Aeroelastic Stability Analysis Research Articles

Geometrically Exact Aeroelastic Stability Analysis of Composite Helicopter Rotor Blades in Hover by Updated VABS

Geometrically Exact Aeroelastic Stability Analysis of Composite Helicopter Rotor Blades in Hover by Updated VABS

Subsonic Aeroelastic Stability Analysis and Vibration Control of a Plate by Using Nonlinear Energy Sink

Vibration suppression and stability control are classic issues in the field of vibration and control. The nonlinear energy sink (NES) is an effective approach for vibration reduction proposed in recent years. It has the advantages of wide frequency vibration isolation properties and without inputting excessive energy. This paper focuses on the stability and passive vibration control of a plate in subsonic airflow by applying the NES. Two kinds of NESs with linear stiffness and with cubic stiffness are proposed and their vibration control performances are compared. The kinetic equations of the plate with NES are established by using the extended Hamilton principle and analyzed by the incremental harmonic balance (IHB) method. The advantages of the hybrid stiffness NES are demonstrated by comparing with the cubic nonlinear stiffness NES. From the results, the vibration suppression effect of the hybrid stiffness NES is more significant than the purely cubic one. However, the effective vibration reduction range of the cubic stiffness NES is wider than the hybrid one. The optimal design parameters of the NES and the effect of the installation position are also discussed.

Geometrically exact aeroelastic stability analysis of helicopter composite rotor blades in forward flight

In this paper, a sophisticated method for analyzing the geometrically exact aeroelastic stability of composite rotor blades in forward flight has been proposed. The unique advantage of the proposed method is to use the geometrically exact beam model with the updated Variational Asymptotic Beam Sectional analysis (VABS) for structural modeling to not only calculate the blade cross-sectional properties and blade spanwise deformations more accurately, but also take into account the effect of transverse shear deformation and blade initial twist and curvatures sophisticatedly. The Peters finite state airloads theory and the Peters-He finite state dynamic inflow model are coupled to calculate the three-dimensional unsteady airloads applied on the blade. The auto-pilot trim scheme is adopted to determine the blade pitch controls. The finite element spatial discretization method, the Newmark numerical integration method, the Newton-Raphson method and the moving-block analysis method are combined to solve the established geometrically exact aeroelastic equations and obtain the geometrically exact aeroelastic stability of composite rotor blades. The proposed method is validated by correlation with existing analytical results. The investigations show that the effect of transverse shear deformation on the aeroelastic stability of composite hingeless rotors in forward flight is non-negligible. Blade initial curvatures have significant effect on the aeroelastic stability of composite hingeless rotors in forward flight, which is not only related to the blade elastic couplings, but also to the advance ratio.

A two-level strategy for aeroelastic optimization of a 3D wing with constant and variable stiffness skins

In this work, optimization strategies employing a standard heuristic free-derivative algorithm combined with a first-order gradient approach are used to maximize the flutter or divergence airspeed, using the fibre material orientations as design variables. The aeroelastic stability analysis calculations are performed by a classical PK method. The finite element method is used to obtain the structural modes and frequencies and the unsteady aerodynamic influence coefficient matrices are obtained with a doublet-lattice model. Numerical studies are performed with a complex 3D model that includes curved surfaces and internal elements such as spars and ribs. The main goal of the article is to use the heuristic part with a small number of parameters, to reduce the design space and provide an efficient initial guess for the gradient search, so that the optimization complexity is substantially reduced. Results for constant and variable stiffness composite wings are presented for laminates with different numbers of plies. It is shown by several examples that the pres.

Dynamic Response of a Flexible Multi-Body in Large Wind Turbines: A Review

Dynamic response of flexible multi-body large wind turbines has been quickly growing in recent years. With the new normal economic policy, the economy of China is developing innovatively and stably. New energy development and utilization is an important strategy for people’s lives and economic development around the world. It is feasible to analyze from a broad perspective. In particular, the development and application of wind power is affecting the economic development of industry to a certain extent. Persistent and significant large wind turbines have cast concern over the prospects of wind power technology, and a comprehensive development potential of wind power technology has been analyzed its potential use in the future. The multi-body dynamics method can better analyze and describe the impact of flexible blade elastic deformation on motion characteristics and provides a practical analysis method for the aeroelastic stability analysis and control system design of wind turbines.

Nonlinear aeroelastic stability analysis of a folding wing by using geometrically exact fully intrinsic beam equations

In this paper, the aeroelastic instability of folding wings by using the geometrically exact fully intrinsic beam equations is investigated. The important advantages of these equations in comparison with other structural beam equations are complete modeling without simplifying assumptions in large deformations, low-order nonlinearities, and thus less complexity. For the first time, folding angles have been implemented in the geometrically exact fully intrinsic beam equations and hence this is the main novelty of this study. The applied aerodynamic loads in an incompressible flow regime are determined using Peter’s unsteady aerodynamic model. In order to check the stability of the system, first the resulting non-linear partial differential equations are discretized by employing the central finite difference method, and then linearized about the nonlinear steady-state condition. By obtaining the eigenvalues of the linearized system, the stability of the wing is evaluated. Furthermore, investigation of the effects of some important parameters such as stiffness ratio and length ratio on the flutter speed of the folding wing for various folding angles, is another achievement of this study. It is observed that the geometrically exact fully intrinsic beam equations can model the folding angles for the aeroelastic analysis more accurately and the capabilities of these equations became more specific.

Aeroelastic stability analysis of rotor blade with complex three-dimensional design

A rotor dynamic analysis method for the complex three-dimensional design blade was developed and applied to analyzing its aeroelastic stability. Based on the medium-size deformation beam theory and Hamilton principle, the joint transfer matrix was used in the blade kinematic and the deformation compatibility principle was used in the assembled finite element matrix to develop the complex three-dimensional rotor structural dynamics model. The BO105 rotor was used to validate this method and the aeroelastic characteristic of the complex three-dimensional rotor was analyzed in detail. The results showed that the negative structural coupling of flap-torsion was appeared with tip sweep, and the 1/rev torsion modal frequency was decreased, and the 1/rev torsion modal damping ratio was maximally decreased about 90%. The positive structural coupling of lag-torsion was appeared with tip droop, the 2/rev lag modal frequency was decreased, the 1/rev torsion modal damping ratio was maximally decreased about 62%. The torsion stability was sharply decreased with tip sweep and droop design.

A numerical investigation on direct and data-driven flutter prediction methods

Three alternative algorithms for dynamic aeroelastic stability analysis are investigated. They are based either on direct search of oscillatory conditions of the coupled system or on eigenvalue analysis from frequency-domain sampling of the unsteady aerodynamics. The aerodynamic forcing is obtained with a harmonic-balanced solver developed for a general-purpose finite-volume fluid dynamics solver. This new implementation is first verified against experimental flutter results from the literature. A wing with relatively low bending stiffness is then used to explore the relative performance of each approach, both in terms of the numerical robustness and of their usability to support aeroelastic design.

Frequency-Domain Lifting-Line Aerodynamic Modelling for Wing Aeroelasticity

A frequency-domain lifting-line solution algorithm for the prediction of the unsteady aerodynamics of wings is presented. The Biot–Savart law is applied to determine the normalwash generated by the wake vorticity distribution, whereas steady and unsteady airfoil theories (Glauert’s and Theodorsen’s, respectively) are used to evaluate the sectional aerodynamic loads, namely the lift and pitching moment. The wake vorticity released at the trailing edge derives from the bound circulation through the Kutta condition and is convected downstream with the velocity of the undisturbed flow. The local bound circulation is obtained by the application of the Kutta–Joukowski theorem, extended to unsteady flows. Assuming a bending and torsion wing, this paper provides the aerodynamic matrix of the transfer functions, relating the generalised aerodynamic loads to the Lagrangian coordinates of the elastic deformation. Its rational approximation yields a reduced-order state-space aerodynamic model suitable for an aeroelastic stability analysis and control purposes. The numerical investigation examines the influence of both the wake shed/trailed vorticity modelling and different approximations of the Kutta–Joukowski theorem for unsteady flows on the aerodynamic transfer functions given by the developed frequency-domain lifting-line solver. The accuracy of the solver is assessed by comparison with the predictions obtained by a three-dimensional boundary-element-method solver for potential flows. It is shown that, at least for the frequency range considered, regardless of the approximation of the Kutta–Joukowski theorem applied, the formulation based on the Theodorsen theory provides predictions that are in very good agreement with the results from the boundary element method for a slender wing. This agreement worsens as the wing aspect ratio decreases. A lower level of accuracy is obtained by the application of the sectional loads given by the Glauert theory. In this case, the predictions are more sensitive to the approximation used to express the Kutta–Joukowski theorem for unsteady flows.

Time-domain Analytical Method for Aeroelastic Analysis of High Aspect Ratio Wing Using Unsteady Indicial Aerodynamics

This paper deals with the development of a novel time-domain analytical method to perform an aeroelastic stability analysis of a high aspect ratio wing. The aerodynamic model in this paper is built upon the frequency domain of Theodorsen aerodynamics. An inverse Fourier transform technique is applied to convert the Theodorsen frequency domain transfer function to the Wagner time-domain response function. Later, lift and moment expressions, containing aerodynamic lag states are obtained using the indicial function approach which performs the convolution of the unit step response Wagner lift function with arbitrary input and its time derivative using the principle of superposition. Additional equations containing the derivative of aerodynamic lag states are coupled with previously obtained lift and moment expressions to fully get the complete unsteady aerodynamic model in the time-domain. This time-domain unsteady aerodynamic model is then coupled with a combined bending torsion beam finite element model, using the state space approach. A complex eigenvalue analysis of this state space system is performed, using MATLAB, to determine both the static and dynamic aeroelastic stability boundary. Finally, in this paper, aeroelastic stability analysis of the high aspect ratio wing is performed using the current method and results are validated with MSC Nastran aeroelastic analysis and those available in the literature.

Aeroelasticity of Flying-Wing Aircraft Subject to Morphing: A Stability Study

In this work, we present a study on the effects of modifications on wing geometric configurations via morphing. Specifically, we investigate the resulting impacts on aeroelastic stability. In the primary analysis presented, we assess a wall-mounted configuration for an airfoil section of a two-dimensional wing. This morphing-wing system comprises a torsional spring at the trailing-edge flap hinge, which induces the morphing phenomenon. The behavior of this system is studied within the context of divergence and reversal. The analysis following this examines a highly flexible flying-wing configuration, subject to a transient morphing scheme. The geometries corresponding to the unmorphed and morphed configurations are acquired from a physical morphing trailing-edge wing prototype, and the structural modeling and cross-sectional properties are obtained using the Gmsh tool and variational asymptotic beam sectional analysis. Furthermore, we evaluate the effects of the geometric variations on the aeroelastic stability through leveraging the computer program, NATASHA (which stands for nonlinear aeroelastic trim and stability analysis of high-altitude long-endurance aircraft). The results obtained from this analysis insinuate the favorable impact on the aeroelastic stability of the system, namely, in terms of flutter characteristics.

Vibration and aeroelastic stability analysis of hexagonal honeycomb core sandwich panels in supersonic airflow

This work investigates the vibration and aeroelastic stability behavior of honeycomb core sandwich panels with four-side simply supported boundaries in supersonic airflow. The sandwich panel includes a hexagonal honeycomb core layer with equal wall thickness, and upper and lower isotropic face sheets. The quasi-steady first order piston theory is used to model the aerodynamic pressure, and aeroelastic equations are established using Hamilton’s principle and a finite element approach. The effects of honeycomb core parameters on vibration and critical dynamic pressures of the honeycomb core panel are analyzed in two cases: Case 1, the dimensions of the simply supported hexagonal honeycomb sandwich panel is the same as the basic isotropic model; Case 2, the masses of the honeycomb sandwich panels are n(0<n≤1) times of the basic isotropic panel. The results show that the hexagonal honeycomb core can improve the natural frequencies of the panel. The honeycomb core thickness has a major influence on the critical dynamic pressure of the honeycomb sandwich panel, and the cell thickness, the cell angle and internal aspect ratio have no significant effect on the critical dynamic pressure. Compared with the basic isotropic panel, the mass can be reduced by nearly 70% using the honeycomb panel in the condition of the same critical dynamic pressure, which is of great significance to reduce the weight of the aircraft panel.

Transonic flutter suppression with tuned mass damper by model-based stability analysis method

Flutter as a self-excited oscillation can cause catastrophic damage to the aircraft structure. Tuned mass damper (TMD) is one of the vibration suppression methods widely used in engineering. However, traditional linear aerodynamic methods are not accurate in transonic flow. In this study, we first establish an unsteady aerodynamic model of the NACA0012 airfoil using the system identification method based on the Auto-Regressive with eXogenous input (ARX) model. Then, a flutter suppression model is constructed by coupling the TMD with the aeroelastic system. The parameters of the TMD are investigated using the model-based aeroelastic stability analysis. It is found that the flutter instability mode of the original system has changed due to the participation of the TMD in the system modal coupling. The proposed reduced-order model (ROM) provides a fast stability analysis method for flutter suppression with TMD as well as significant guidance for TMD design and optimization.

An open-source framework for the uncertainty quantification of aeroelastic wind turbine simulation tools

The uncertainty quantification of aeroelastic wind turbine simulations is an active research topic. This paper presents a dedicated, open-source framework for this purpose. The framework is built around the uncertainpy package, likewise available as open source. Uncertainty quantification is done with a non-intrusive, global and variance-based surrogate model, using PCE (i.e., polynomial chaos expansion). Two methods to handle the uncertain parameter distribution along the blades are presented. The framework is demonstrated on the basis of an aeroelastic stability analysis. A sensitivity analysis is performed on the influence of the flapwise, edgewise and torsional stiffness of the blades on the damping of the most critical mode for both a Bladed linearization and a Bladed time domain simulation. The sensitivities of both models are in excellent agreement and the PCE surrogate models are shown to be accurate approximations of the true models.

Aeroelastic Stability Analysis of a Quad-Rotor Wind Turbine

This paper presents the aeroelastic stability analysis of a quad-rotor wind turbine and identifies modes with low damping that are otherwise not present on a single-rotor wind turbine. The non-linear dynamics of a wind turbine model in SIMPACK, without considering wind shear and tower shadow, is linearized around a steady-state; followed by MBC transformation resulting in LTI model. Standard eigenvalue analysis of LTI model is carried out to capture the natural frequency and damping of a quad-rotor wind turbine as a function of wind speed. Results show that several modes with low damping (besides the low damping modes observed on a single-rotor wind turbines) are identified where the damping ratio is less than 1% over the entire operation range.

Nonlinear aeroelastic stability analysis of a two-stage axially moving telescopic wing by using fully intrinsic equations

During the process of span extension for an aircraft wing equipped with a telescopic morphing mechanism, the wing aspect ratio increases, and hence, the geometrical nonlinearities might become more significant. In this regard, this paper aims to investigate the effect of structural nonlinearity on the aeroelasticity of span morphing wings using the exact fully intrinsic equations for the first time. Furthermore, the effects of various parameters such as thrust force, engine location, chord size, flight altitude, initial angle of attack, and overlapping mass on the aeroelasticity of the wing are studied. The applied aerodynamic loads in an incompressible flow regime are determined using Peters’ unsteady aerodynamic model. In order to check the stability of the system, first the resulting nonlinear partial differential equations are discretized by using the central finite difference method and then linearized about the static equilibrium. Finally, by obtaining the eigenvalues of the linearized system, the stability of the wing is evaluated. It is observed that by using the fully intrinsic equations, the instability of the axially moving telescopic wing can be determined more accurately. Moreover, the results show that the morphing length and overlapping mass have significant effects on the aeroelastic stability of the telescopic wing.

Aeroelastic stability analysis of a pyrotechnic separation plate in subsonic airflow

Pyrotechnic separation devices are widely used in aerospace engineering. In separation process, the pyrotechnic separation device breaks into several parts, and the velocity of the separated structure changes intricately, which make the pyrotechnic separation device and the external airflow a complex fluid-structure coupling system. Since the stability of the structure is crucial for the safety, it is necessary to investigate the aerodynamic stability of the pyrotechnic separation device interacting with surrounding airflow. In the present study, the aeroelastic stability of a pyrotechnic separation plate in axial subsonic airflow is studied. The velocity of the residual plate is derived from the momentum theorem. The dynamic model of the pyrotechnic separation plate in subsonic airflow is established based on the linear potential flow theory and the von Kármán plate theory. The effects of the residual length, the pyrotechnic explosion strength and the separation velocity on the stability of the plate are investigated, and the vibration properties of the plate are discussed. From the results, the plate loses stability rapidly when it subjects to the explosion, and restores stability under the negative pressure. The displacement jumping phenomenon is observed. The amplitude of the plate in unstable period increases rapidly, which may cause damage to the structure.

Pseudospectral Continuation for Aeroelastic Stability Analysis

AbstractThis technical note is concerned with aeroelastic flutter problems: the analysis of aeroelastic systems undergoing airspeed-dependent dynamic instability. Existing continuation methods for parametric stability analysis are based on marching along an airspeed parameter until the flutter point is found—an approach that may waste computational effort on low-airspeed system behavior, before a flutter point is located and characterized. Here, we describe a pseudospectral continuation approach that instead marches outward from the system’s flutter points, from points of instability to points of increasing damping, allowing efficient characterization of the subcritical and supercritical behavior of the system. This approach ties together aeroelastic stability analysis and abstract linear algebra and, by reducing the sample space in which the analysis needs to take place, provides efficient methods for computing practical aeroelastic stability properties—for instance, flight envelopes based on maximum modal damping and the location of borderline-stable zones.

The effect of elastic couplings and material uncertainties on the flutter of composite high aspect ratio wings

In this paper, the stochastic aeroelastic stability analysis of a composite high aspect ratio wing with various elastic couplings is investigated. The wing consists of a rectangular spar-box made from composite materials. Due to its high aspect ratio, the wing structure is modelled using the exact beam formulation, and the aerodynamic loads acting on the wing are simulated using an unsteady lifting line theory. A composite spar-box cross section is considered, and the effect of various effective parameters on the aeroelastic stability of the wing is studied. First, a baseline composite wing is designed and the effect of three different elastic couplings on the stability of the wing is determined. These three elastic couplings that affect the aeroelastic design of the composite wing are the out-of-plane (flap)-twist, the in-plane (lag)-twist and the extension-twist. Furthermore, the effect of uniformly distributed load on the aeroelastic stability of the wing is assessed for various layups. Finally, the effect of material uncertainties on the aeroelastic stability of the composite wing with various couplings is studied. It is observed that the type of elastic coupling has a significant effect on the sensitivity of the flutter speed and frequency of the composite wing due to the randomness of the material properties. In particular, the aeroelastic behaviour of the wing with lag-twist coupling is more sensitive to the material uncertainties than other two layups.

Geometrically nonlinear flutter analysis with corotational shell finite element analysis and unsteady vortex-lattice method

In this paper, an aeroelastic framework developed in the previous works has been extended for a geometrically nonlinear aeroelastic stability analysis. In the aeroelastic stability analysis, modal mass and stiffness matrices are constructed using shell finite elements with the corotational approach, which can take into account the geometric stiffening under large deformations. A generalized aerodynamic force matrix is derived by accommodating the unsteady vortex-lattice method based on a modal approach. The derived modal aeroelastic equations are solved using the p-k method. Individual modules to calculate generalized structural matrices with the corotational approach and aerodynamic forces based on the unsteady vortex-lattice method are verified. The present geometrically nonlinear aeroelastic framework for aeroelastic stability analysis is also validated in a comparison with an experimental result in the flutter wind tunnel test showing a reasonable accuracy for a prediction of flutter speed, while there still is room for further improvement in the estimation of flutter frequency. In addition, the present method allows studying the flutter characteristics of flexible wings with different incident angles, which cannot be evaluated by traditional linear flutter simulations. Finally, effects of geometric nonlinearity and large deformation on flutter characteristics of flexible and high-aspect-ratio wings were explored by using the present method. The present method can help to understand aeroelastic stability characteristics for such high-aspect-ratio wings.