Vibration characteristics of multiple functionally graded nonuniform beams

Abstract

Based on the Euler–Bernoulli beam theory, the natural vibration behavior of functionally graded nonuniform multiple beams has been investigated. It is assumed that the beams are joined by elastic translational springs, and the properties of the beams vary along the axial direction. The Chebyshev spectral collocation method has been used to convert the governing differential equations of transverse motion into a system of algebraic equations that are put in the matrix–vector form. Then, the dimensionless transverse frequencies are obtained by solving the eigenvalue problem. The influence of several factors, such as the stiffness parameters of the coupling translational springs, the properties of the cross section of the beams, and the boundary conditions on the frequencies, has been carried out. The results generated from the Chebyshev spectral collocation method have been verified by comparing them with those reported in other studies and references from the literature. Several numerical examples have been presented and discussed to analyze the system under consideration. The authors hope that the findings of the current study are helpful in designing and characterizing multiple nonuniform thin engineering structures.