Dynamic equations for solid isotropic radially functionally graded circular cylinders

Abstract

A hierarchy of dynamic equations for solid isotropic functionally graded circular cylinders is derived based on the three dimensional elastodynamic theory. The material parameters are assumed to vary in the radial direction. Using Fourier expansions in the circumferential direction and power series expansions in the radial direction, equations of motion are obtained for longitudinal, torsional, flexural and higher order motion to arbitrary Fourier and power orders. Numerical examples for eigenfrequencies and plots on mode shapes and stress distributions curves are presented for simply supported cylinders for different material distributions. The results illustrate that the present approach renders benchmark solutions provided higher order truncations are used, and act as engineering cylinder equations using low order truncation.

Bending and free vibrational analysis of bi-directional functionally graded beams with circular cross-section

“…Till now, the free vibrations of FG circular cylinders have seldom been discussed. Abadikhah and Folkow [29] adopted the Fourier and power series expansions to calculate the eigenfrequencies of simply supported cylinders by using the 3D elastodynamic theory for radially varying material inhomogeneities. Zhang et al [30] proposed a higher-order shear deformation based spectral element model to calculate the natural frequency of FG cylindrical beams, where the material properties were assumed to vary along the r-axis.…”

“…However, there are very few bending and eigenfrequency results reported for FG circular cylinders with radially or/and axially varying material inhomogeneities. Abadikhah and Folkow [29] adopted the three-dimensional (3D) elastodynamic theory to study the dynamic behaviors of simply supported FG cylinders with power-and exponential-law distributions of the material properties. Zhang et al [30] introduced a higher-order shear deformation based spectral element model to calculate the stochastic natural frequency of radially FG beams with a circular cross-section.…”