Exact Radial Natural Frequencies of Functionally Graded Hollow Long Cylinders

Year 2017, Volume: 9 Issue: 4, 28 - 41, 27.12.2017

Vebil Yıldırım

https://doi.org/10.24107/ijeas.336621

Abstract

In 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.

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