Thermo-mechanical vibration and instability of carbon nanocones conveying fluid using nonlocal Timoshenko beam model

In this paper, thermo-mechanical vibration analysis of carbon nanocones (CNCs) conveying fluid based on nonlocal elasticity theory is investigated. The governing equations are developed using Hamilton's principle and a general eigenvalue problem is obtained by discretizing the resulting equations using the finite element method. In this paper, the non-uniform cross-section Timoshenko beam theory is utilized and the influences of apex angle, top radius, length, temperature change, thickness, small-scale parameter, and flow direction are surveyed on the fundamental frequency and the critical flow velocity associated with an instability condition. The results of the present study have been validated with available results in the literature. It is found that the apex angle has a considerable effect on the instability behavior of CNCs. Also, critical flow velocity is reduced by increasing the small-scale parameter. Furthermore, the direction of fluid has a crucial effect on both the fundamental frequency and critical flow velocity.