The Classic Dynamic Theory of Thick Curved Beams in the Context of Functionally Graded Materials

Abstract

During the last two decades materials, that exhibit graded properties, left their essence 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. Neither in what can be considered new uses of given structures, nor in the development of new theories to explain certain effects. Models for straight and curved beams are normally reported in the scientific literature as the easiest way to understand certain existing aspects in mechanics of structures. Most of these models are formulated appealing to numerical approaches such as the finite element or differential quadrature methods among others without taking into account theoretical aspects that can be quite useful to reduce algebraic complexity. In the present work the classical strength-of-materials theory for dynamic analysis of thick curved beams is deduced in the context functionally graded materials. The derivation process consists in the reduction of the algebraic handling by employing the concept of material neutral–axis shifting. This leads to the possibility to find analytical solutions of the governing differential system, even if the differential system has variable coefficients. Parametric studies on natural frequencies are offered to show the versatility of the adopted formulation by means of solutions handled with the Power Series Method.