On the large-amplitude vibration of rotating pre-twisted graphene nanocomposite blades in a thermal environment

The goal of the present research is to examine the Natural Frequencies (NFs) of perfect and imperfect Graphene Nanoplatelet Reinforced Nanocomposite (GNPRN) structures of revolution (conical and cylindrical shells and annular plate structures) resting on elastic foundations under general boundary conditions (BCs). The graphene nanoplatelet material is implemented to compose the nanocomposite enhanced by a polymeric matrix including porosities. The springs technique is applied to define the general BCs of GNPRN structures of revolution. Elastic foundations are described by two parameters, i.e., Winkler-Pasternak Foundations (WPFs). Additionally, Donnell's hypothesis and first-order shear deformation theory (FSDT) are employed to figure out the primary formulations associated with the GNPRN structures of revolution. In contrast, the equations of motion are found using Hamilton's principle. Then the equations of motion are then discretized using the well-known Generalized Differential Quadrature Method (GDQM). Next, the standard eigenvalue solution is assigned to obtain the NFs of the perfect/imperfect GNPRN structures of revolution. Finally, various benchmarks are addressed to verify the approach suggested for evaluating the NFs of the perfect/imperfect GNPRN structures of revolution. Furthermore, several novel examples highlight the effects of the change in geometrical and material properties, arbitrary boundary conditions, and WPFs on the NFs of the perfect/imperfect GNPRN structures of revolution. 

Natural frequency analysis of imperfect GNPRN conical shell, cylindrical shell, and annular plate structures resting on Winkler-Pasternak Foundations under arbitrary boundary conditions

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. 

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

On the frequencies of graphene nanoplatelet agglomerated nanocomposite paired paraboloidal-cylindrical shells under arbitrary boundary conditions

Vibration characteristics of composite doubly curved shells reinforced with graphene platelets with arbitrary edge supports

In this study, the flutter analysis of a rotating pre-twisted functionally graded graphene nanoplatelets reinforced composite (FG GPLRC) blade under supersonic airflow is investigated. The pre-twisted blade is multi-layered and reinforced with graphene nanoplatelets (GPLs) evenly distributed in each layer while the GPL weight fraction changes from layer to layer through the thickness direction. The effective Young's modulus is determined by Halpin-Tsai micromechanical model while the Poisson's ratio and mass density are predicted by Voigt's rule for GPLRC layers. According to assumptions of the first-order shear deformation theory (FSDT), the first-order piston theory and shell theory, the dynamic model of rotating pre-twisted GPLRC blades subjected to supersonic flow is developed. Meshless the improved moving least-square Ritz method (IMLS-Ritz) is used to derive the discrete dynamic equations of rotating pre-twisted GPLRC blades under aerodynamic load. The accuracy of the IMLS-Ritz method for this problem is validated by comprehensive convergence studies and careful comparison studies. A detailed parameter investigation of the effects of GPL distribution configuration, rotation velocity and geometrical parameters on flutter behavior characteristics of GPLRC blades is systematically conducted.

Xu Ouyang

Papers

Meshless numerical approach to flutter analysis of rotating pre-twisted nanocomposite blades subjected to supersonic airflow

On the dynamics of rotating cracked functionally graded blades reinforced with graphene nanoplatelets