On transverse vibrations of functionally graded polar orthotropic rotating solid disk with variable thickness and constant radial stress

In this work a polar orthotropic rotating solid disk with variable thickness made of functionally graded material is considered. A special stress distribution with the constant radial stress condition is proposed. Functionally graded material behavior is achieved by radially varying the degree of orthotropy (Jain, Ramachandra and Simha (1999). Rotating Anisotropic Disk of Uniform Strength, International Journal of Mechanical Sciences, 41: 639-648). The thickness of the solid disk is also assumed to vary exponentially with any power of the radius. The natural frequencies of rotating disk are calculated by Rayleigh-Ritz method. The effect of this special stress distribution on increasing the natural frequency of transverse vibrations is demonstrated.