Analytical and numerical investigation of free vibration for stepped beam with different materials

Abstract

This work describes the application of classical Rayleigh method (CRM), modified Rayleigh method (MRM), and ANSYS finite element method (FEM) to calculate the natural frequency of non-homogenous cantilever beam. Two-step cantilever stepped beam was investigated through six studied cases. Each step has different material properties and the same cross section area. Results showed that the combination of materials is useful in order to increase the natural frequencies and reduce the weight of the beam at the same time when the cantilever beam is fixed by the side of the stronger material. There is a good agreement between the CRM and FEM for the region with length larger than half length of beam, on the other hand, there is an excellent agreement between the MRM and FEM for the region with length smaller than half length of beam.