Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Abstract

A two-dimensional functionally heterogeneous thick hollow cylinder with a finite length is considered and its natural modes and frequencies are determined. Since mode shapes of a thick cylinder are three-dimensional, even with axisymmetric conditions, three-dimensional theory of elasticity implemented for problem formulation. The axisymmetric conditions are assumed for the cylinder. The material properties of the two-dimensional functionally graded material (2D-FGM) cylinder are varied in the radial and axial directions with power law functions. Effects of volume fraction distribution on the different types of anti-symmetric mode shape configuration and vibrational 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 variational method. The study shows that the 2D-FGM cylinder exhibit interesting vibrational characteristics and mode shapes when the constituent volume fractions are varied.

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

“…Table 4 has demonstrated the first ten natural frequencies comparison of a 1D-FG cone with free-clamped boundary condition reported by Tornabene (2009), Qu and Meng (2014), and Asgari (2017). In this case, the internal and external surface of the cone is constructed with pure ceramic and pure metal, respectively.…”

“…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).…”