, and shells made from functionally graded materials. The dynamic behavior of shells is governed by a set of partial differential equations with variables coefficients. The present procedure enables to deal directly with the governing equations, while this might not always hold for other approaches. The solution is based on assuming harmonic vibrations in time, and for closed axisymmetric shells, an expansion of the variables in circumferential direction into several one-term analyses of the Fourier series. The solution in the meridian direction is done by employment of the Exact Element Method. The dynamic analysis of the shell has been done by the Dynamic Stiffness Method. The dynamic stiffness matrix which is derived from the differential equations of motion is free of membrane and shear locking as the shape functions that are used are the exact solution of the differential equations of motion.

            The procedure for assembling the element matrices is based on the requirement of compatibility at the element nodes. For a shell structure which is analyzed by the thin shell theory the structure is combined by connecting the segments at the line of midsurface intersection. Connection of thick segments with noncollinear meridians is achieved by using a transition segment which was derived to overcome problems of thick segments connectivity, and represent completely the corner connection of the segments. Many  numerical examples are presented in order to demonstrate the applicability and versatility of the present method.