Abstract
An exact generalised formulation for the free vibration of shells of revolution with general shaped meridians and arbitrary boundary conditions is introduced. Starting from the basic shell theories, the vibration governing equations are obtained in the Hamilton form, from which dynamic stiffness is computed using the ordinary differential equations solver COLSYS. Natural frequencies and modes are determined by employing the Wittrick-Williams (W-W) algorithm in conjunction with the recursive Newton’s method, thus expanding the applications of the abovementioned techniques from one-dimensional skeletal structures to two-dimensional shells of revolution. A solution for solving the number of clamped-end frequenciesJ0in the W-W algorithm is presented for both uniform and nonuniform shell segment members. Based on these theories, a FORTRAN program is written. Numerical examples on circular cylindrical shells, hyperboloidal cooling tower shells, and spherical shells are given, and error analysis is performed. The convergence of the proposed method onJ0is verified, and comparisons with frequencies from existing literature show that the dynamic stiffness method is robust, reliable, and accurate.
Highlights
Shells of revolution form an important class of structures that are used in a variety of engineering applications, for example, pipes, chimneys, cooling towers, containment vessels, and aircraft fuselages
Since COLSYS is capable of controlling the error tolerance due to its self-adaptability, the number of clamped-end frequencies exceeded by ω∗ on submesh (̂e) has to be zero, suggesting that J0(̂e) = 0
A FORTRAN program was written by the authors to determine the eigenproblems of a shell of revolution with general shaped meridians and arbitrary boundary conditions, and numerical examples provided in this paper are all computed by this program
Summary
Shells of revolution form an important class of structures that are used in a variety of engineering applications, for example, pipes, chimneys, cooling towers, containment vessels, and aircraft fuselages These structures usually operate in complex conditions subject to dynamic loads. A recent paper [31] applied the dynamic stiffness method and the W-W algorithm to the free vibration analysis of thin circular cylindrical shells. A generalised formulation for free vibration of shells of revolution with general shaped meridians and arbitrary boundary conditions is presented, enriching the literature on shell vibration using the dynamic stiffness method. Numerical results on the vibration behaviour of circular cylindrical shells, cooling tower shells, and spherical shells are given, showing that the exact dynamic stiffness method is applicable, accurate, and robust
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