The dynamics of thick curved beams constructed with functionally graded materials

Abstract

During the last two decades materials, that exhibit graded properties, left their spirit of conceptual laboratory specimens to become a technological reality with a well established background. However structural applications of these materials are not a fulfilled research. Models of straight and curved beams are normally reported in the scientific literature as the easiest way to understand some existing aspects in mechanics of structures. Most of these models are formulated appealing to numerical approaches such as the finite element method among others, without taking into account theoretical aspects that can be quite useful to reduce algebraic complexity. In the present work a technical theory for dynamic analysis of thick curved beams is deduced within the context of functionally graded materials. The concept of material neutral-axis shifting is employed in the deduction procedure in order to reduce the algebraic handling and complexity of the motion equations. This leads to find analytical solutions of the governing differential system, even if it has variable coefficients. Parametric studies on the dynamics of curved beams are offered to show the versatility of the adopted formulation by means of solutions handled with the power series method.