Nonlinear high-frequency flutter of a plate

In recent studies of the problem of linear stability of a plate in a supersonic gas flow a new (“high-frequency”) type of flutter, which cannot be obtained by means of the piston theory usually employed in these problems, was found to exist together with the classical (“low-frequency”) type. In the present study a new method of calculating the pressure acting on a high-frequency vibrating plate is proposed and, using this method, high-frequency flutter is investigated in the nonlinear formulation and the flutter vibration amplitudes are determined.     

High-frequency plate flutter

Earlier, using the global instability method, the stability of a strip plate in a supersonic gas flow was investigated. In addition to the classical (low-frequency) flutter developing upon the interaction between the plate oscillation modes, a novel (high-frequency) flutter type in which the oscillations are unimodal was detected. In the present study, the effect on the high-frequency flutter of the plate width (earlier only an asymptotic analysis for a width tending to infinity was performed), its damping characteristics, and the presence of a gas at rest on the side opposite the flow is investigated.     

Numerical investigation of supersonic plate flutter using the exact aerodynamic theory

In classical investigations of panel flutter it is usually assumed that the gas pressure acting on the plate can be calculated within the framework of the piston theory, an approximation exact for high Mach numbers. The loss of stability revealed in these investigations is of the “coupled” type, involving the interaction of two oscillation modes. Recently, the use of asymptotic methods revealed another single-mode type of stability loss, which cannot be obtained within the framework of the piston theory. In the present study this type of stability loss is investigated numerically using the Bubnov-Galerkin method.     

Panel flutter prediction in two dimensional flow with enhanced piston theory

Piston theory may be used in the high Mach number supersonic flow region and/or in very high frequency subsonic or supersonic flow. In this flow model, the pressure at a point on the fluid-solid interface only depends on the downwash at the same point. However the classical piston theory may not be sufficient for some phenomena in aeroelasticity and aeroacoustics (far field prediction). Dowell and Bliss have created an extension of piston theory that allows for higher order effects that take into account the effect the distribution of downwash on pressure at any point. For simple harmonic motion, expansions in reduced frequency, inverse reduced frequency and/or inverse (square of) Mach number have all been created; The effects of higher order terms in these several expansion in creating an enhanced piston theory was illustrated for plunge and pitch motion of an airfoil (discrete system) by Ganji and Dowell. In the present paper, flutter prediction for a flexible panel in two –dimensional flow is investigated using enhanced piston theory. The goal of the present paper is to demonstrate that an enhance version of piston theory can analyze single degree of freedom flutter of a panel as compared to the classical piston theory and quasi-steady aerodynamic models which can only treat coupled mode flutter.     

采用压电材料提高超声速飞行器壁板结构的颤振特性

采用压电材料对结构进行振动主动控制已经进行了广泛研究,论文进一步采用压电材料改进超声速壁板结构的气动弹性颤振特性,研究中考虑压电材料力电耦合效应的影响.采用Hamilton原理和Rayleigh-Ritz方法建立壁板及压电材料整体结构的运动方程,采用超声速活塞理论模拟气动力,利用加速度反馈控制策略对压电材料施加外电压,获得结构的主动质量.求解运动方程的特征值问题获得固有频率,进而确定气动弹性颤振边界,分析了反馈控制增益对超声速飞行器壁板结构主动颤振特性的影响,研究表明,采用压电材料可以提高超声速壁板结构的气动弹性颤振特性.     

Flutter of a Wide Strip Plate in a Supersonic Gas Flow

The stability of an elastic plate in the form of a wide strip in a supersonic inviscid gas flow is investigated in the linear approximation. An expression for the dependence of the pressure on the plate deflection, asymptotically exact for wide plates, is used. Two qualitatively different instability types are obtained: flutter with respect to a single oscillatory mode due to negative aerodynamic damping and flutter of a related type due to the interaction of oscillatory modes. For each type the stability criterion and the frequency at which the oscillation amplitude grows most intensely are found.     

Vibration characteristics and flutter analysis of a composite laminated plate with a store

The effects of an external store on the flutter characteristics of a composite laminated plate in a supersonic flow are investigated. The Dirac function is used to formulate the interaction between the plate and the store. The first-order piston theory is used to describe the aerodynamic load. The governing equation of the composite laminated plate with an external store is established based on the Hamilton principle. The mode shapes are constructed by the admissible functions which are a set of characteristic orthogonal polynomials generated directly by the Gram-Schmidt process, and the boundary constraint is modeled as the artificial springs. The frequency and mode shapes of the plate under different boundaries are determined by the Rayleigh-Ritz method. The validity of the proposed approach is confirmed by comparing the results with those obtained from the finite element method (FEM). The effects of the mounting position, the center of gravity position and the mounting points spacing of the external store on the flutter boundary are discussed for both the simply supported and cantilever plates, respectively, which correspond to the two installation sites of the external store, i.e., the belly and wings of the aircraft.     

On the formulation of the problem of strip oscillations and stability in supersonic gas flow

The formulation of the strip flutter problem based on a refined expression for the excess pressure is proposed. Two cases are considered: almost transverse and almost longitudinal flow past the strip. In the first case, an exact expression for the excess pressure, fundamentally different from the formulas of piston theory, which leads to novel, little studied eigenvalue problems is obtained. In the second case, an exact expression is obtained for the flow potential and, for purely longitudinal flow, for the excess pressure also. It is shown that for purely longitudinal flow at high supersonic velocities the critical flutter velocity is equal to the phase velocity of perturbation propagation along the strip, which coincides with the results of piston theory.     

高速小展弦比机翼颤振的微分求积法分析

引入微分求积法,分析高速小展弦比机翼的气动弹性问题。将小展弦比机翼等效为悬臂板,基于一阶活塞气动力理论建立机翼颤振偏微分方程,采用微分求积法将偏微分方程转化为常微分方程,根据频率重合理论对颤振问题进行求解。分析了机翼的固有频率及颤振速度,并与有限元软件计算结果进行比较,误差在2％以内,很好的验证了微分求积法求解小展弦比机翼颤振问题的有效性。分析了机翼面积、展弦比及厚度对颤振速度的影响,结果表明,小展弦比机翼的颤振速度受结构尺寸的影响较大,颤振速度随面积和展弦比的增大而减小,随机翼厚度的增大而增大。     

Experimental observation of single mode panel flutter in supersonic gas flow

Single mode flutter is a type of panel flutter, which cannot be analyzed theoretically using conventional piston theory, and for this reason it is studied very little. No previous experiments, where this type of panel flutter was clearly detected, were conducted. In this paper a plate, designed such that it cannot experience “classical” coupled-mode type flutter, but can experience single mode flutter, is tested. Analysis of the tested data clearly indicates the occurrence of single mode panel flutter.     

结合CFD和当地流活塞理论的全机组合体超声速颤振分析

针对翼．身组合体飞行器面对称布局的特点,利用模态振型的对称和反对称性,以分枝模态法建立结构的运动微分方程,结合CFD的当地流活塞理论计算飞行器的非定常气动力,建立飞行器全机组合体的气动弹性数学模型。对飞行器进行了来流为1．5～7马赫数下的颤振分析,结果与全CFD／CSD耦合时域仿真结果较好吻合,验证了本文方法在工程设计中的有效性和可行性。本文方法的效率在相同精度下比CFD／CSD耦合的时域方法高100倍。     

高超声速舵面颤振的数值模拟影响因素研究

针对某高超声速舵面颤振风洞试验模型开展了数值模拟研究,采用多种气动力模型和耦合迭代策略,研究对颤振预测结果的影响。计算结果表明,采用三阶活塞理论、统一升力面理论、Euler方程和N-S方程的颤振动压预测结果较接近,与试验值误差均在7%以内。采用时域方法计算时,松耦合方法的误差较大,超过15%。同时还发现,支撑机构会带来激波边界层干扰效应,一定程度上提高了颤振动压,考虑该因素的预测结果与试验值更接近。     

On bimodal flutter behavior of a flexible airfoil

The dynamic aeroelastic behavior of an elastically supported airfoil is studied in order to investigate the possibilities of increasing critical flutter speed by exploiting its chord-wise flexibility. The flexible airfoil concept is implemented using a rigid airfoil-shaped leading edge, and a flexible thin laminated composite plate conformally attached to its trailing edge. The flutter behavior is studied in terms of the number of laminate plies used in the composite plate for a given aeroelastic system configuration. The flutter behavior is predicted by using an eigenfunction expansion approach which is also used to design a laminated plate in order to attain superior flutter characteristics. Such an airfoil is characterized by two types of flutter responses, the classical airfoil flutter and the plate flutter. Analysis shows that a significant increase in the critical flutter speed can be achieved with high plunge and low pitch stiffness in the region where the aeroelastic system exhibits a bimodal flutter behavior, e.g., where the airfoil flutter and the plate flutter occur simultaneously. The predicted flutter behavior of a flexible airfoil is experimentally verified by conducting a series of systematic aeroelastic system configurations wind tunnel flutter campaigns. The experimental investigations provide, for each type of flutter, a measured flutter response, including the one with indicated bimodal behavior.     

Numerical Investigation of the Flutter of a Rectangular Plate

The flutter of a rectangular plate with an arbitrary direction of the velocity vector relative to the plate side is studied. A numerical no-saturation algorithm is constructed to solve the eigenvalue problem. Calculation results for the critical flutter velocity and corresponding eigenmodes are given.     

激波主导流动下壁板的热气动弹性稳定性理论分析

针对激波主导流动下弹性壁板的热气动弹性稳定性分析问题,建立了基于当地活塞流理论的分析模型,并用数值仿真方法来验证其正确性. 首先基于Hamilton原理和Von-Karman大变形理论,建立壁板的热气动弹性运动方程,其中假设壁板受热后温度均匀分布,激波前后区域的气动力模型采用当地一阶活塞流理论;利用Galerkin方法将具有连续参数系统的偏微分颤振方程离散为有限个自由度的常微分方程;基于李雅普诺夫间接法将非线性颤振方程组在平衡位置处进行线化,再用Routh-Hurwits判据来判断线性系统的稳定性,从而来推论出非线性颤振系统的气动弹性稳定性. 在时域中采用龙格--库塔法对非线性颤振方程进行数值积分,得到壁板非线性颤振响应的时间历程,与理论分析结果进行对比. 研究结果表明,壁板受到斜激波冲击时,更容易发生颤振失稳,并且激波强度越大,极限环幅值和频率越大;激波主导流场中的壁板失稳边界不同于传统单纯超声速气流中壁板颤振的失稳边界;只有在斜激波前后不同的动压值都满足颤振稳定性边界的条件下,壁板才可能保持其气动弹性稳定性.      

基于当地流活塞理论的气动弹性计算方法研究

发展了一种高效、高精度的超音速、高超音速非定常气动力计算 方法------基于定常CFD技术的当地流活塞理论. 运用当地流活塞理论计算非定常 气动力，耦合结构运动方程，实现超音速、高超音速气动弹性的时域模拟. 运用这 种方法计算了一系列非定常气动力算例和颤振算例，并和原始活塞理论、非定 常Euler方程结果作了比较. 由于局部地使用活塞理论假设，这种方法大大地克服 了原始活塞理论对飞行马赫数、翼型厚度和飞行迎角的 限制. 与非定常Euler方程方法相比，当地流活塞理论的效率很高.     

热过屈曲功能梯度壁板的气动弹性颤振

功能梯度材料的宏观物理性能随空间位置连续变化,能充分减少不同组份材料结合部位界面性能的不匹配因素.功能梯度壁板用作高速飞行器的热防护结构,能有效消除气动加热带来的壁板内部热应力集中.本文考虑热过屈曲变形引入的结构几何非线性,分析功能梯度壁板的气动弹性颤振边界.基于幂函数材料分布假设,采用混合定律计算功能梯度材料的等效力学性能.根据一阶剪切变形板理论、冯·卡门应变-位移关系和一阶活塞理论,基于虚功原理建立超声速气流中受热功能梯度壁板的非线性气动弹性有限元方程.采用牛顿-拉弗森迭代法数值求解壁板的热屈曲变形,分析超声速气流对热屈曲变形的影响机理.在壁板热过屈曲的静力平衡位置分析动态稳定性,确定了壁板的颤振边界.研究表明,当陶瓷-金属功能梯度壁板的组份材料沿厚度方向梯度分布时,会破坏结构的对称性导致壁板在面内热应力作用下发生指向金属侧的热屈曲变形.超声速气流中壁板热屈曲变形最大的位置随气流速压增大向下游推移,并伴随屈曲变形量的减小.热过屈曲壁板的几何非线性效应会提高壁板的颤振边界,这种影响在高温、低无量纲速压且壁板发生大挠度热屈曲变形时表现显著.较高无量纲气流速压下由于壁板的热屈曲变形被气动力限定在小挠度范围,几何非线性效应不明显.      

宽带噪声作用下黏弹性板的矩Lyapunov指数

主要研究了在超音速流中受宽带噪声作用的黏弹性板随机振动系统的矩Lyapunov指数.首先, 采用vonKarman板弯理论, 活塞理论以及Galerkin近似法建立了两个自由度耦合的系统运动的随机微分方程. 其次, 应用随机平均法将四维系统降为二维系统. 接着, 对系统采用极坐标变换,通过Girsanov定理和Feynmann-Kac公式得到后向微分算子. 通过对特征函数进行正交Fourier余弦级数展开得到系统矩Lyapunov指数的近似解析式. 并通过MonteCarle仿真得到系统矩Lyapunov指数的数值解验证了近似解析式的可信性. 最后研究了系统参数、气动力参数以及随机噪声谱密度对黏弹性板稳定性的影响.      

Parametric study on supersonic flutter of angle-ply laminated plates using shear deformable finite element method

The influence of fiber orientation,flow yaw angle and length-to-thickness ratio on flutter characteristics of angle-ply laminated plates in supersonic flow is studied by finite element approach.The structural model is established using the Reissner-Mindlin theory in which the transverse shear deformation is considered.The aerodynamic pressure is evaluated by the quasi-steady first-order piston theory.The equations of motion are formulated based on the principle of virtual work.With the harmonic motion assumption,the flutter boundary is determined by solving a series of complex eigenvalue problems.Numerical study shows that (1) The flutter dynamic pressure and the coalescence of flutter modes depend on fiber orientation,flow yaw angle and length-to-thickness ratio;(2) The laminated plate with all fibers aligned with the flow direction gives the highest flutter dynamic pressure,but a slight yawing of the flow from the fiber orientation results in a sharp decrease of the flutter dynamic pressure;(3) The angle-ply laminated plate with fiber orientation angle equal to flow yaw angle gives high flutter dynamic pressure,but not the maximum flutter dynamic pressure;(4) With the decrease of length-to-thickness ratio,an adverse effect due to mode transition on the flutter dynamic pressure is found.     

A finite element study on the large amplitude flexural vibration characteristics of FGM plates under aerodynamic load

The large amplitude flexural vibration characteristics of functionally graded material (FGM) plates are investigated here using a shear flexible finite element approach. Material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of the constituents. The effective material properties are then evaluated based on the rule of mixture. The FGM plate is modeled using the first-order shear deformation theory based on exact neutral surface position and von Kármán’s assumptions for large displacement. The third-order piston theory is employed to evaluate the aerodynamic pressure. The governing equations of motion are solved by harmonic balance method to study the vibration amplitude of FGM plates under supersonic air flow. Thereafter, the non-linear equations of motion are solved using Newmark’s time integration technique to understand the flexural vibration behavior of FGM plates in time domain (simple harmonic or periodic or quasi-periodic). This work is new in the sense that it deals with the non-linear flutter characteristics of FGM plates under high supersonic airflow accounting for both the geometric and aerodynamic non-linearities. Some parametric study is conducted to understand the influence of these non-linearities on the flutter characteristics of FGM plates.