Vibration, Buckling and Stability Analyses of Spinning Bi-Directional Functionally Graded Conical Shells

Abstract

This paper investigates the free vibration, buckling and dynamic stability of spinning bi-directional functional gradient materials (BDFGMs) conical shells. The material properties vary along the thickness and axial direction. The dynamics model is established based on the first-order shear deformation theory and the governing equations and boundary conditions of the conical shell are derived employing Hamilton’s principle. Subsequently, the differential quadrature (DQ) method is employed to discretize the governing equations into an algebraic system of equations for solving and analyzing the free vibration characteristics of the conical shell. The theoretical model’s accuracy and the solution method’s reliability are rigorously verified. The effects of temperature, functional gradient index, and rotation on the vibration characteristics, traveling wave vibration and critical speed of the conical shell in a thermal environment are systematically explored through numerical analysis. The results indicate that both the material gradient index and temperature increase lead to a decrease in the shell’s natural frequency. For the spinning BDFGMs shell, elevated temperature causes the occurrence of trailing wave vibration to advance to the critical speed. Centrifugal force emerges as the primary factor influencing the critical buckling load and unstable region variation of the spinning shell.