Closed-form solution for free vibration of variable-thickness cylindrical shells rotating with a constant angular velocity. (September 2021)

• Record Type: Journal Article
• Authors: Taati, Ehsan; Fallah, Famida; Ahmadian, Mohamad Taghi
• Is Part Of: Thin-walled structures. Volume 166(2021)
• Publication Date: 2021-09
• Subjects: Free vibration -- Rotating cylindrical shells -- Axisymmetric thickness variation -- Classical Love's shell theory -- Galerkin's method; Thin-walled structures -- Periodicals; 690.1
• DOI: 10.1016/j.tws.2021.108062
• Languages: English
• ISSNs: 0263-8231

Abstract

Abstract: Based on the classical Donnell's and Love's shell theories, free vibration behavior of variable-thickness thin cylindrical shells rotating with a constant angular velocity is analyzed. The equations of motion and corresponding boundary conditions of rotating homogenous cylindrical shells with axisymmetric variation of thickness are derived using Hamilton's principle. This formulation includes effects of initial hoop tension due to the centrifugal force as well as Coriolis and centrifugal accelerations. Considering the variation of stiffness coefficients in axial direction, the classical Love's theory results in a coupled system of two second-order and one fourth-order partial differential equations with variable coefficients in terms of kinematic variables. The Galerkin's method is used to obtain a closed-form expression of sixth-order frequency equation with coefficients in terms of rotation speed ( Ω ) for with boundary conditions. The natural frequencies of stationary and rotating cylindrical shells with constant thickness, as special cases, are validated with existing ones in the literature. Case studies are presented for three different patterns of thickness variation in forms of arbitrary power, axisymmetric modal and stepwise functions. It is seen that the influence of thickness variation on the natural frequencies and mode shapes is a function of different parameters including rotation speed, boundary conditions, and geometric ratios, especially this effect is much more pronounced for cantilever long shells with a high rotation speed. Also, differences in results predicted by the Donnell's and Love's theories become larger for long and cantilever shells in vibration mode shape corresponding to ( m = 1, n = 2 ), i.e., the ovalization of cross section. Highlights: For the first time, a closed-form solution is developed for free vibration of variable-thickness cylindrical shells rotating with a constant angular velocity. Three practical patterns of thickness variation are considered. A small variation in wall thickness or form of thickness distribution can affect the natural frequencies and corresponding mode shapes. The effect of thickness variation is much more pronounced for the cantilever long shells with a high rotation speed. The difference in results within the Donnell's and Love's theories becomes larger for long and cantilever shells due to the ovalization of cross section.