Application of the Chebyshev–Ritz route in determination of the dynamic instability region boundary for rotating nanocomposite beams reinforced with graphene platelet subjected to a temperature increment

Abstract

The Chebyshev–Ritz route is exploited for the sake of the examination of the principal parametric resonance instability boundary of a rotating nanocomposite beam subjected to a temperature rising. The parametric resonance excitation is because of a time varying rotational speed. It is assumed that the rotating speed oscillates harmonically about a constant value. Resorting to the Halpin–Tsai micromechanical, the practical mechanical and thermal characteristics are estimated. The Newton–Raphson scheme is utilized to determine the prestressed configuration. The structural damping influence is incorporated to the motion equations. By the assumption that the frequency of the harmonically varying term of the rotating speed is approximately twice the one of the natural frequencies, the principal parametric resonance excitation is activated. The Bolotin’s technique alongside the Floquet theory are utilized to define the instability region boundaries. The impacts of various effectual parameters including the graphene platelet weight fraction, and its dispersion pattern, the design value of the damping constant, the boundary condition type, and the rotating speed on the instability region are examined. It is inferred that by the increment of the weight fraction of the graphene platelet as well as the design value of the damping ratio, the critical excitation amplitude increases.