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.     

High-frequency flutter of a rectangular plate

In our recent study of strip plate flutter, two flutter types, low-and high-frequency, were revealed. The first arises due to interaction of the oscillation modes and has been investigated in detail in numerous studies using an approximate piston theory. The high-frequency flutter, detected for the first time, is a consequence of the presence of negative aerodynamic damping and cannot be obtained using the piston theory. In the present study, the high-frequency flutter of a rectangular plate 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.     

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.     

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.     

自由正交异性矩形厚板的动态稳定

对在一条边上作用着均匀分布的非保守跟随力的四边自由正交异性矩形厚板的动态稳定进行了分析，通过把位移和剪力展成重傅立叶级数解，把微分方程简化成了代数方程。计算表明厚度的微小变化会引起颤振载荷明显的减小。这个明显减小是因为存在剪切变形。     

粘弹性夹芯层合旋转圆板的气动弹性动力稳定性分析

基于哈密尔顿原理,考虑作用于圆板上的空气动力载荷以及粘弹性复模量本构模型,本文建立了含有粘弹性夹芯层的旋转圆板的空气动力学模型,并给出了相应的稳定性的控制方程及边界条件。运用Galerkin方法,文中数值求解并给出了夹芯层合旋转圆板的动力学基本特征,以及结构几何参数、材料参数对于其前、后行波振动频率、阻尼和动力稳定性的影响。结果表明：通过优化合理选取粘弹性夹芯层合旋转圆板的几何参数和材料参数,可提高旋转圆板的临界转速和颤振速度,从而增强其稳定性。     

Numerical study of the dependence of the critical flutter speed and time of a plate on rheological parameters

The nonlinear flutter of some aircraft elements is modeled. A viscoelastic model is used. Numerical algorithms for solving integro-differential equations are developed. The critical flutter speed and time for a viscoelastic plate are determined __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 97–104, June 2008.     

非匀质地基上正交异性矩形厚板的动态稳定

本文把伽辽金法和富里哀级数相结合,用以分析非匀质地基上的自由边正交异性矩形厚板的动态稳定。在板的自由边上作用着均匀分布的非保守跟随力,力的方向受到控制,使其与加载边的转角成定比。分析基于理论,因此包括了剪切变形的影响。力是非保守的,会有颤振和发散两种形式的失稳,力是保守的,只会有发散形式的失稳。     

Flutter and resonances of a flag near a free surface

We investigate the effects of a nearby free surface on the stability of a flexible plate in axial flow. Confinement by rigid boundaries is known to affect flag flutter thresholds and fluttering dynamics significantly, and this work considers the effects of a more general confinement involving a deformable free surface. To this end, a local linear stability is proposed for a flag in axial uniform flow and parallel to a free surface, using one-dimensional beam and potential flow models to revisit this classical fluid–structure interaction problem. The physical behaviour of the confining free surface is characterized by the Froude number, corresponding to the ratio of the incoming flow velocity to that of the gravity waves. After presenting the simplified limit of infinite span (i.e. two-dimensional problem), the results are generalized to include finite-span and lateral confinement effects. In both cases, three unstable regimes are identified for varying Froude number. Rigidly-confined flutter is observed for low Froude number, i.e. when the free surface behaves as a rigid wall, and is equivalent to the classical problem of the confined flag. When the flow and wave velocities are comparable, a new instability is observed before the onset of flutter (i.e. at lower reduced flow speed) and results from the resonance of a structural bending wave and one of the fundamental modes of surface gravity waves. Finally, for large Froude number (low effect of gravity), flutter is observed with significant but passive deformation of the free surface in response of the flag’s displacement.     

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.     

A theoretical computational model of a plate in hypersonic flow

A theoretical model of an elastic panel in hypersonic flow is derived to be used for design and analysis. The nonlinear von Kármán plate equations are coupled with 1st order Piston Theory and linearized at the nonlinear steady-state deformation due to static pressure differential and thermal loads. Eigenvalue analysis is applied to determine the system’s stability, natural frequencies and mode shapes. Numerically time marching the equations provides transient response prediction which can be used to estimate limit cycle oscillation amplitude, frequency and time to onset. The model’s predictive capability is assessed by comparison to an experiment conducted at a free stream flow of Mach 6. Good agreement is shown between the theoretical and experimental natural frequencies and mode shapes of the fluid–structure system. Stability analysis is performed using linear and nonlinear methods to plot stability, flutter and buckling zones on a free stream static pressure vs temperature differential plane.     

Low speed flutter and limit cycle oscillations of a two-degree-of-freedom flat plate in a wind tunnel

This paper explores the dynamical response of a two-degree-of-freedom flat plate undergoing classical coupled-mode flutter in a wind tunnel. Tests are performed at low Reynolds number (Re~2.5×10⁴), using an aeroelastic set-up that enables high amplitude pitch–plunge motion. Starting from rest and increasing the flow velocity, an unstable behaviour is first observed at the merging of frequencies: after a transient growth period the system enters a low amplitude limit-cycle oscillation regime with slowly varying amplitude. For higher velocity the system transitions to higher-amplitude and stable limit cycle oscillations (LCO) with amplitude increasing with the flow velocity. Decreasing the velocity from this upper LCO branch the system remains in stable self-sustained oscillations down to 85% of the critical velocity. Starting from rest, the system can also move toward a stable LCO regime if a significant perturbation is imposed. Those results show that both the flutter boundary and post-critical behaviour are affected by nonlinear mechanisms. They also suggest that nonlinear aerodynamic effects play a significant role.     

二元机翼颤振的分叉点类别的判定

应用中心流形理论将二元机翼颤振这一四维系统降为二维系统，用后继函数判别法对分叉点的真假中心及稳定性问题进行了分析．     

Instability of an Unbounded Elastic Plate in a Gas Flow

The stability of an unbounded plane elastic plate in gas moving on one side of the plate and at rest on the other is analyzed. The gases are inviscid and in general different. The plate is under tension and has flexural stiffness. It is shown that the system is always unstable to plane sinusoidal perturbations with wave vector parallel to the velocity. As limiting cases, a tangential discontinuity between the two gases and unilateral flow past a plate with constant pressure on the opposite side are considered. In these cases, the conditions of stability to plane perturbations are non-trivial and are investigated below.     

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.      

Aeroelastic dynamics stability of rotating sandwich annular plate with viscoelastic core layer

A dynamic model for a rotating sandwich annular plate with a viscoelastic core layer is developed. All fundamental equations and boundary conditions are established based on Hamilton’s principle, and the rotation effect and viscoelastic properties of the sandwich structure are taken into account. The aerodynamics force acting on the plate is described by a rotating damping model, and the constitutive behavior of the viscoelastic core layer is formulated by the frequency-dependent complex modulus. The effects of geometrical and material parameters on frequencies and damping of forward and backward traveling waves and the dynamic stability for the rotating sandwich plate are numerically analyzed by means of Galerkin’s method. The results show that the critical and flutter speeds of the rotating plate can be increased at some certain parameters of the viscoelastic core layer.     

Flutter of a rectangular plate

We address theoretically the linear stability of a variable aspect ratio, rectangular plate in a uniform and incompressible axial flow. The flutter modes are assumed to be two-dimensional but the potential flow is calculated in three dimensions. For different values of aspect ratio, two boundary conditions are studied: a clamped-free plate and a pinned-free plate. We assume that the fluid viscosity and the plate viscoelastic damping are negligible. In this limit, the flutter instability arises from a competition between the destabilising fluid pressure and the stabilising flexural rigidity of the plate. Using a Galerkin method and Fourier transforms, we are able to predict the flutter modes, their frequencies and growth rates. The critical flow velocity is calculated as a function of the mass ratio and the aspect ratio of the plate. A new result is demonstrated: a plate of finite span is more stable than a plate of infinite span.     

联接刚度对机翼／外挂系统颤振边界特性的影响

本文对带外挂物二元机翼的颤振特性进行了理论和实验研究,主要分析机翼与外挂物之间俯仰联接刚度对颤振边界的影响。在大量算例的分析基础上,给出了颤振频率及颤振边界变化的一般规律及对颤振边界类型的一般判别方法,颤振模型的风洞实验验证了理论分析结果的正确性。