Exact Radial Natural Frequencies of Functionally Graded Hollow Long Cylinders

Authors : Vebil YILDIRIM

Pages : 28-41

Doi:10.24107/ijeas.336621

View : 11 | Download : 5

Publication Date : 2017-12-27

Article Type : Research Paper

Abstract :I n this work the exact free axisymmetric pure radial vibration of hollow infinite cylinders made of hypothetically functionally power-graded materials having identical inhomogeneity indexes for both Young’s modulus and the material density is addressed. The equation of motion is obtained as a linear second-order Bessel’s ordinary differential equation with constant coefficients based on the axisymmetric linear elasticity theory.  For traction free boundaries, a closed form frequency equation is offered. After verifying the present results for cylinders made of both isotropic and homogeneous materials, and isotropic functionally graded materials, an extensive parametric study is carried out to investigate the influences of both the thickness and inhomogeneity indexes on the natural frequencies. Results are presented in both graphical and tabular forms. It was revealed that the fundamental frequency in the radial mode is principally affected from the inhomogeneity parameters than the higher ones. However, the natural frequencies except the fundamental ones are dramatically affected from the thickness of the cylinder. As the thickness decreases, the natural frequencies considerably increase.  It is also revealed that, there is a linear relationship between the fundamental frequency and others in higher modes.
Keywords : Free vibration, natural frequency, thick walled hollow cylinder, functionally graded