Nonlinear vibrations of a cantilevered conical beam with axially functionally graded material carrying a longitudinally loaded mass

Abstract

In this article, the free and forced vibrations of a cantilevered conical beam with axially functionally graded material 1 , carrying a concentrated mass and subjected to a distributed load, are investigated. The beam has a rectangular cross-section with a variable thickness and properties along the length. The governing equation of the system is derived using the Euler–Bernoulli beam theory based on the Hamilton principle. The response of the system is determined under the assumption of the first mode dominance using the method of multiple scales 2 . The validity of the results is confirmed by comparing them with the results of the numerical solution. This investigation breaks new ground by examining the nonlinear effects of curvature and inertia, which contribute to the occurrence of hardening and softening behavior in the frequency response. Additionally, this article provides new insights into the profound impact of material distribution on the system’s frequency response at the initial resonance state. Therefore, the motivation of this study lies in the convergence of FGM, nonlinear behavior, and resonance of a beam.