Flutter of an elastic strip in a longitudinal supersonic flow

An elastic strip in a longitudinal supersonic gas flow is considered. An excess pressure formula is obtained on the basis of the linearized theory of supersonic potential flow. It is shown that, in the case of high-speed supersonic flow, the critical flutter velocity is equal to the phase velocity of perturbation waves propagated along the strip. In the framework of the classical piston theory, the flutter problem is solved for the case of a rigidly fixed strip in a longitudinal flow.     

To a formulation of the flutter problem for a conical shell with a small apex angle

The well-known piston theory formula for the excess aerodynamic pressure is used in the majority of works devoted to the panel flutter of shells. In this paper a refined expression for the excess pressure is proposed to take into account the irregularity of undisturbed flow parameters. The case of moderate supersonic velocities is studied in detail. The critical velocity problem is reduced to a new eigenproblem in the panel flutter theory.     

Thermoelastic stability of closed cylindrical shell in supersonic gas flow

In this paper the problem of linear stability of a closed cylindrical shell under the action of both non-uniform temperature field and supersonic gas flow is considered. The stability conditions for the unperturbed state of the aerothermoelastic system are obtained. It is shown that, by the combined action of the temperature field and the ambient supersonic flow, the process of linear stability can be controlled and the temperature field affects significantly the critical flutter speed.     

DEVELOPMENT OF A THREE-DIMENSIONAL VISCOUS AEROELASTIC SOLVER FOR NONLINEAR PANEL FLUTTER

A new three-dimensional (3-D) viscous aeroelastic solver for nonlinear panel flutter is developed in this paper. A well-validated full Navier–Stokes code is coupled with a finite-difference procedure for the von Karman plate equations. A subiteration strategy is employed to eliminate lagging errors between the fluid and structural solvers. This approach eliminates the need for the development of a specialized, tightly coupled algorithm for the fluid/structure interaction problem. The new computational scheme is applied to the solution of inviscid two-dimensional panel flutter problems for subsonic and supersonic Mach numbers. Supersonic results are shown to be consistent with the work of previous researchers. Multiple solutions at subsonic Mach numbers are discussed. Viscous effects are shown to raise the flutter dynamic pressure for the supersonic case. For the subsonic viscous case, a different type of flutter behavior occurs for the downward deflected solution with oscillations occurring about a mean deflected position of the panel. This flutter phenomenon results from a true fluid/structure interaction between the flexible panel and the viscous flow above the surface. Initial computations have also been performed for inviscid, 3-D panel flutter for both supersonic and subsonic Mach numbers.     

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.     

Implications of cubic physical/aerodynamic non-linearities on the character of the flutter instability boundary

The present paper deals with a study of the benign and catastrophic characters of the flutter instability boundary of 2-D lifting surfaces in a supersonic flow field. The objectives of this work are: (i) to contribute to a better understanding of the implications of aerodynamic and physical non-linearities on the character of the flutter boundary and (ii), to outline the effects exerted in the same respect by some important parameters of the aeroelastic system. With the aim of addressing this problem, the method based on the First Liapunov Quantity is used to study the bifurcational behavior of the aeroelastic system in the vicinity of the flutter boundary. The expected outcomes of this study are: (a) to greatly enhance the scope and reliability of the aeroelastic analysis and design criteria of advanced aircraft and, (b) to provide a theoretical basis for the analysis of more complex non-linear aeroelastic systems.     

Flutter of a viscoelastic plate in a supersonic gas flow

The flutter of a viscoelastic plate in a supersonic gas flow is studied. A technique and algorithm for numerical solution of nonlinear integro-differential equations with weakly singular kernels are elaborated. The critical flutter speed of viscoelastic plates is determined     

Flutter of a cylindrical shell subjected to an internal supersonic gas flow

The piston theory formula for the excess aerodynamic pressure is used in the majority of works devoted to the flutter of shells. The problem on the flutter of a cylindrical shell subjected to an internal supersonic gas flow is solved in a new formulation     

热环境下壁板非线性颤振分析

基于一阶活塞气动力理论,采用Von Karman大变形应变-位移关系建立了无限展长壁板热环境下颤振方程,采用伽辽金方法对方程进行离散处理.取温度为分叉参数,研究壁板颤振时的分叉及混沌等复杂动力学特性.结果表明:温度载荷降低了系统的颤振临界动压,改变了颤振特性.在整个分岔参数范围内,系统呈现出较为复杂的变化,包括衰减振动、极限环振动、拟周期振动和混沌型振动.当考虑材料热效应时,系统的颤振动压将进一步降低,其响应也表现出更为丰富的非线性动态力学行为.     

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.     

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.      

AEROELASTIC PROPERTIES OF SANDWICH BEAM WITH PYRAMIDAL LATTICE CORE CONSIDERING GEOMETRIC NONLINEARITY IN THE SUPERSONIC AIRFLOW

The equation of motion of sandwich beam with pyramidal lattice core in the supersonic flow considering geometric nonlinearity is formulated using Hamilton's principle. The piston theory is used to evaluate aerodynamic pressure. The structural aeroelastic properties are analyzed using frequency- and time-domain methods, and some interesting phenomena are observed. It is noted that the flutter of sandwich beam occurs under the coupling effect of low order modes. The critical flutter aerodynamic pressure of the sandwich beam is higher than that of the isotropic beam with the same weight, length and width. The influence of inclination angle of core truss on flutter characteristic is analyzed.     

Optimization of the Flutter Load by Material Orientation

Abstract

The present work concerns optimization of the stability of composite plates for supersonic flutter. A Finite element model of the structure is applied. The individual material orientation within each finite element defines the degrees of freedom in the design space. Design iterations are based on analytical sensitivity analyses, derived by Pedersen and Seyranian. Plaut's flutter instability condition is discussed. The condition implies the possibility of an accurate flutter analysis without reducing the eigenvalue problem. For one particular choice of material, an optimal design, in the case of a rectangular, simply supported plate, is found. Design iterations on a delta-shaped plate supported as a cantilever are discussed. A condition for when static divergence is not a possible consequence of the aerodynamic load for any design is derived.     

基于拓扑优化技术的导弹折叠舵结构颤振优化设计

在高超声速飞行的过程中,导弹舵面会出现颤振问题,可在短短几秒内导致结构破坏甚至解体. 为了改善舵面颤振特性,并让设计过程更加科学和高效,结合拓扑优化技术,开发了相应的优化程序应用于导弹折叠舵结构颤振抑制设计,获得比原始设计方案拥有更大颤振临界速度的折叠舵结构. 结果表明该方法具有如下优点：相比传统的配重等方法,从拓扑优化的新思路高效、准确地获得新构型;将拓扑优化的前沿技术创造性地应用到改善导弹折叠舵颤振特性的实际工程问题上,并在设计后进行强度校核;将颤振这种复杂的流固耦合问题从结构动力学问题逐步简化为静力学模型,进而用拓扑优化方法高效解决.     

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.     

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.     

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.     

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.     

Ultrasonic jet in an external acoustic field

The interaction of supersonic jets with external acoustic waves is investigated in connection with the emission of sound of discrete frequency by the jets. A plausible physical scheme explaining the appearance and maintenance of the oscillations of supersonic jets with discrete frequency was proposed in [1]. A model problem of the effect of pressure perturbations of a given frequency, traveling along the surface of a two-dimensional jet is also investigated there. The results of the solution of this problem (in particular, the presence of critical frequencies at which the perturbations in the jet grow indefinitely in the direction of motion of the flow) substantiate the hypothesis that by virtue of its periodic (cellular) structure a supersonic jet has the properties of a resonator. In [1] the more general problem of interaction of a supersonic jet with an external acoustic field is also formulated, which is in complete correspondence with the physical scheme of the phenomena developed in that article. In the present work this problem is solved in its complete form for plane and cylindrical jets for symmetric and antisymmetric perturbations in an external acoustic field, and also in the presence of subsonic accompanying flow in the outer medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 105–113, March–April 1974.     

复合材料层合板的颤振特性及振动抑制研究

研究了超声速流中压电复合材料层合板的颤振特性及振动抑制方法。采用一阶活塞理论计算了超声速流场中的气动压力,基于经典层合板理论和Hamilton原理推导了压电复合材料层合板的动力学模型,设计了滑模观测器以减少观测溢出,通过Lyapunov方法证明观测器的稳定性,应用观测状态设计了LQR控制器,讨论了几何参数、铺设角度对压电复合材料层合板颤振特性的影响,利用SIMULINK仿真求解了层合板的脉冲响应,验证了控制器的有效性。结果表明,合理规划层合板的几何参数和铺设角度可提高系统颤振稳定性,滑模观测器能够较为准确地追踪原始系统且具有良好的鲁棒性,LQR控制可以在一定范围内消除层合板的颤振点,并且能够有效地控制压电复合材料层合板在颤振边界处的振动,Q矩阵越大,振动控制效果越好,压电层厚度越大,LQR控制效果越好。