Free Vibration Analysis of a Simply Supported Axial Functionally Graded Beam Using the Rayleigh Method.

This study aims to make investigation for the free vibration problem of simply supported axial-FGB by applying the Rayleigh method. The model of (power law) is adopted to describe the change in physical mechanical and properties through the axial direction. The computer program is built in this work. The accuracy of Rayleigh method is checked by comparison of the results of Rayleigh method with the results available in literatures and a very good accuracy was found. The combined effects of power-law index, modulus-ratio and density-ratio on the fundamental frequency and mode shapes of axial-FGBs are investigated. The results explain that the non-dimensional frequency parameter at any modulus-ratio is approximately constant when the power-law index increases. When the power-law index is smaller than (1), the effect of modulus-ratio is greater than the effect of density-ratio. While the effect of modulus-ratio is smaller than the effect of density-ratio when the power-law index is greater than (1). Also, when density-ratio equals (1), the dimensionless deflection (or amplitude) increases with reducing of power-law index (β). When the modulus-ratio is smaller than (1), the dimensionless deflection increases with increasing the power-law index (β). From results, the Rayleigh method is able to calculate the natural frequency and mode shape of simply supported axial-FGM beam. [ABSTRACT FROM AUTHOR]