Vibration investigation of an imperfect FGM cylindrical shell reinforced by various types of stiffeners with temperaturedependent properties resting on an elastic foundation

This study examines the vibration response of imperfect functionally graded (FG) cylindrical shells reinforced with different types of eccentrically placed stiffeners. The material composition follows a power-law distribution, varying with different grading indices. The analysis is conducted analytically under simply supported boundary conditions, considering longitudinal and transverse stiffeners of circular, rectangular, and triangular crosssections. The cylindrical shell, resting on an elastic foundation, is subjected to thermo-mechanical loading. The governing equations are derived using the first-order shear deformation theory, incorporating von Kármán-Donnell nonlinear geometric formulation and the smeared stiffener method. A numerical approach combining the fourthorder Runge-Kutta method and Galerkin's procedure is employed to evaluate the dynamic response and natural frequencies. Results reveal that increasing foundation stiffness enhances natural frequencies by 15% and reduces vibration amplitude. Conversely, elevated temperature leads to a 12% reduction in natural frequencies and a decrease in structural rigidity, highlighting the coupled effects of thermal and mechanical loads on the shell's dynamic behavior.