Studying the nonlinear response of incompressible hyperelastic thin circular cylindrical shells with geometric imperfections

Abstract

This study presents a comprehensive analysis of hyperelastic thin cylindrical shells exhibiting initial geometrical imperfections. The nonlinear equations of motion are derived using an improved formulation of Donnell’s nonlinear shallow-shell theory and Lagrange’s equations, incorporating the small strain hypothesis. Mooney–Rivlin constitutive model is employed to capture the hyperelastic behavior of the material. The coupled nonlinear equations of motion are analytically solved using Multiple-Scale method, which effectively accounts for the inherent nonlinearity of the system. To ensure the model’s accuracy, the linear model is verified by comparing the results with those obtained through hybrid finite element method. Subsequently, the model with only geometrical nonlinearity is evaluated against other research works existing in the open literature to ensure its reliability and precision. Finally, the results of the model, considering both geometrical and physical nonlinearity, are verified against the results obtained from Abaqus software. The main objective of this research is to provide a detailed understanding of the response of hyperelastic thin cylindrical shells in the presence of initial geometric imperfections. In this order, the impact of three distinct geometric imperfections – axisymmetric, asymmetric, and a combination of driven and companion modes – on the natural frequency is examined. The behavior of each of these geometric imperfections is investigated by varying their respective coefficients. The numerical results indicate that geometric imperfections enhance the natural frequency, and employing different models for imperfections leads to a variation in this trend. In the amplitude response of hyperelastic cylindrical shells, two peaks coexist, reflecting the softening and hardening responses of the system. Distinct initial geometric imperfections influence these two peaks.