Exact receptance function of a tapered AFG beam with nonlinearly varying ratios of beam properties carrying concentrated masses

Abstract

This paper presents a method for establishing the exact receptance function of a tapered axially functionally graded (AFG) beam with nonlinear ratios of properties using the Adomian method. In current papers, the Adomian method was applied for linearly tapered beams where the geometric series was used conveniently. However, for nonuniform AFG beams with nonlinearly varying ratios of properties, the geometric series cannot be used, thus the other type of power series needs to be established and applied. In this paper, the derivation of the power series applied for obtaining the exact receptance function of a nonuniform AFG beam with nonlinearly varying ratios of properties is presented. Numerical simulation results of the receptance function of a tapered AFG beam with nonlinearly varying ratios of beam properties carrying concentrated masses are conducted and provided. The influences of the concentrated masses and the varying ratios of properties of beam on the receptance matrix are also investigated and presented.