Dynamical stability of bi-directionally graded moving beams

Abstract

This article gravitates toward analyzing the vibration response of a moving beam functionally graded (FG) in two orthogonal directions. In order to gain a high level of accuracy, higher-order shear deformation theory for beam structures is employed to define the displacement field and determine the system’s governing differential equations. Also, this study considers the effect of different sets of boundary conditions to find the oscillatory response of the system in a more comprehensive way. This matter leads the authors to utilize the differential quadrature method (DQM) as a numerical solution to solve the governing differential equations. The accuracy of the applied solution is examined and confirmed by comparing its results with those available in the literature. In this study, the natural frequency of a moving beam with varying properties along both the axial and transverse directions was investigated. The study examined the influence of boundary conditions, gradational properties, axial velocity, and the parameter L/h on the natural frequency. One of the applicable results for related industries is that designers should pay special attention to the FG power index, and the type of boundary conditions of the moving beams. This study provides novel insights to adjust design factors in order to gain a high level of vibration response for moving loads.