A model for forced vibrations of ceramic/metallic thick rings

In this paper a general model for transient dynamic analysis of functionally graded material (FGM) thick arch/ring is introduced. The material is arbitrarily distributed between metal (aluminium or steel) and ceramic (Alumnina or Silicon carbide) phases, according to several types of functional distributions, including exponential law, power law, sigmoid law, among others. The model, developed within the context of strength-of-materials theory, includes many others theories as particular cases. For example, Timoshenko beam and other first-order shear deformation theories. The material properties such as Young’s modulus, shear modulus, density, can arbitrarily vary along the generally-shaped cross-section (that can be a multiply connected region), however holding symmetry with respect to the motion plane. The tangential stresses are consistently featured by the classical internal equilibrium equations in polar coordinates. This allows the proper calculation of the shear coefficient, which is crucial in this class of theories. The three fully coupled motion equations are solved in order to carry out studies of natural vibrations as well as transient dynamics under a general type of applied loads. The transient solution is reached by means of a modal superposition method appealing to “ad hoc” orthogonality conditions. Numerical studies are presented to show qualitatively and quantitatively the vibratory features of ceramic/metallic thick arches/rings with graded properties.