Nonlinear Analysis and Bifurcation Characteristics of Whirl Flutter in Unmanned Aerial Systems

Aerial drones have improved significantly over the recent decades with stronger and smaller motors, more powerful propellers, and overall optimization of systems. These improvements have consequently increased top speeds and improved a variety of performance aspects, along with introducing new structural challenges, such as whirl flutter. Whirl flutter is an aeroelastic instability that can be affected by structural or aerodynamic nonlinearities. This instability may affect the prediction of potentially dangerous behaviors. In this work, a nonlinear reduced-order model for a nacelle-rotor system, considering quasi-steady aerodynamics, is implemented. First, a parametric study for the linear system is performed to determine the main aerodynamic and structural characteristics that affect the onset of instability. Multiple polynomial nonlinearities in the two degrees of freedom nacelle-rotor model are tested to simulate possible structural nonlinear effects including symmetric cubic hardening nonlinearities for the pitch and yaw degrees of freedom; purely yaw nonlinearity; purely pitch nonlinearity; and a combination of quadratic, cubic, and fifth-order nonlinearities for both degrees of freedom. Results show that the presence of hardening structural nonlinearities introduces limit cycle oscillations to the system in the post-flutter regime. Moreover, it is demonstrated that the inclusion of quadratic nonlinearity introduces asymmetric oscillations and subcritical behavior, where large and potentially dangerous deformations can be reached before the predicted linear flutter speed.

High-Fidelity Fin–Actuator System Modeling and Aeroelastic Analysis Considering Friction Effect

Both the dynamic characteristics and structural nonlinearities of an actuator will affect the flutter boundary of a fin–actuator system. The actuator models used in past research are not universal, the accuracy is difficult to guarantee, and the consideration of nonlinearity is not adequate. Based on modularization, a high-fidelity modeling method for an actuator is proposed in this paper. This model considers both freeplay and friction, which is easy to expand. It can be directly used to analyze actuator characteristics and perform aeroelastic analysis of fin–actuator systems. Friction can improve the aeroelastic stability, but the mechanism of its influence on the aeroelastic characteristics of the system has not been reported. In this paper, the LuGre model, which can better reflect the friction characteristics, was integrated into the actuator. The influence of the initial condition, freeplay, and friction on the aeroelastic characteristics of the system was analyzed. The comparison of the results with the previous research shows that oversimplified friction models are not accurate enough to reflect the mechanism of friction’s influence. By changing the loads, material, and geometry of contact surfaces, flutter can be effectively suppressed, and the power loss caused by friction can be minimized.

Characterization of typical aeroelastic sections under combined structural concentrated nonlinearities

Structural nonlinearities are usually present in aeroelastic systems. The analysis of this system commonly comprises a study involving only one type of nonlinearity, influencing a particular motion of the airfoil. However, practical applications of aeroelastic systems can be affected by different types of structural nonlinearities. It becomes essential to study the stability of the aeroelastic system under these conditions to assess more real operational flight procedures. In this context, this article presents an investigation of a typical aeroelastic section response with trailing edge control surface subjected to combinations of concentrated structural nonlinearities. Different nonlinear scenarios involving cubic hardening stiffness in pitching and free play, free play with preload, and slip dry friction in the trailing edge control surface motion are analyzed. The mathematical model is based on linear unsteady aerodynamics coupled to a three-dof typical aeroelastic section. Hopf bifurcations diagrams are obtained from direct time integration of the equation of motion. The post-flutter limit cycle oscillations are investigated, revealing supercritical and subcritical bifurcations. A complete parametric study of the nonlinear parameters is carried out, thereby allowing a sensitivity analysis of each nonlinear scenario. The results show that aeroelastic tailoring considering the mild post-flutter behavior can be achieved through an appropriate choice of combined nonlinear effects. Moreover, combined nonlinearities can mitigate the undesired subcritical aeroelastic responses caused by free play.

System Reliability Assessment of Cable-Supported Bridges under Stochastic Traffic Loads Based on Deep Belief Networks

A cable-supported bridge is usually a key junction of a highway or a railway that demands a higher safety margin, especially when it is subjected to harsh environmental and complex loading conditions. In comparison to short-span girder bridges, long-span flexible structures have unique characteristics that increase the complexity of the structural mechanical behavior. Therefore, the system safety of cable-supported bridges is critical but difficult to evaluate. This study proposes a novel and intelligent approach for system reliability evaluation of cable-supported bridges under stochastic traffic load by utilizing deep belief networks (DBNs). The related mathematical models were derived taking into consideration the structural nonlinearities and high-order statically indeterminate characteristics. A computational framework is presented to illustrate the steps followed for system reliability evaluation using DBNs. In a case study, a prototype suspension bridge is selected to investigate the system reliability under stochastic traffic loading based on site-specific traffic monitoring data. The numerical results indicated that DBNs provide an accurate approximation for the mechanical behavior accounting for structural nonlinearities and different system behaviors, which can be treated as a meta-model to estimate the structural failure probability. The dominant failure modes of the suspension bridge are the fracture of suspenders followed by the bending failure of girders. The degradation of suspenders due to fatigue-corrosion damage has a significant effect on the system reliability of a suspension bridge. The numerical results provide a theoretical basis for the design on cable replacement strategies.

Experimental Nonlinear Flutter Analysis of a Cantilever Wing/Store

This paper studies experimentally the nonlinear aeroelastic and flutter behavior of a cantilever plate wing with an external store. The wing model that is constructed from plexiglass sheet is designed and tested in a closed-circuit subsonic wind tunnel. To deal with the structural nonlinearities of the model, various analysis tools such as time history plots, phase-plane projections and Fast Fourier Transform (FFT) have been used for detecting the critical and post-critical behaviors of the structure. The results show that flutter takes place by the coupling between the torsional and bending modes. A good correlation between the present experiments and previous numerical results is obtained. The nonlinear aeroelastic response and flutter boundary are investigated for different sweep angles. The flutter velocity and amplitudes of limit cycle oscillations (LCOs) increase rapidly with increasing sweep angle. The nonlinear response of the wing with an external store is also investigated, with the effect of store location on the nonlinear flutter boundary evaluated.

Nonlinear Aeroelastic in-Plane Behavior of Suspension Bridges under Steady Wind Flow

The nonlinear aeroelastic behavior of suspension bridges, undergoing dynamical in-plain instability (galloping), is analyzed. A nonlinear continuous model of bridge is formulated, made of a visco-elastic beam and a parabolic cable, connected each other by axially rigid suspenders, continuously distributed. The structure is loaded by a uniform wind flow which acts normally to the bridge plane. Both external and internal damping are accounted for the structure, according to the Kelvin-Voigt rheological model. The nonlinear aeroelastic effects are evaluated via the quasi-static theory, while structural nonlinearities are not taken into account. First, the free dynamics of the undamped bridge are addressed, and the natural modes determined. Then, the nonlinear equations ruling the dynamics of the aeroelastic system, close to the bifurcation point, are tackled by the Multiple Scale Method. This is directly applied to the partial differential equations, and provides the finite-dimensional bifurcation equations. From these latter, the limit-cycle amplitude and its stability are evaluated as function of the mean wind velocity. A case study of suspension bridge is analyzed.

The Construction Technology of High Pier Verticality Control Based on Rapid Construction of Super High Pier in Mountainous Area and Unscented Kalman Filter

Based on engineering examples, the paper carried out research on the rapid construction technology of high piers in mountainous areas, and used unscented Kalman filter technology to eliminate the influence of measurement factors, man-made construction factors, and structural nonlinearities on the pre-deflection. The research results show that this technology can significantly improve the verticality of ultra-high piers in mountainous areas and has important application value.

Effect of Structural Nonlinearity on a Piecewise Linear Aeroelastic System

Aeroelasticity is the study of the interaction of aerodynamic, elastic and inertia forces. When flexible structures, such as an airfoil, undergo wind excitation, divergence or flutter instability may arise. We study the dynamics of a two-degree-of-freedom (pitch and plunge) aeroelastic system with cubic structural nonlinearities. The aerodynamic forces are modeled as a piecewise linear function of the effective angle of attack. Stability and bifurcations of equilibria are analyzed. The effect of the structural nonlinearity is investigated. We find border collision, rapid, Hopf, saddle-node and pitchfork bifurcations. Bifurcation diagrams of the system were calculated utilizing MatCont and Mathematica.