Aeroelastic tailoring of a plate wing with functionally graded materials

A functionally graded material (FGM) provides a spatial blend of material properties throughout a structure. This paper studies the efficacy of FGM for the aeroelastic tailoring of a metallic cantilever plate-like wing, wherein a genetic algorithm provides Pareto trade-off curves between static and dynamic aeroelastic metrics. A key comparison is between the effectiveness of material grading, geometric grading (i.e. plate thickness variations), and using both simultaneously. The introduction of material grading does, in some cases, improve the aeroelastic performance. This improvement, and the physical mechanism upon which it is based, depends on numerous factors: the two sets of metallic material parameters used for grading; the sweep of the plate; the aspect ratio of the plate; and whether the material is graded continuously or discretely.     

Aeroelastic stability of a wing with bracing struts (Keldysh problem)

The problem of the influence of bracing struts of two types on the aeroelastic stability of a wing is studied. The formulation of the problem follows that considered by M. V. Keldysh [1]. The behavior of the eigenvalues is studied in the complex plane and the stability, flutter, and divergence domains are constructed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 151–162, January–February, 1998.     

Aeroelastic instability of composite wings by the consideration of different structural constitutive assumptions

The aeroelastic instability of composite wings modeled as Circumferentially Asymmetric Stiffness (CAS) thin-walled composite beams with closed cross-section is carried out. The objective has been to investigate the effects of different assumptions of constitutive equations on the aeroelastic instability behavior. Non-classical effects such as restrained warping and transverse shear are included in the beam model. The unsteady incompressible airloads are presented using Wagner׳s function. A comparison of the results based on different constitutive equations for a number of configurations including three types of stacking sequence for a box cross-section and two types of stacking sequence for a biconvex cross-section, is performed. The effects of the values of twist as well as twist-bending stiffness coefficients have been studied carefully on the results. As an outcome of this investigation it is revealed that the different choices of structural constitutive equations which result in different values of stiffness quantities; namely, twist and twist-bending stiffness, significantly affect the predicted results. For example, a difference of up to 45% in the aeroelastic critical speed has been observed between different sets of constitutive equations in some cases.     

Aeroelastic prediction of the limit cycle oscillations of a cropped delta wing

The flutter and limit cycle oscillation (LCO) behavior of a cropped delta wing are investigated using a newly developed computational aeroelastic solver. This computational model includes a well-validated Euler finite difference solver coupled to a high-fidelity finite element structural solver. The nonlinear structural model includes geometric nonlinearities which are modelled using a co-rotational formulation. The LCOs of the cropped delta wing are computed and the results are compared to previous computations and to experiment. Over the range of dynamic pressures for which experimental results are reported, the LCO magnitudes computed using the current model are comparable to those from a previous computation which used a lower-order von Karman structural model. However, for larger dynamic pressures, the current computational model and the model which used the von Karman theory start to differ significantly, with the current model predicting larger deflections for a given dynamic pressure. This results in a LCO curve which is in better qualitative agreement with experiment. Flow features which were present in the previous computational model such as a leading edge vortex and a shock wave are enhanced in the current model due to the prediction of larger deflections and rotations at the higher dynamic pressures.     

Effect of thrust on the aeroelastic instability of a composite swept wing with two engines in subsonic compressible flow

This paper aims to investigate aeroelastic stability boundary of subsonic wings under the effect of thrust of two engines. The wing structure is modeled as a tapered composite box-beam. Moreover, an indicial function based model is used to calculate the unsteady lift and moment distribution along the wing span in subsonic compressible flow. The two jet engines mounted on the wing are modeled as concentrated masses and the effect of thrust of each engine is applied as a follower force. Using Hamilton's principle along with Galerkin's method, the governing equations of motion are derived, then the obtained equations are solved in frequency domain using the K-method and the aeroelastic instability conditions are determined. The flutter analysis results of four example wings are compared with the experimental and analytical results in the literature and good agreements are achieved which validate the present model. Furthermore, based on several case studies on a reference wing, some attempts are performed to analyze the effect of thrust on the stability margin of the wing and some conclusions are outlined.     

基于螺旋桨滑流效应的大展弦比机翼气动弹性分析

以高空长航时大展弦比太阳能无人机机翼为研究对象,针对分布式电驱螺旋桨滑流和大展弦比机翼之间耦合的复杂气动干涉问题,采用滑移网格方法、动网格技术、SST k-ω RANS湍流模型和CFD/CSD （Computational Fluid Dynamics/Computational Structural Dynamics）双向流固耦合技术,研究了螺旋桨不同转速、布局方式和气动阻尼对机翼气动弹性响应的影响。数值计算结果表明,螺旋桨滑流会改变机翼表面的压力分布;螺旋桨流场对机翼的扰动频率接近机翼的结构固有频率时,机翼会发生共振;螺旋桨的位置越靠近翼尖,或螺旋桨的数量增多,都将增加机翼气动弹性响应的幅值。     

Linear instability in the wake of an elliptic wing

Linear global instability analysis has been performed in the wake of a low aspect ratio three-dimensional wing of elliptic cross section, constructed with appropriately scaled Eppler E387 airfoils. The flow field over the airfoil and in its wake has been computed by full three-dimensional direct numerical simulation at a chord Reynolds number of \(Re_{c}=1750\) and two angles of attack, \(\mathrm{{AoA}}=0^\circ \) and \(5^\circ \). Point-vortex methods have been employed to predict the inviscid counterpart of this flow. The spatial BiGlobal eigenvalue problem governing linear small-amplitude perturbations superposed upon the viscous three-dimensional wake has been solved at several axial locations, and results were used to initialize linear PSE-3D analyses without any simplifying assumptions regarding the form of the trailing vortex system, other than weak dependence of all flow quantities on the axial spatial direction. Two classes of linearly unstable perturbations were identified, namely stronger-amplified symmetric modes and weaker-amplified antisymmetric disturbances, both peaking at the vortex sheet which connects the trailing vortices. The amplitude functions of both classes of modes were documented, and their characteristics were compared with those delivered by local linear stability analysis in the wake near the symmetry plane and in the vicinity of the vortex core. While all linear instability analysis approaches employed have delivered qualitatively consistent predictions, only PSE-3D is free from assumptions regarding the underlying base flow and should thus be employed to obtain quantitative information on amplification rates and amplitude functions in this class of configurations.     

Plane instability problem for a composite reinforced with a periodic row of short parallel fibers

The instability of a composite material reinforced with a periodic row of parallel short fibers is studied considering the interaction of neighboring fibers. Emphasis is on the mutual influence of short fibers in the matrix during loss of stability, depending on the distance between them. A piecewise-homogeneous medium model and the three-dimensional linearized theory of stability of deformable bodies are used     

利用虚拟激励法结合CFD技术进行复合材料机翼的阵风响应分析

利用随机振动高效算法-虚拟激励法结合CFD技术,分析复合材料机翼模型的大气紊流响应。计算过程中的虚拟激励法和CFD方法均应用自主产权软件平台DDJ-W。虚拟激励法的使用显著提高了计算效率,同时CFD技术的引入可以准确地确定结构的气动参数。利用Dryden模型得到大气紊流频谱激励下机翼的功率谱响应和方差。计算过程表明,虚拟激励法结合CFD技术可以准确高效地进行复合材料机翼的阵风响应分析。     

Non-linear study of electrohydrodynamic Rayleigh-Taylor instability in a composite fluid-porous layer

The non-linear electrohydrodynamic RTI in presence of electric field bounded above by porous layer and below by a rigid surface, have been studied based on electrohydrodynamic approximations in the effect similar to the Stokes and lubrication approximations. The non-linear problem is studied numerically in the present paper using the Adams-Bashforth predictor and Adams-Moulton corrector numerical techniques. In the conclusion, the non-linear problem discussed here is quite different from that of Babchin et al. (1983) [10] considering the plane Couette flow. The present problem is greatly influenced by the slip velocity at the interface between porous layer and thin film. It is not amenable to analytical treatment as that of Babchin et al. [10]. Therefore, numerical solutions have to be found. Fourth-order accurate central differences are used for spatial discretization using predictor and corrector numerical technique.     

复合材料机翼加筋壁板稳定性分析

利用工程及有限元方法分别分析了加筋壁板整体和局部稳定性.分析发现:在有限元计算中模型边界条件的选取对分析结果有着较大的影响.通过大型有限元软件MSC.Patran/Nastran,计算了不同边界条件下加筋壁板稳定性,将结果与工程计算结果比较,得到一种有限元分析稳定性中较合适的模型及边界条件.同时运用论证的有限元模型及边界条件,分析了相同横截面积下,不同桁条设计方案的壁板整体稳定性,结果显示桁条横截面设计对加筋壁板的稳定性有着很大的影响.     

Stability,instability and interaction of solitary pulses in a composite medium

The questions of a dynamical stability and instability of soliton-like solutions (solitary pulses) of the Hamiltonian equations, describing planar waves in nonlinear elastic composites are considered, both in the presence as well as in the absence of the anisotropy. In the anisotropic case one has the slow and the fast two-parametric soliton families on the background of the quiescent state. In the absence of the anisotropy these two families coalesce into the unique three parametric family. It was shown recently that solitary pulses of the slow family in the anisotropic composite and pulses in the isotropic composite are stable when their speeds lie inside a certain range, the so-called range of stability. In the present paper, on the basis of numerical solving of the Cauchy problem for the basic governing equations, the classification is given of the types of instability of solitary pulses from the fast family for all range of speeds as well as in the case of the slow family and in the isotropic case, when the speeds of the pulses lie without the range of stability. The first type of instability is the blow-up instability for the slow anisotropic and isotropic pulses, living without the range of stability and also for high amplitude fast anisotropic pulses. The second type of instability is the instability resulting in energy exchange between the components of strain tensor for low amplitude fast anisotropic solitary pulses. The reasons of the both types of instability are discussed in detail.The interaction between the pairs of solitary pulses of different nature is investigated both analytically as well as numerically. It is found out that solitary pulses having the different polarization, i.e. different sign of amplitudes, can form bound states, oscillating about the common center, subjected to a motion with a constant speed, approximately equal to the average of speeds of two pulses when they are far apart.     

Aeroelastic behavior of a flag in ground effect

The aeroelastic behavior of a flexible plate subjected to a uniform axial flow is investigated in the presence of a rigid plane set parallel to the plate. It is shown that the ground effect reduces the flutter inflow velocity and strengthens the possibility of using the flag for extracting energy from winds and currents. The numerical analysis is carried out assuming that both the unsteady potential incompressible flow and the plate can be described with 2D models, i.e., a lumped vortex panel method and a nonlinear Euler–Bernoulli beam model, respectively, without losing the essential features of the fluid–structure interaction. Asymmetry of post-critical behavior (limit-cycle oscillations) and sensitivity of the results to the main flag parameters (distance from the ground, mass ratio and damping) are also considered, including also the energy distribution over the identified proper orthogonal modes. The investigated reduction of the flutter velocity in ground effect has been also confirmed with experimental tests relative to a polypropylene flag with and without the rigid panel mimicking the presence of the ground.     

Thermally induced dynamic instability of laminated composite conical shells

Thermally induced dynamic instability of laminated composite conical shells is investigated by means of a perturbation method. The laminated composite conical shells are subjected to static and periodic thermal loads. The linear instability approach is adopted in the present study. A set of initial membrane stresses due to the elevated temperature field is assumed to exist just before the instability occurs. The formulation begins with three-dimensional equations of motion in terms of incremental stresses perturbed from the state of neutral equilibrium. After proper nondimensionalization, asymptotic expansion and successive integration, we obtain recursive sets of differential equations at various levels. The method of multiple scales is used to eliminate the secular terms and make an asymptotic expansion feasible. Using the method of differential quadrature and Bolotin's method, and imposing the orthonormality and solvability conditions on the present asymptotic formulation, we determine the boundary frequencies of dynamic instability regions for various orders in a consistent and hierarchical manner. The principal instability regions of cross-ply conical shells with simply supported–simply supported boundary conditions are studied to demonstrate the performance of the present asymptotic theory.     

The effect of a centrally located midplane delamination on the instability of composite panels

The buckling loads of eight-ply graphite-epoxy cylindrical panels with midplane delamination were determined experimentally. The study included two different ply orientations, two different aspect ratios, two different delamination sizes, and one set of boundary conditions; clamped along the top and bottom edges and simply supported along the vertical sides. The experimental test results are compared to the linear bifurcation and nonlinear collapse loads of panels with square cutouts obtained from the STAGSC-1 finite-element computer code. Paper was presented at the 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14.     

Aeroelastic stability analysis considering a continuous flight envelope

This paper presents a new methodology to analyze aeroelastic stability in a continuous range of flight envelope with varying parameter of velocity and altitude. The focus of the paper is to demonstrate that linear matrix inequalities can be used to evaluate the aeroelastic stability in a region of flight envelope instead of a single point, like classical methods. The proposed methodology can also be used to study if a system remains stable during an arbitrary motion from one point to another in the flight envelope, i.e., when the problem becomes time-variant. The main idea is to represent the system as a polytopic differential inclusion system using rational function approximation to write the model in time domain. The theory is outlined and simulations are carried out on the benchmark AGARD 445.6 wing to demonstrate the method. The classical pk-method is used for comparing results and validating the approach. It is shown that this method is efficient to identify stability regions in the flight envelope.