A wavelet-based method for vibration analysis of cylindrical shells with arbitrary cross-sections

The cylindrical shell with an arbitrary cross-section exhibits a pronounced variation in circumferential curvature, which presents a major challenge to the structural vibration analysis. This work develops a wavelet-based method to analyze the vibration of cylindrical shells with arbitrary cross-sections. First, the detailed process of shell vibration modeling is provided by the variational method. Then, with the optimized basis function selection and matrix element integration strategy, the Gaussian wavelet-based method is presented, and verified against the finite element method results. Finally, the numerical results reveal the effects of the cross-sections on the natural frequencies and circumferential mode shapes. The wavelet-based method developed in this work can effectively resolve the vibration characteristics of cylindrical shells with arbitrary cross-sections, and can be also extended to other structures with complex geometric configurations in engineering.