Natural Vibrations of Open-Variable Thickness Circular Cylindrical Shells in High Temperature Field

The feasibility of using the transfer matrix method (TMM) to analyze open-variable thickness circular cylindrical shells exposed to a high-temperature field is explored theoretically. In the approach to the problem, the thermal degradation (TG) of thermoelastic characteristics of the material is considered. Natural frequencies and mode shapes for the cylindrical shells are investigated in detail by combining the vibration theory with the TMM. The governing equations of vibration for this system are expressed by the matrix differential equations, and the coefficient matrices are derived. After the relationship between the transfer matrix and the coefficient matrix is established, the fourth-order Runge-Kutta method is used numerically to solve the matrix equation. Once the transfer matrix of single component has been obtained, the product of each component matrix can compose the matrix of the entire structure. The frequency equations and mode shape are formulated in terms of the elements of the structural matrices. Finite-element numerical simulation has validated the present formulas of natural frequencies. Numerical illustrations, supplying pertinent information on the implications of the TG, are presented for various curvatures, aspect ratios, boundary conditions, and thickness ratios, and the pertinent conclusions are outlined.