Cylindrical corrugated shell structures in vibration analysis: A comprehensive study on lower and higher order theories

Abstract

This study offers an extensive and unified semi-analytical framework to compare a wide range of polynomial and non-polynomial theories concerning the free vibration of innovative shell configurations. The focus is on shell structures characterized by planforms that are either convex/concave or corrugated-shaped with a circular cross-section. A general formulation is employed, representing multiple theoretical approaches from classical to quasi-3D theories with/without normal/shear deformations. The general governing equations of motion are derived using Hamilton's principle. The solution procedure is based on the Jacobi-Ritz method, where incorporation of orthogonal polynomials enhances the convergence rate and solution stability. Additionally, a spring penalty approach is implemented to enable modeling all combinations of classical and elastic boundary conditions. This provides an additional layer of versatility, enabling the formulation to adapt to different boundary restraint scenarios. The prominent novelties of this study includes, the development of a generalized mathematical model capable of accommodating convex, concave, and corrugated cylindrical shell geometries. This model is not only generalized but also optimized for rapid convergence, ensuring that the solutions are both reliable and computationally efficient. Moreover, the study provides a comprehensive comparison of various theoretical frameworks, providing insights into their respective strengths and limitations when applied to such complex geometries.