Vibration Analysis of Rotary Tapered Axially Functionally Graded Timoshenko Nanobeam in Thermal Environment

Abstract

In this paper, vibration analysis of rotary tapered axially functionally graded (AFG) Timoshenko nanobeam is investigated in a thermal environment based on nonlocal theory. The governing equations of motion and the related boundary conditions are derived by means of Hamilton’s principle based on the first order shear deformation theory of beams. The solution method is considered using generalized differential quadrature element (GDQE) method. The accuracy of results are validated by other results reported in other references. The effect of various parameters such as AFG index, rate of cross section change, angular velocity, size effect and boundary conditions on natural frequencies are discussed comprehensively. The results show that with increasing angular velocity, non-dimensional frequency is increased and it depends on size effect parameter. Also, in the zero angular velocity, it can be seen with increasing AFG index, the frequencies are reducing, but in non-zero angular velocity, AFG index shows complex behavior on frequency.