Vibration characteristics of cylindrical shells with discontinuous connections based on the spectral element method

Abstract

Common shell of revolution, such as cylindrical, conical, and spherical shells, are widely used in marine, aerospace, and other engineering fields due to their excellent support and pressure-resistant properties. Research on their vibration characteristics has progressed from single shells to composite shells, from ribbed shells to those with complex internal substructures, and from uniform to discontinuous connections. The discontinuities in wave propagation at the boundaries of discontinuously connected cylindrical shells result in highly complex equation of vibration control, leading to limited studies in this area. This study first models the uniform cylindrical shell and annular plate as spectral elements, using trigonometric and Bessel functions to describe displacement solutions and obtain vibration responses for arbitrary boundary conditions. Then, based on artificial virtual spring theory and the weighted least squares method, the discontinuous connection between the cylindrical shell and annular plate is modeled as a circumferentially varying stiffness distribution, leading to the derivation of dynamic stiffness matrices for both continuous and discontinuous connections. Finite element simulations are conducted using ABAQUS to analyze the vibration characteristics of the discontinuously connected cylindrical shell under free, clamped, and simply supported boundary conditions. Finally, an experimental setup is used to measure the vibration response under harmonic excitation and perform impedance testing with an impact hammer. The results show that the spectral element method accurately calculates the natural frequencies of the stiffened cylindrical shell, with an overall error of less than 2 %, while the maximum error for the experimental shell is 5.8 %.