In-Plane Free Vibration of Laterally Symmetric Functionally Graded Material Arches

This study aims to analyze the in-plane free vibrations of arches comprising the laterally symmetric functionally graded materials. Emphasis is placed on the circular arch whose material properties vary laterally symmetrically about the centroidal axis by a power-law function. The differential equations governing the mode shape of the arch were derived under the boundary conditions and were numerically solved to calculate the natural frequencies using the Runge–Kutta and Regula–Falsi methods. Calculation results of this study for natural frequencies compare well with those of the finite element method. The effects of various arch parameters on natural frequencies are highlighted and discussed in detail.