Vibration analysis of multiple-stepped functionally graded beams with general boundary conditions

Abstract

In this paper, an effective formulation for vibration analysis of multiple-stepped functionally graded beams with general boundary conditions is presented. The material properties are assumed to change continuously in the thickness direction according to a power law distribution of the volume fraction of the constituents. The theoretical model is formulated on the basis of a variational method in conjunction with the first-order shear deformation theory. The essence of the present formulation is to express the displacement and rotation components by nodeless Fourier sine functions and nodal Lagrangian polynomials. Since the boundary nodal displacement information is introduced into the admissible functions, the interface continuity and boundary conditions are easily handled. Based on this, each structure component may be further partitioned into appropriate segments in order to accommodate the computing requirements of higher-order vibration modes. A variety of numerical examples are presented to demonstrate the accuracy, reliability and computational efficiency of this method. Furthermore, the effects of the material properties, geometric parameters as well as boundary conditions on the frequencies of the beam structures are discussed.