Thickness Configuration Effect on Frequency and Critical Speed of Spinning Variable-Thickness Cylindrical Shells

The thickness configuration effect on natural frequency and critical speed of spinning variable-thickness cylindrical shells is investigated in this paper. Based on Love's thin shell theory, the eigenfrequency equation is derived by employing the Rayleigh-Ritz method in conjunction with Chebyshev polynomials, considering the effects of Coriolis and centrifugal forces due to rotation. Seven types of thickness configurations and various classical boundary conditions are taken into account. Backward and forward wave frequencies, the critical speed, and the mode shapes of the spinning variable-thickness cylindrical shells are solved. Results show that the thickness configuration not only changes circumferential wave number corresponding to the lowest natural frequency, but also affects the critical speed. However, the influence of thickness configuration on mode shapes of the shell is not obvious. The stronger the boundary constraints, the more obvious effect of slope of thickness variation on the critical speed of spinning cylindrical shells.