A Model for In-Plane and Out-of-Plane Vibrations of Non-Homogeneous Non-Uniform Curved Beams

Abstract

In this paper the vibration patterns of slender structures with curved axis are addressed. A survey on the literature concerning dynamics of beams with non-homogeneous or functionally graded properties shows that there is a lack of papers devoted to the vibration analysis of curved beams made of graded materials. This problem was tackled by a few authors through two-dimensional approaches where material properties can vary in the radial direction. In-plane bending motions were analyzed with those approaches. However one dimensional models developed to study the out-of-plane motion of FGM curved beams are practically absent in the technical literature. The scope of this article is twofold. The first one is related to the introduction of a linear model of non-homogeneous curved beams containing out-of-plane and in-plane motions. The second topic consists in studying the vibration patterns of different graded materials and geometrical parameters under the presence of initial stresses states. The model is developed by adopting a consistent displacement field which incorporates second order rotational terms. The model also incorporates the shear flexibility due to bending and warping due to twisting effects. A finite element is developed to solve dynamic problems. The model contains several straight beam theories as well as curved beam theories as particular cases. Some comparisons with the available experimental data of the literature are performed in order to illustrate the predictive features of the model.