Ultrasonic wave propagation in a functionally graded thick cylinder

In this paper, wave propagation in thick-walled and long cylindrical pressure vessels made of functionally graded material (FGM) is investigated. Material properties are considered as a power function of radius and the Poisson’s ratio is assumed as constant. The equation of mo-tion which is a wave equation is obtained and solved analytically. The equation is a Sturm Liouville problem. By an appropriate change of variable, it can be turned into a simple Bessel differential equation. The Eigenvalue equation is obtained based on boundary conditions and using this equation natural frequencies are calculated. A mathematical expression for the mean velocity of radial stress wave propagation is purposed. Wave propagation produced by a dynamic internal pressure is simulated and the results are discussed. The radial and hoop stress are obtained for different material distributions. The mean wave velocity relation with inhomogeneity constants is studied. Finally, the analytical results are verified by finite ele-ment methods.

کلیدواژه ها:

Research Assistant Professor ، Mechanical Rotary Equipment Research Dept. ، Niroo Research Institute ، at the end of Shahid Dadman Blvd. ، Shahrak Ghods ، ۱۴۶۸۶۱۳۱۱۳ ، Tehran ، Iran.