Coupled Flexural-Torsional Free Vibration of an Axially Functionally Graded Circular Curved Beam

The coupled flexural-torsional free vibration of circular horizontally curved beams made of an axially functionally graded (AFG) material was investigated. Beams with rectangular and elliptical cross-sections were designed to obey quadratic functions of Young’s modulus and the mass density in the axial direction. Using the Timoshenko and St. Venant beam theories, the governing differential equations of motion were derived. Based on the trial eigenvalue method together with the numerical integration method, the differential equations were solved to obtain the natural frequencies. For validation purposes, the frequencies computed in this study and ADINA were compared. Parametric studies were also performed to clarify how the natural frequency of the flexural-torsion coupling depends on modular ratio, cross-sectional shape, aspect ratio, slenderness ratio, and opening angle of the beams.