This research presents a continuous element model for solving vibration problems of stepped composite cylindrical shells surrounded by Pasternak foundations with various boundary conditions. Based on the First Order Shear Deformation Theory (FSDT), the equations of motion of the circular cylindrical shell are introduced and the dynamic stiffness matrix is obtained for each segment of the uniform shell. The interesting assembly procedure of continuous element method (CEM) is adopted to analyze the dynamic behavior of the stepped composite cylindrical shell surrounded by an elastic foundation. Free vibrations and harmonic responses of different configurations of stepped composite cylindrical shells on elastic foundations are examined. Effects of structural parameters, stepped thickness and elastic foundations on the free vibration responses of stepped composite cylindrical shells are also presented. Comparisons with previously published results and finite element (FE) analyses show that the proposed technique saves data storage volume and calculating time, and is accurate and efficient for widening the studied frequency range.

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Abstract. This article studies the free vibration of composite ring-stiffened cylindrical shells by the continuous element method (CEM). The dynamic stiffness matrix (DSM) of the studied structure has been constructed based on the analytical solutions of the governing equations of motion for composite cylindrical shells and annular plates. By applying the assembly procedure of the continuous elements method, natural frequencies and harmonic responses of composite ring-stiffened cylindrical shells are determined. In addition, the proposed model allows to exactly extract ring-stiffener vibration modes. Numerical examples confirm advantages of the proposed model: high precision solution even in medium and high frequencies, saving in calculating time and volume of data storage.