Two Dimensional Functionally Graded Material Finite Thick Hollow Cylinder Axisymmetric Vibration Mode Shapes Analysis Based on Exact Elasticity Theory

Abstract

Abstract. A thick hollow cylinder with finite length made of twodimensional functionally graded material (2D-FGM) is considered and its natural modes are determined, based on great importance of mode shapes information in order to understand vibration behaviour of structures. Three dimensional theory of elasticity implemented for problem formulation, since mode shapes of a thick cylinder are three dimensional even with axisymmetric conditions. The axisymmetric conditions are assumed for the 2D-FGM cylinder. The material properties of the cylinder are varied in the radial and axial directions, with power law functions. Effects of volume fraction distribution on the different types of symmetric mode shapes configuration and vibration behaviour of a simply supported cylinder are analyzed. Three dimensional equations of motion are used and the eigen value problem is developed, based on direct variation method.

Three-dimensional natural frequency investigation of bidirectional FG truncated thick hollow cone

“…Numerous studies such as static, thermal stresses, buckling and vibration analysis have been conducted for different kinds of structures. Many studies on the linear vibration of FG thick hollow cylinders and FG cylindrical shells using different methods have been conducted (Loy et al ., 1999; Pradhan et al ., 2000; Asgari and Akhlaghi, 2011, Pilafkan et al ., 2013; Qu et al ., 2013; Qu and Meng, 2014, Asgari, 2015, Kandasamy et al ., 2016; Asgari, 2017).…”