Flapwise bending vibration analysis of functionally graded rotating beams with concentrated mass

Abstract

A rotating cantilever beam made of functionally graded material with concentrated mass is considered to study on flapwise bending natural frequencies of the beam. The material properties of the beam symmetrically vary continuously in thickness direction from core at mid section having metal to the outer surface having ceramic according to power law form. The equations of motions are derived by using Kane’s method. Rayleigh-Ritz method is used to estimate the natural frequencies of the beam. Dirac delta function is employed to represent the concentrated mass in the system. The influence of the material morphology, concentrated mass, its location, hub radius ratio and angular speed on flapwise bending natural frequencies of the functionally graded beam are investigated.