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

•Methodology: We introduce a novel analytical approach based on the spectral element method for assessing the vibrational characteristics of discontinuously connected cylindrical shell structures. The method's validity is corroborated by comparing the vibrational frequency responses from finite element computations and experimental tests, demonstrating accurate predictions of structural vibrations.•Frequency analysis: The inherent frequencies of rib-reinforced cylindrical shells calculated using the spectral element method show a high degree of agreement with those obtained from ABAQUS finite element analysis, with a total error margin of less than 2 %. Minor discrepancies in peak magnitudes are noted; however, the general trends, peak positions, and numerical values of the frequency responses are fundamentally aligned.•Comparative evaluation: When juxtaposed with the test results from the discontinuously connected cylindrical shell test rig, the acceleration frequency response curves derived from free-state mechanical impedance tests, finite element simulations, and analytical method analyses exhibit a high level of congruence in both overall trends and numerical values. The maximum relative errors in the natural frequencies across the three test conditions are 4.2 %, 5.8 %, and 2.6 %, respectively, for experimental calculations and finite element simulations. 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 derivati