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The aerodynamic characteristics of flapping rotary wings (FRWs) have received considerable attention in design. In this study, optimizations of aerodynamic performance and kinematics of FRWs over the parameter space are explored. A well-validated Quasi-Steady model is employed to estimate the aerodynamic characteristics of FRWs in hovering flight, and a genetic algorithm is utilized for optimizing. It is assumed that flapping and pitching motion are given by motion parameters actively, while rotation is produced passively. Our results show that the optimal kinematic parameters are independent of flapping frequencies. The maximum lift comes from the high rotational speed caused by the small pitching amplitude, and the maximum power factor is from the large pitching amplitude. The dimensionless optimization of the flapping velocity as reference velocity is comparable to the dimensional results. The optimization model proposed in this study can be applied to the actual model for qualitative analysis. Rotational equilibrium power factor can reach more than 80% of the maximum value without rotation equilibrium constraint, but which rotational status can achieve the maximum power factor depends on the pitching angle at the mid-downstroke (αd). This study is helpful for the kinematic parameter design and further research of FRWs. [ABSTRACT FROM AUTHOR]

The thorax is the central component of the insect flight drivetrain, making it essential to understand how thoracic muscles influence insect flight for flapping wing microair vehicle design. This paper presents a theoretical model that takes into account the influence of thoracic muscles on flapping wing motion with reference to real insects. The thoracic muscle effect is simulated by the chordwise torsional spring, whose stiffness is derived from a comparison test with the results of real insect experiments. The elastic deformation of the flexible flapping wing is modeled by the von Kármán nonlinear plate theory. The predictive quasi-steady aerodynamic model based on the blade element theory can estimate the aerodynamic force, and the modeling of the spanwise bending and twisting is done with quadratic polynomials. The equations of motion are solved using the Newmark-Raphson method. Results suggest that including the influence of thoracic muscles decreases cycle-averaged lift and power, but enhances the efficiency of lift production by 23%. Moreover, it also postpones pitching motion and reduces its amplitude, though the movement trends of the flapping motion remain approximately unchanged regardless of the inclusion of the thoracic muscle effect. [ABSTRACT FROM AUTHOR]

In this study, analytical solutions are developed for the super-critical vibration of fluid-conveying pipes with elastic supports. By accounting for the geometric nonlinearity, the nonlinear buckling problem is solved and the equilibrium configurations are obtained. Using a coordinate transform, the dynamic model of a super-critical pipe is obtained for the vibrations around the non-trivial equilibrium configuration. The present analytical solutions of interest for the equilibrium configurations, the natural frequencies, the mode shape, and the transient response are obtained by combining the Laplace transform method with the complex mode method. The Laplace transform method is applied to formulate a steady-state Green's function solution. Using the complex mode methodology, vibration characteristics of the super-critical pipe around the equilibrium configurations are presented. The present analytical solutions can be readily reduced to classical boundary conditions by setting end-spring parameters to zero or infinity. Numerical simulations are conducted to understand the impact mechanisms of the elastic support parameters on the free and forced vibration characteristics. This work offers important guidance for optimization and design of super-critical fluid-conveying pipes with elastic supports for engineering applications. [ABSTRACT FROM AUTHOR]

The theoretical modeling of a functionally graded (FG) graphene nanoplatelet (GPL)-reinforced assembled beam–plate structure resting on elastic supports is presented for the first time, and its free vibration analysis is performed. Herein, the assembled structure is modeled according to the Kirchhoff plate theory and the Rayleigh beam theory. The graphene nanoplatelets (GPLs) gradiently distribute in the beam's radial direction and in the plate's thickness direction, respectively. By adopting the rule of mixture and the Halpin–Tsai model, the effective material properties can be obtained. By employing the Lagrange's equation and considering the effects of Coriolis force and centrifugal force, the coupled governing equations of the assembled structure are determined. Furthermore, the assumed modes method and substructure modal synthesis method are applied to obtain the frequencies of the assembled beam–plate structure. A comprehensive numerical investigation is carried out to discuss the influence of the structural and material parameters on the vibration behavior of the beam–plate structure. [ABSTRACT FROM AUTHOR]