How the Thermal Gradient Affects the Vibration Behavior of a Spinning Orthotropic Oval Cylindrical Shell

Abstract

Based on the framework of Flügge's shell theory, transfer matrix approach and Romberg integration method, we investigated how the thermal gradient affects the vibration behavior of rotating isotropic and orthotropic oval cylindrical shells. The governing equations of orthotropic oval cylindrical shells, under parabolically varying thermal gradient around its circumference, with consideration of the effects of initial hoop tension and centrifugal forces due to the rotation are derived, and they are put in a matrix differential equation as a boundary-value problem. As a semianalytic solution, the trigonometric functions are used with Fourier's approach to approximate the solution in the longitudinal direction, and also to reduce the two-dimensional problem in to an one-dimensional one. Using the transfer matrix approach, the equations can be written in a matrix differential equation of first-order and solved numerically as an initial-value problem. The proposed model is applied to get the natural frequencies and vibratory displacement of the symmetrical and antisymmetrical vibration modes. The sensitivity of the vibration behavior to the rotational speed, the thermal gradient, the ovality and orthotropy of the shell is studied for different type-modes of vibration. The present method is found to be accurate when compared with the results available in the literature.