Experimental and theoretical approaches to vibration models for multi-domain asymmetrical stepped cylindrical shells: Customizing mass distribution

Abstract

This research explores the free vibration of asymmetrically stepped cylindrical shells using three-dimensional (3D) elasticity theory. In many real-world structures, the thickness is not uniform but exhibits sudden changes in cross-section that are not symmetrical about the midplane or includes attached components, such as flanges, leading to significant geometric discontinuities. These discontinuities become particularly influential in thick asymmetric shells. This study aims to achieve realistic modeling of these complex structures by carefully considering geometric discontinuities and coupling a series of cylindrical segments. The mass distribution along the shell’s length is tailored based on a constant total mass to fine-tune vibrational responses. The two-directional generalized differential quadrature (2D-GDQ) method is employed to accurately enforce boundary and matching conditions at the interfaces of adjacent multi-domain structures. In practical applications, steps in cylindrical structures are frequently asymmetric. Consequently, the proposed approach enables precise modeling of asymmetric stepped shells with non-aligned mid-surfaces without resorting to simplifications. The theoretical results are validated through experimental modal testing, finite element modeling (FEM) and those previously published in literature. Subsequently, the study examines the effects of key parameters, including boundary condition, step location, step configurations (external, internal, and dual), symmetrical/asymmetrical thickness, and mass distribution.