Formulation of Pre-stressed Spectral Element for Vibration Analysis of Thick Circular Cylindrical Shells Stiffened by Longitudinal Stiffener

This paper presents a concise yet comprehensive method for formulating new spectral elements of circular cylindrical shells subjected to internal pressure and stiffened with longitudinal beam. The method is based on the dynamic stiffness matrix, built using first-order shear deformation theory, and natural frequencies are easily calculated. The formulation of the dynamic stiffness matrix requires coupling pre stressed shell and longitudinal stiffener. The dynamic analysis is executed with numerical examples to determine the performance of the proposed model and the effect of the internal pressure and stiffener on the natural frequencies. The response of the system is resolute with applied equivalent loads on element boundaries. The Comparison of responses of an unstiffened cylinder and cylinder with one beam stiffener show that stiffened cylindrical shells have higher natural frequencies than unstiffened cylindrical shells as the axial mode number increases. For higher-order longitudinal mode numbers, the stiffener performs better. Results regarding the relationship between longitudinal and circumferential mode number and the influence of static pressure on eigenfrequencies were observed. Responses of stiffened pre-stressed shells have been compared with Finite Element Method (FEM) results. Numerical examples demonstrate the performance of this approach. The method reduces size and computing time with higher accuracy in the high-frequency range.