Aeroelastic Stability Research Articles

Aeroelastic analysis of an air-to-air refueling hose–drogue system through an efficient novel mathematical model

This paper presents an accurate hose and drogue model for aerial refueling. This model includes the influence of the bending forces on the hose, the downwash angle induced by the tanker-role aircraft wing and the phase lag angle between the aerodynamic forces on the hose and its oscillating motion. A time linearization concerning the hose and drogue static equilibrium position is performed to investigate the aeroelastic stability of the resulting system. Flutter of the time linearized system is computed by the tracking of the roots method. The influence of the different parameters on the flutter characteristics is analyzed. In all cases considered, flutter always occurs by a single mode of oscillation corresponding to the first mode of the hose.

Theoretical analysis for the effect of static pressure differential on aeroelastic stability of flexible panel

The static pressure differentials have been neglected in almost all of theoretical analysis models for panel flutter in the supersonic flow, which are established on the basis of the classic aeroelastic model by Dowell in 1966. However, in actual engineering, flexible panels are still subjected to the static pressure differentials under some circumstances. By using the numerical methods, Dowell et al. found that the static pressure differentials as small as 10−2 psi may significantly alter the flutter boundary. In this paper, a novel strategy for a theoretical analysis model is proposed to study the effect of static pressure differential on aeroelastic stability of flexible panel in the supersonic airflow. We regard the final total displacement of the panel as the superposition of dynamic displacement and static deformation, which is in accord with the actual situation of physicality. The static deformation is obtained by solving the static aeroelastic equation. Using the curve/surface fitting method, the static deformations are described by two approaches with/without considering the interaction between the static deformation and steady aerodynamic loads. And then the static deformation is introduced into the dynamic aeroelastic equations in the form of the stiffness through the nonlinear induced loading. The dynamic aeroelastic equation is solved by using the Galerkin discrete method, which can truncate the partial differential equations into a set of ordinary equations. Lyapunov indirect method is utilized to evaluate the aeroelastic stability of the flexible panel. According to the known expression of static deformation and Routh-Hurwitz criterion, a theoretical solution for the aeroelastic stability boundary under the action of the arbitrary static pressure differentials is derived. The theoretical results show that (1) The static pressure differential can significantly enhance the aeroelastic stability of the flexible panel, which is consistent with the numerical results. (2) Whether the actual coupling between the static deformation and aerodynamic loads is considered or not, the stability boundaries obtained are quite different. (3) The increase of the stiffness of structure induced by the static deformation can increase the critical flutter dynamic pressures, but it is not the dominant factor to lead to such a remarkable improvement of the stability of the flexible panel under the action of the static pressure differential. The actual coupling between the static deformation and aerodynamic loads plays a significant role in substantially improving the aeroelastic stability of the flexible panel.

Aeroelastic vibration analysis of wind turbine blade with Gurney flap

In this paper, based on the parametric design of 3 D blades including typical cross-section and natural frequency calculation of the equivalent model, an integral method for aerodynamic performance and aeroelastic vibration analysis of blade with Gurney flap is proposed. Parametric design and unstructured grid are used to pre-process the blades with/without the Gurney flap. The discrete aerodynamic performance parameters distribution including the lift, drag, and torsion coefficients calculated by Fluent is fitted by the nonlinear least square method based on the trust-region algorithm, and the natural frequencies of the rotating blade are accurately solved by the equivalent thin-walled beam model and Green’s functions. Based on the aerodynamic performance coefficients and natural frequencies obtained by the accurate calculation above, the aeroelastic response equation of typical cross-section considering local aerodynamic damping matrix is established, and the vibration response of blade in flap and torsion direction is further described. From the analysis results, it can be seen that the Gurney flap structure can not only bring higher lift performance to the blade, but also can reduce the amplitude and vibration range of aeroelastic vibration, improve the aeroelastic stability of the blade, and prove the effectiveness of Gurney flap.

Non-linear panel instabilities at high-subsonic and low supersonic speeds solved with strongly coupled CIRA FSI framework

Nonlinear aspects of aeroelastic stability are here investigated for two and three dimensional panels in high subsonic and low supersonic flows. The effects of edge constraints and initial conditions on post-flutter behaviour are also studied.Such phenomena are crucial for spatial launchers development, that has renewed interest due to a larger number of commercial companies in the frame of space flight access.Numerical analyses are carried out with a framework developed at CIRA, able to deal with Fluid Structure Interaction simulation in a partitioned approach. The CIRA multi-block structured flow solver for unsteady Navier–Stokes equations was updated and tightly coupled with the open-source finite element method code CalculiX in a modular approach.The results are compared in terms of static divergence and Limit Cycle Oscillations with literature results.

Robust passive control methodology and aeroelastic behavior of composite panels with multimodal shunted piezoceramics in parallel

The increasing use of composite materials in the aeronautical industry has made it possible to build lighter structures with better mechanical properties. Since lighter structures tend to be more flexible, undesirable vibrations and noise are increased and strategies that improve the aeroelastic stability are key issues to be addressed. With the use of intelligent materials, it is possible that the structure has the ability to dissipate energy and stabilize itself when subjected to external dynamic loadings imposed by airflow. This work demonstrates the feasibility of using a passive control tool to increase the supersonic flutter boundary of composite panels using a multimodal shunted piezoceramic in parallel topology. For an application of industrial interest, uncertainties in the electrical parameters of the shunt circuit are considered in the control system design. Numerical applications are presented and the main features and capabilities of the proposed methodology are highlighted.

GALLOPING INSTABILITY ANALYSIS OF A CABLE-DAMPER SYSTEM

Viscous dampers are used widely to mitigate cable vibrations cable-stayed bridges. A damper attached to a stay cable leads to complex modes. The complexity can highly affect the aeroelastic stability of the cable. A galloping instability analysis of cable with an attached damper will be presented. A numerical example points out errors of conventional galloping analysis. The complexity of the mode shapes leads the cable being more unstable than ignoring it by treating the mode shapes as real.

Nonlinear electro-thermo-mechanical dynamic behaviors of a supersonic functionally graded piezoelectric plate with general boundary conditions

A unified analytical model is developed to investigate the nonlinear aeroelastic behaviors of a supersonic functionally graded piezoelectric material (FGPM) plate with general boundary conditions under electro-thermo-mechanical loads. The formulation is derived by first-order shear deformation theory (FSDT) and supersonic piston theory, and the geometrical nonlinearity is considered based on von Karman large deformation theory. The motion equations of the supersonic FGPM plate are obtained through Hamilton principle and a modified Fourier series with auxiliary functions is employed to satisfy the possible mechanical and electric boundary conditions. Nonlinear aeroelastic responses of the FGPM plate are solved via Newmark integration technique combined with Newton-Raphson iterative scheme. Convergence and comparison studies show that the proposed model has sufficient accuracy in predicting aeroelastic stability and nonlinear dynamic responses as well as possess reliability in handling arbitrary boundary conditions. Numerical examples are carried out to demonstrate that several key parameters can significantly affect flutter and thermal buckling of the plate. Additionally, the effects of thermal and electric loads on limit cycle oscillation and dynamic bifurcation of nonlinear FGPM plate are examined. A higher temperature rise can result in the transition of the system from stable to chaos and more complicated evolution of dynamic motions.

Multifidelity Sensitivity Study of Subsonic Wing Flutter for Hybrid Approaches in Aircraft Multidisciplinary Design and Optimisation

A comparative sensitivity study for the flutter instability of aircraft wings in subsonic flow is presented, using analytical models and numerical tools with different multidisciplinary approaches. The analyses build on previous elegant works and encompass parametric variations of aero-structural properties, quantifying their effect on the aeroelastic stability boundary. Differences in the multifidelity results are critically assessed from both theoretical and computational perspectives, in view of possible practical applications within airplane preliminary design and optimisation. A robust hybrid strategy is then recommended, wherein the flutter boundary is obtained using a higher-fidelity approach while the flutter sensitivity is computed adopting a lower-fidelity approach.

Investigation of Sloshing Effects on Flexible Aircraft Stability and Response

The present paper provides an investigation of the effects of linear slosh dynamics on aeroelastic stability and response of flying wing configuration. The proposal of this work is to use reduced order model based on the theory of the equivalent mechanical models for the description of the sloshing dynamics. This model is then introduced into an integrated modeling that accounts for both rigid and elastic behavior of flexible aircraft. The formulation also provides for fully unsteady aerodynamics modeled in the frequency domain via doublet lattice method and recast in time-domain state-space form by means of a rational function approximation. The case study consists of the so-called body freedom flutter research model equipped with a single tank, partially filled with water, located underneath the center of mass of the aircraft. The results spotlight that neglecting such sloshing effects considering the liquid as a frozen mass may overshadow possible instabilities, especially for mainly rigid-body dynamics.

Aeroelastic analysis and structural parametric design of composite rotor blade

Based on FEM theory, a method of dynamic analysis for hingeless rotors considering anisotropic composite materials is established. A parametric modeling method of composite blade with typical profile and high simulation degree for design is proposed. Through the finite element method, the profile characteristics of rotor blade can be obtained efficiently and accurately, and the synchronization of parametric design and finite element analysis of structural characteristics can be realized. Then a 23-degrees of freedom non-linear beam element is used to simulate the extended one-dimensional beam, thereby a non-linear differential equation describing the elastic motion of the rotor is established. To obtain the cross-sectional target characteristics of the blades, an inverse design method is proposed for cross-section components based on combinatorial optimization algorithm. The calculation and validation work show that the proposed model can effectively analyze the aeroelastic characteristics of general composite rotors. Further, the influence of cross-sectional parameters on the aeroelastic stability and hub loads of hingeless rotor is analyzed and some remarkable conclusions are obtained.

Aeroelastic analysis of an idealized landing gear door in subsonic potential flow

Landing gear doors on aircraft have experienced flutter during preliminary flight testing. While designs vary widely, landing gear doors are typically plate-like structures with a relatively rigid actuator attached to their inside surface. To better understand the aeroelasticity of landing gear doors, this study investigates the aeroelastic stability of an idealized model. The model consists of a hinged plate with an interior constraint approximating the actuator attachment. The plate is subject to uniform flow, and an unsteady vortex lattice model is coupled to the structural model to predict critical flow velocities. The location and footprint area of the internal constraint, along with plate aspect and mass ratios, are varied to investigate a large parameter space. Results reveal that the critical flow speed and instability mechanism are sensitive to the postulated actuator placement. In general, flutter is the dominant mode of instability when the actuator is postulated in the leading quarter of the plate. In other postulated locations, divergence dominates. However, the exact shape and location of the boundary between flutter and divergence is configuration dependent and found to be especially sensitive to changes in aspect ratio.

PSO-LSSVR: A surrogate modeling approach for probabilistic flutter evaluation of compressor blade

Compressor blade seriously affects the reliability and stability of aircraft engine. Probabilistic flutter evaluation of compressor blade can effectively quantify failure risk and improve aeroelastic stability. To improve the computational efficiency of probabilistic flutter evaluation, a surrogate modeling approach (called as PSO-LSSVR) is presented by absorbing the strength of particle swarm optimization (PSO) algorithm and least-squares support vector regression (LSSVR). We first mathematically modeled the PSO-LSSVR and then introduce the corresponding probabilistic flutter framework. With respect to high-nonlinearity and strong coupling of limit-state function, the probabilistic flutter evaluation of NASA Rotor 37 is performed to evaluate the proposed approach. Compared with Monte Carlo method, quadratic polynomial (QP), regular support vector regression (SVR and LSSVR), the presented PSO-LSSVR possesses the highest computing efficiency while keeping acceptable computing precision.

Supersonic Aeroelasticity and Dynamic Instability of Functionally Graded Porous Cylindrical Shells Using a Unified Solution Formulation

This study provides an overview on the effect of porosity on free vibrations and more importantly aeroelastic stability margins of cylindrical shells. A general formulation for cylindrical shells is first developed including the effects of shear deformation and rotary inertia along with Sander’s rigid body rotation modification. Two porosity distributions of even and uneven are considered for functionally graded shells. The most general form of power-law model which is known as four-parameter power-law is utilized to provide a clear understanding for the qualification of functionally graded material. A Ritz-based solution algorithm being capable of representing all combinations of symmetric and asymmetric boundary conditions by a penalty method is also introduced. In addition to the capability of satisfying all boundary conditions, the presented solution method is very fast in terms of convergence and computational effort. Various parametric studies are provided and practical results are reported.

Advanced aeroelastic robust stability analysis with structural uncertainties

Robust flutter analysis described in this paper is based on the robust control theory framework. Therefore, a time-domain linear fractional transformation representation of the perturbed aeroelastic system is modeled. Then, the robust stability is analyzed by means of the structured singular value mu, which is defined as an alternative measure of robustness. Robust flutter analysis deals with aeroelastic (or aeroservoelastic) stability analysis taking structural dynamics, aerodynamics and/or unmodeled system dynamics uncertainties into account. Flutter is a well-known dynamic aeroelastic instability phenomenon caused by an interaction between structural vibrations and unsteady aerodynamic forces, whereby the level of vibration may trigger large amplitudes, eventually leading to catastrophic failure of the structure. The primary motivation of the robust flutter analysis is that this method allows the computation of the worst-case flutter velocity which can support, for example, the flight test program by a valuable robust flutter boundary. This paper addresses the issue of an approach for aeroelastic robust stability analysis with structural uncertainties with respect to physical symmetric and asymmetric stiffness perturbations on the wing structure by means of tuning beams.

Parametric analysis on flutter performance of a long-span quadruple-tower suspension bridge

Flutter is a critical point of concern in the wind-resistant design of long-span suspension bridges. As a novel realization, the multi-tower suspension bridge is becoming more and more popular in engineering communities. The aeroelastic stability of this kind of bridge attracts intensive attentions. To better understand the flutter performance of multi-tower suspension bridges, a long-span quadruple-tower suspension bridge (QTSB) with three main spans is designed in this study by extension from Taizhou Bridge, which is a triple-tower suspension bridge (TTSB) with double main spans. Considering the role of some important structural parameters in flutter performance, a parametric analysis is carried out for the long-span QTSB with comparisons to the TTSB that has the same length in each main span. The parameters of focus include sag-to-span ratio of the main cable, vertical and torsional rigidities of the girder, mass of the girder as well as longitudinal rigidities of middle towers. The analytical results indicate that increasing the torsional rigidity of the girder and longitudinal rigidities of middle towers can effectively improve the critical wind velocities. Changing the sag-to-span ratio or the mass of girder would cause complicated results, in which the transition of the dominant mode is observed. The mode transition phenomenon can be reasonably utilized in the wind-resistant design of a long-span QTSB.

Aeroelastic stability analysis of aircraft wings with initial curvature

In this study, the aeroelastic instability of a wing with an initial out-of-plane curvature is determined. The structural dynamics of the wing is modelled by using the geometrically exact beam equations, and the aerodynamic loads are determined using an incompressible unsteady aerodynamic model. The wing is considered to have initial out-of-plane curvature, and the effect of the curvature on the flutter velocity and flutter frequency of the wing is determined. Two curved wing cases are considered here. In the first case, the length of the wing is assumed to be constant and therefore, as the wing is curved, the projected area of the wing decreases. In the second case, the wing is assumed to have a constant projected area and therefore different curvature angles result from different wing lengths. When the wing is designed to have an initial out-of-plane curvature, the wing dynamics change, and therefore the aeroelastic stability of the curved wing is also affected. It is shown that as the initial curvature of the wing increases, initially the flutter velocity decreases but then increases, and finally a sudden jump occurs in the flutter velocity due to the change of the coupled modes contributing to flutter. Moreover, the flutter frequency also first decreases as the curvature of the wing increases, and then there is a sudden jump in the frequency, and from this point again the frequency decreases. Finally, results highlighting the importance of the initial curvature and the length of the curved segment on the stability velocity and frequency of the curved wing are presented.

A general modal frequency-domain vortex lattice method for aeroelastic analyses

The generalized aerodynamic force (GAF) matrix is derived for the Unsteady Vortex Lattice Method (UVLM) without the assumption of out-of-plane dynamics. As a result, the approach naturally includes in-plane motion and forces unlike the doublet lattice method (DLM). The derived UVLM GAF is therefore applicable to industry-standard techniques for aeroelastic stability analyses, such as the p–k method. In this work, the fluid–structure interpolation is performed with radial basis functions for surface interpolation. The generalized aerodynamic forces computed with the UVLM are verified against the DLM from NASTRAN on a simple flat plate configuration. The ability of the UVLM to include steady loads is verified with a T-tail flutter case and the results confirm the importance of including steady loads for T-tail flutter analysis. The modal frequency domain VLM therefore provides the same level of efficiency and accuracy than the DLM, but without the restrictions and with the ability to handle complex geometries. It is therefore a viable replacement to the DLM.

An efficient coupled-mode flutter analysis method for turbomachinery

An efficient aeroelastic eigenvalue method based on time domain system identification has been developed to analyze coupled-mode flutter in turbomachinery. The aeroelastic stability problem is transformed into a generalized eigenvalue problem (GEP) by incorporating the aeroelastic equation and an aerodynamic modal force model. The aerodynamic modal force model correlates the generalized aerodynamic modal force with generalized motion variables by influence coefficient matrices which are calculated through a time domain system identification method. The aerodynamic damping ratios and the corresponding eigenfrequencies for all interblade phase angles (IBPA) can be obtained conveniently from a single time domain aerodynamic computation. The proposed method has been validated and demonstrated by presenting results for NASA Rotor 67 flutter cases in this paper.

Gradient-Based Optimization of Solar-Regenerative High-Altitude Long-Endurance Aircraft

This paper uses gradient-based optimization to minimize the mass of a solar-regenerative high-altitude long-endurance flying-wing aircraft while accounting for nonlinear aeroelastic effects. The aircraft is designed to fly year round at 35° latitude at 18 km above sea level and subjected to energy capture, energy storage, material failure, local buckling, stall, longitudinal stability, and coupled flight and aeroelastic stability constraints. The optimized aircraft has an aspect ratio of 54.52, a surface area of , a mass of 349.5 kg; exhibits little aeroelastic deflection at the design airspeed; and is primarily stability constrained. Several parameter sweeps are performed to determine sensitivity to altitude, latitude, battery specific energy, solar efficiency, avionics and payload power requirements, and minimum design velocity.

The effect of curved tips on the dynamics of composite rotor blades

In this paper, the dynamics of a tailored composite rotating blade with curved tips are investigated, with a view to improving the dynamic behaviour of the blade in flight. The blade tip is curved either in the out-of-plane or in the in-plane directions. The composite blade is modelled by using the exact beam formulation, and the cross-sectional properties of the blade are obtained using the variational asymptotic method. The resulting nonlinear partial differential equations are discretised using a time-space scheme, and the stationary and rotating frequencies of the blade are obtained from the eigenvalues of the linearised system. Three case studies are considered here each of them representing one of the main elastic couplings that might happen in a composite blade. These three elastic couplings are the flap-twist, lag-twist, and extension-twist couplings. All these couplings are very important in the blade design as they can affect the twist and hence the dynamics of the blade. The blade tip length and curvature value are two main parameters that this paper is focused on. It is shown that the curved tip of the blade affects the blade frequencies by adding extra couplings, and therefore could be used as a potential morphing concept for tuning the frequencies, enhancing the aeroelastic stability or performance of the blade in flight.