Analysis of free vibrations in axisymmetric functionally graded thermoelastic cylinders

The free vibrations of an axisymmetric functionally graded, transversely isotropic, thermoelastic hollow cylinder have been modeled and analyzed. The material has been assumed to be graded according to a simple power law in the radial coordinate. The Laplace transform method has been used to solve the problem. The complex Laplace transform parameter has directly been used to find the natural frequencies of free vibrations without performing inversion of the transforms. The frequency equations of free vibrations in a hollow cylinder have been solved by using the software Maple. The natural frequencies of the first ten modes for different values of the grading index have been computed numerically for zinc material. The numerical results for radial stress, circumferential stress, temperature change, frequency shift, and thermoelastic damping (inverse quality factor) have been presented graphically. The closed form solutions obtained here are interesting and allow further parametric studies of functionally graded structures. The inhomogeneity parameter is useful in design and it can be tailored for specific applications as a controller.