Dynamic response with fraction laws: Eigen solution of clamped-simply supported rotating shell

The shell problem in this work is modeled as a rotating cylindrical shell with three distinct volume fraction rules. There is a connection between polynomial, exponential, and trigonometric fraction laws and the governing equations for shell motion. The fundamental natural frequency is examined for several parameters, including height-radius and length-to-diameter ratios. The resulting backward and forward frequencies rise with rising height-to-radius ratios, whereas frequencies decrease with increasing length-to-radius ratios. Furthermore, as the angular speed increases, the forward and reverse frequencies decrease and increase, respectively. By using MATLAB coding, the eigen solutions of the frequency equation have been found. The findings for the clamped simply supported condition have been taken out of this numerical procedure in order to examine the properties of shell vibration. The generated results provide evidence for the applicability of the current shell model and are also supported by previously published material.