THE EFFECT OF MATERIAL INHOMOGENEITY ON THE FREE VIBRATIONS OF FGM CIRCULAR BEAMS

Abstract

Vibrations of heterogeneous curved beams have recently been investigated by the authors of the present paper. Various papers deal with, among others, the issue what effect the central load has on the vibrations of curved beams made of heterogeneous material with distinct supports. To find numerical solution, the authors determined the Green function matrices for pre-loaded beams. Then they reduced the eigenvalue problems, which yield the eigenfrequencies as a function of the load, to eigenvalue problems governed by a system of Fredholm integral equations. In this paper the most important properties of the model and the governing differential equations are provided for elastically restrained pre-loaded beams. Then the question how functionally graded material distribution can affect the eigenfrequencies is replied through examples.