Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model

摘要: A free vibration analysis of shallow and deep curved functionally graded (FG) nanobeam is presented. Differential equations boundary conditions are obtained using Hamilton’s principle, then, nonlocal theory employed to derive differential in small scale. Properties the material FG radial direction. In order investigate effects beam, extensional stiffness, bending–extension coupling bending stiffness calculated case, analytically. By employing Navier method, an analytical solution Results compared validated with available studies, a good agreement seen. The influences effective parameters such as geometrical term, parameter, opening angle, aspect ratio, mode number, gradient index discussed detail. It found that frequency higher than one, ratio significantly affects this difference decrease. Also, it concluded power can notably influence amount frequency.