Research on Free Vibration Frequency Characteristics of Rotating Functionally Graded Material Truncated Conical Shells with Eccentric Functionally Graded Material Stringer and Ring Stiffeners

Abstract

Abstract In this research work, an exact analytical solution for frequency characteristics of the free vibration of rotating functionally graded material (FGM) truncated conical shells reinforced by eccentric FGM stringers and rings has been investigated by the displacement function method. Material properties of shell and stiffeners are assumed to be graded in the thickness direction according to a simple power law distribution. The change of spacing between stringers is considered. Using the Donnell shell theory, Leckhnisky smeared stiffeners technique and taking into account the influences of centrifugal force and Coriolis acceleration the governing equations are derived. For stiffened FGM conical shells, it is difficult that free vibration equations are a couple set of three variable coefficient partial differential equations. By suitable transformations and applying Galerkin method, this difficulty is overcome in the paper. The sixth order polynomial equation for w is obtained and it is used to analyze the frequency characteristics of rotating ES-FGM conical shells. Effects of stiffener, geometrics parameters, cone angle, vibration modes and rotating speed on frequency characteristics of the shell forward and backward wave are discussed in detail. The present approach proves to be reliable and accurate by comparing with published results available in the literature.

Keywords

• Rotating truncated conical shell
• Free vibration
• Frequency characteristics
• FGM stiffener
• Functionally graded material (FGM)