ANALYSIS OF FREE VIBRATION OF MODERATELY THICK CIRCULAR CYLINDRICAL SHELLS USING THE DYNAMIC STIFFNESS METHOD

This paper extends the dynamic stiffness method to the free vibration analysis of moderately thick circular cylindrical shells. Starting from the shell theory with the consideration of the transverse shear deformation and rotational inertia, the free vibration of circular cylindrical shells is decomposed into a series of one-dimensional free vibration problems with definite sinusoidal waves in the circumferential direction. This one-dimensional problem is solved by the ODE solver COLSYS to obtain the element dynamic stiffness. Natural frequencies and modes are found by applying the Wittrick-Williams algorithm and the recursive Newton's method. Since the governing equations are solved exactly when calculating the dynamic stiffness, the proposed method is exact. In the section of numerical examples, the counting method of segment clamped-ends natural frequencies J0 is verified. In general, the application of the dynamic stiffness method for the free vibration analysis of moderately thick circular cylindrical shells is reliable and accurate.