Vibration Characteristics of Rotating Pre-Twisted Porous P-FGM and E-FGM Cylindrical Shells with Bi-Directional Thickness Variation under Nonlinear Temperature Gradient

This study investigates the free vibration behaviour of rotating, pre-twisted, porous, functionally graded (FG) cylindrical shells with variable thickness, representing turbomachinery blades operating under coupled thermo-mechanical fields. The effective material properties are assumed to vary through the thickness according to power-law and exponential gradation schemes, incorporating even and uneven porosity distributions and temperature dependence. A nonlinear temperature profile is established using Fourier’s heat conduction equation. The governing equations of motion are derived based on Lagrange’s energy formulation, and natural frequencies are obtained by solving the corresponding eigenvalue problem. A comprehensive parametric study is performed to assess the influence of the gradient index, porosity type and factor, gradation law, taper ratio, pre-twist angle, shell geometry, rotational speed, and temperature gradient. Results show that increasing the gradient index, pre-twist, or temperature gradient leads to a reduction in natural frequencies, while rotation increases them through centrifugal stiffening. Porosity decreases frequencies at higher gradient indices but may enhance them at lower indices. The effects of geometry and taper are also significant: long shells exhibit higher stiffness than intermediate and short shells, and spanwise taper yields greater frequency enhancement than chordwise taper. The results provide valuable design guidelines for optimizing the dynamic performance of rotating FG cylindrical shells in high-temperature applications.