Free vibration analysis of a multi-stepped functionally graded curved beam with general boundary conditions

Abstract

In this paper, a Haar wavelet discretization method (HWDM) for analyzing the free vibration of the multi-stepped functionally graded (FG) curved beam with general boundary conditions is presented. It is assumed that the material properties of the beam change continuously in the thickness direction according to the distribution characteristics of the material determined by four parameters. The individual steps of the multi-stepped functionally graded curved beam are combined by a continuous condition. For generalization of boundary conditions, the artificial elastic spring technique is introduced. The displacement fields are determined by the first-order shear deformation theory (FSDT) and the motion equation is obtained by using Hamilton’s principle. All displacement functions including boundary and continuity conditions are expressed in the form of a Haar wavelet series and its integral, and a characteristic equation discretized based on the Haar wavelet is obtained. The reliability and accuracy of the proposed method are confirmed through convergence and validation studies. The results indicate that this method has high accuracy and reliability, also a higher convergence rate in attaining the frequencies of the multi-stepped FG curved beam. Then, the frequency parameters and mode types of the multi-stepped FG curved beam obtained by the proposed method are given with numerical examples. These new numerical results can be used as benchmark data for research in this field.