Thermoelastic free vibration of rotating pretwisted porous p-FGM, e-FGM, and s-FGM conical shells in nonlinear temperature distribution

The free vibration response of rotating pretwisted functionally graded (FG) conical shells in nonlinear thermal conditions is investigated using a finite element approach with the purpose of application in turbomachinery blades. With the aid of power, exponential, and sigmoid laws, the pretwisted conical shell is functionally graded in its transverse direction. The distribution of both even and uneven porosity is considered. The one-dimensional Fourier heat conduction equation is used to assess the nonlinear temperature distribution across the thickness of the FG conical shell. Lagrange’s equation is used to obtain the dynamic equation of motion of the rotating pretwisted FG conical shell. The proposed finite element model employs an eight-noded isoparametric shell element with five degrees of freedom per node. The effect of several factors, including porosity, temperature, twist angle, and rotational speed on the free vibration response of the FG porous conical shell has been investigated. The findings reveal that the porosity volume fraction has a significant influence on the natural frequency. The nonlinear temperature difference and pretwist angle both cause stiffness reduction to the FG conical shell upon increasing, whereas the presence of rotational speed inducts geometrical stiffness resulting in centrifugal stiffening.