Green’s functions for nonhomogeneous curved beamswith applications to vibration problems

Abstract

In the open literature we have found no report on the Green function matrices of curved beams except papers [1, 2, 3] by Szeidl at al. These works assume that the material of the beam is homogeneous and isotropic. In the present paper we assume that the beam is made of heterogeneous material in such a way that the material properties depend on the cross-sectional coordinates. Under this condition we have the following aims: (1) we would like to determine the Green function matrices in a closed-form for (a) fixed-fixed, (b) pinnedpinned and (c) pinned-fixed circular beams. (2) With the knowledge of the Green function matrices we can reduce those eigenvalue problems which provide the natural frequencies of the free vibrations to eigenvalue problems governed by homogeneous Fredholm integral equations. Our goal in this respect is to solve the latter eigenvalue problems numerically and compare the results obtained with the results of finite element (FE) computations. Our numerical solutions show a good agreement with the commercial FE computations.

Thermoelastic analysis of thick-walled functionally gradedspherical pressure vessels with temperature-dependent material properties

“…There are a number of works where multilayered or heterogeneous structural components are analysed, for example in [6][7][8][9]. The paper of Obata and Noda [10] studied a one-dimensional steady-state thermal stress problem for functionally graded hollow circular cylinders and hollow spheres by the use of a perturbation approach to achieve the effect of the composition on stresses and to design the optimum FGM hollow circular cylinder and hollow sphere, under different assumptions of temperature distributions.…”