Traveling wave vibration analysis of rotating reinforced functionally graded conical shells

The purpose was to analyze the traveling wave vibration characteristics of a rotating reinforced functionally graded (FG) conical shell. Initially, the energy equation of the FG shell with internal rib and carbon nanotubes (CNTs) was obtained by using the microscopic mechanics model. Secondly, the admissible displacement function was represented by the Chebyshev orthogonal polynomials. The characteristic equation of the rotating reinforced FG shell was derived by using the Rayleigh-Ritz method. Thereafter, the feasibility of the theoretical model was verified by comparing with several cases. Finally, the effects of the rotational speed, ceramic volume fraction index, semi cone angle, internal rib position, rib thickness to diameter ratio and rib length to diameter ratio on the traveling wave modal frequencies were examined. Results indicate that the rotating reinforced FG conical shell with clamped-clamped boundary condition is the most stable as the rotational speed increases. The X-type CNTs with a ceramic volume fraction index in the range of 0 to 5 has the greatest influence on the traveling wave modal frequencies. The internal rib position plays an important role in the traveling wave modal frequencies. The traveling wave modal frequencies increase with increasing the rib thickness and decreasing the CNTs volume fraction as well as rib length. The stiffness of the structure decreases with increasing the semi cone angle, which further affects the stability of the conical shell’s movement.