Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods

Authors : Vebil YILDIRIM

Pages : 15-39

Doi:10.24107/ijeas.1071038

View : 12 | Download : 10

Publication Date : 2022-09-02

Article Type : Research Paper

Abstract :In the present paper, the transfer matrix method insert ignore into journalissuearticles values(TMM); is to be employed for the first time in the open literature for the elastic analysis of variable-thickness disks made of functionally graded insert ignore into journalissuearticles values(FG); two orthotropic materials. Those materials are assumed to be continuously radially functionally graded insert ignore into journalissuearticles values(FG); based on the Voigt rule of mixture with two models. An exponential disk profile with two parameters is considered. Effects of the different boundary conditions insert ignore into journalissuearticles values(free-free, fixed-free, and fixed-fixed); and inhomogeneity indexes on the elastic response of the disk rotating at a constant angular speed are also examined. Additionally, direct numerical solutions of the problem with the complementary functions method insert ignore into journalissuearticles values(CFM); are presented in tabular forms together with the transfer matrix method solutions in which CFM was used as an assistant tool. It was observed that both location and amplitude of the maximum equivalent stress are affected by the grading models chosen. Such differences become more obvious for small values of the inhomogeneity indexes. The maximum relative error may reach 18% for the two material grading models in fixed-free disks. Consequently, Model-I may be recommended for just the inhomogeneity indexes equal to or greater than 0.5.
Keywords : Rotating disk, Functionally graded, Polar orthotropic, Variable thickness, Transfer matrix method, Complementary functions method, Initial value problem