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.

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

We study the multi-pulse jumping double-parameter homoclinic orbits and chaotic dynamics of the eccentric rotating ring truss antenna under combined the parametric and external excitations for the first time. Considering combined the parametric and external excitations, the averaged equations of the eccentric rotating circular cylindrical shell are obtained in the case of the primary parametric resonance-1/2 sub-harmonic resonance and 1:2 internal resonance by using the perturbation analysis. From the averaged equation, the theory of normal form is applied to find the explicit expression of the eccentric rotating circular cylindrical shell under combined the parametric and external excitations. Based on the extended Melnikov method, we study the multi-pulse double-parameter homoclinic bifurcation and chaos of the eccentric rotating circular cylindrical shell under combined the parametric and external excitations and also estimate the double-parameter chaotic threshold. Numerical simulations are utilized to study double-parameter chaotic dynamic behaviors of the eccentric rotating circular cylindrical shell under combined the parametric and external excitations based on the double-parameter Lyapunov exponents. When one of the excitations is constant, it is found that the temperature parametric excitation directly decides the occurrence of the chaotic motion and the external excitation determines the paths to chaos. It is also known that the topology shapes of the chaotic motions are similar when the excitations corresponding to the chaotic motions change in a small range. Otherwise, there exists the obvious difference of the shapes for the topological structure of the double-parameter chaotic motions in the eccentric rotating circular cylindrical shell.

Multi-pulse jumping double-parameter chaotic dynamics of eccentric rotating ring truss antenna under combined parametric and external excitations

The primary resonance and nonlinear vibrations of the functionally graded graphene platelet (FGGP)-reinforced rotating pretwisted composite blade under combined the external and multiple parametric excitations are investigated with three different distribution patterns The FGGP-reinforced rotating pretwisted composite blade is simplified to the rotating pretwisted composite cantilever plate reinforced by the functionally graded graphene platelet It is novel to simplify the leakage of the airflow in the tip clearance to the non-uniform axial excitation The rotating speed of the steady state adding a small periodic perturbation is considered The aerodynamic load subjecting to the surface of the plate is simulated as the transverse excitation Utilizing the first-order shear deformation theory, von Karman nonlinear geometric relationship, Lagrange equation and mode functions satisfying the boundary conditions, three-degree-of-freedom nonlinear ordinary differential equations of motion are derived for the FGGP-reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations The primary resonance and nonlinear dynamic behaviors of the FGGP-reinforced rotating pretwisted composite cantilever plate are analyzed by Runge–Kutta method The amplitude–frequency response curves, force–frequency response curves, bifurcation diagrams, maximum Lyapunov exponent, phase portraits, waveforms and Poincare map are obtained to investigate the nonlinear dynamic responses of the FGGP-reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations

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Nonlinear Vibrations of Rotating Pretwisted Composite Blade Reinforced by Functionally Graded Graphene Platelets Under Combined Aerodynamic Load and Air Flow in Tip Clearance

G. Liu

Papers

Saturation phenomena and nonlinear resonances of rotating pretwisted laminated composite blade under subsonic air flow excitation

An equivalent cylindrical shell model of vibration analysis based on simplified repeating unit cell for ring truss structure