Vol. 5, No. 5, 2010

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Dynamic stiffness vibration analysis of thick spherical shell segments with variable thickness

Elia Efraim and Moshe Eisenberger

Vol. 5 (2010), No. 5, 821–835

A dynamic stiffness method is presented for determining the free vibration frequencies and mode shapes of thick spherical shell segments with variable thickness and different boundary conditions. The analysis uses the equations of the two-dimensional theory of elasticity, in which the effects of both transverse shear stresses and rotary inertia are accounted for. The displacement components are taken to be sinusoidal in time, periodic in the circumferential direction, constant through the thickness, and solved exactly in the meridional direction using the exact element method. The shape functions are derived from the exact solutions for the system of the differential equation of motion with variable coefficients. The dynamic stiffness matrix is derived from the exact shape functions and their derivatives. High-precision numerical results are presented for thick spherical shell segments with constant or linearly varying thickness and for several combinations of boundary conditions. Comparison is made with results of published research and with two- and three-dimensional finite element analyses.

vibrations, thick shell, spherical shell, variable thickness, dynamic stiffness, exact element method
Received: 3 January 2010
Revised: 19 April 2010
Accepted: 3 May 2010
Published: 3 December 2010
Elia Efraim
Department of Civil Engineering
Ariel University Center of Samaria
40700 Ariel
Moshe Eisenberger
Faculty of Civil and Environmental Engineering
Technion – Israel Institute of Technology
Technion City
32000 Haifa