In-plane free vibrations of circular beams made of functionally graded material in thermal environment: Beam theory approach

In this paper, in-plane free vibrations of FGM circular beams in thermal environment are studied via the beam theory approach. Axial deformation, shear deformation and rotatory inertia effects are taken into account. Thermal effects are taken into account by assuming the material properties as an arbitrary function of the temperature as well as the position, and by writing the equilibrium equations for the deformed shape of the beam. Necessary simplifications are made in order to obtain the differential equation system of circular beams made of FGM, in thermal environment. The system of linear differential equations with variable coefficients are solved using the matricant. Formulation is validated by comparing the results of numerous examples existing in the literature and FEM software package. Effects of temperature change, material variation, and geometrical parameters such as the ratio of thickness to the length of the beam and the opening angle on free vibration characteristics of FGM circular beams with ceramic inner surface in thermal environment are investigated. It is concluded that such structures can be analyzed with simplistic beam theory approach. Also, new results, which can be used for validation of new approaches are presented.