Dynamic analysis of stepped composite cylindrical shells surrounded by Pasternak elastic foundations based on the continuous element method

Abstract

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.

Dynamic analysis of FG stepped truncated conical shells surrounded by Pasternak elastic foundations

“…On the basis of the assumptions of moderately thick shell theory, the displacement components of an arbitrary point in the FG shell for the first-order shear deformation theory are expressed in terms of the displacements and rotation components of the middle surface as given below [9]…”

“…where m is the number of circumferential wave. Substituting (13) in equations ( 12) and (10), a system of ordinary differential equations in the x-coordinate for the m th mode can be expressed in the matrix form for each circumferential mode m as [9]…”

“…Natural frequencies will be extracted from the harmonic responses of the structure by using the procedure developed in [8,9].…”

“…The continuous element formulations here are established based on the analytical solution of differential equations for composite conical shells giving high precision results. Nam et al [9] presented 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.…”