Nonlinear aeroelastic analysis of a two-dimensional wing with control surface in supersonic flow

Based on the piston theory of supersonic flow and the energy method, a two dimensional wing with a control surface in supersonic flow is theoretically modeled, in which the cubic stiffness in the torsional direction of the control surface is considered. An approximate method of the cha- otic response analysis of the nonlinear aeroelastic system is studied, the main idea of which is that under the condi- tion of stable limit cycle flutter of the aeroelastic system, the vibrations in the plunging and pitching of the wing can approximately be considered to be simple harmonic excita- tion to the control surface. The motion of the control surface can approximately be modeled by a nonlinear oscillation of one-degree-of-freedom. The range of the chaotic response of the aeroelastic system is approximately determined by means of the chaotic response of the nonlinear oscillator. The rich dynamic behaviors of the control surface are represented as bifurcation diagrams, phase-plane portraits and PS diagrams. The theoretical analysis is verified by the numerical results.

Aerothermal-aeroelastic two-way coupling method for hypersonic curved panel flutter

A method to compute aerothermal-aeroelastic two-way coupling for hypersonic curved panel flutter is proposed. The aero-therrno-elastic governing equations of a simply-supported two dimensional curved panel are developed based on the von K＇arrn＇an geometrically non-linear theory. The Galerkin approach is used to simplify the equations into discrete forms, which are solved by the fourth-order Ronger-Kutta method. The third-order piston theory is applied to the aerodynamics. The Eck- ert＇s reference temperature method and the panel heat flux formula are used to compute the aerodynamic heat flux. Several important effects are included, namely 1） two-way coupling considering the effect of elastic deformation on aerodynamic heating and aerodynamic heating on stiffness of structure, 2） accumulation of the aerodynamic heating in real cruise, 3） arbitrary, non-uniform, in-plane and through-thickness temperature distributions, and 4） the effect of initial deformation of curved panel on the flight time to the onset of flutter. Compared with the results of aerothermal-aeroelastic one-way coupling, it is revealed that the two-way coupling which induces decrease of the flight time to the onset of flutter is more dangerous. In addition, importance should be attached to this method in actual analysis.

Aeroelastic stability analysis of heated flexible panel subjected to an oblique shock

The critical conditions for aeroelastic stability and the stability boundaries of a flexible two-dimensional heated panel subjected to an impinging oblique shock are considered using theoretical analysis and numerical computations, respectively. The von-Karman large deflection theory of isotropic flat plates is used to account for the geometrical nonlinearity of the heated panel, and local first-order piston theory is employed in the region before and after shock waves to estimate the aerodynamic pressure. The coupled partial differential governing equations, according to the Hamilton principle, are established with thermal effect based on quasi-steady thermal stress theory.The Galerkin discrete method is employed to truncate the partial differential equations into a set of ordinary differential equations, which are then solved by the fourth-order Runge-Kutta numerical integration method. Lyapunov indirect method is applied to evaluate the stability of the heated panel. The results show that a new aeroelastic instability（distinct from regular panel flutter） arises from the complex interaction of the incident and reflected wave system with the panel flexural modes and thermal loads. What＇s more, stability of the panel is reduced in the presence of the oblique shock. In other words, the heated panel becomes aeroelastically unstable at relatively small flight aerodynamic pressure.

Shape sensitivity analysis of flutter characteristics of a low aspect ratio supersonic wing using analytical method

Shape sensitivities of flutter characteristics can predict the moving of flutter boundary as wing shape varies. The nonlinear relationship between mass, stiffness and damping matrices of aeroelastic systems and shape variables makes the flutter characteristics vary nonlinearly as shape variables change. The computation cost of finite difference method is high and it cannot solve precisely shape sensitivities. An analytic method is developed to compute sensitivities of flutter characteristics of low aspect ratio wings to shape parameters, which include aspect ratio, taper ratio, sweep angle, and area. On the basis of the equivalent plate model and piston theory, analytic sensitivities of mass, stiffness and damping matrices with respect to various shape parameters are computed. The equivalent plate model is a continuous aeroelasticity analysis model oriented toward wing design. The flutter equation is solved by tracking the root locus of the system state space model. Lancaster's adjoint method is used to solve the eigenvalue derivatives and shape sensitivities of flutter characteristics. Linear Taylor approximation based on the analytic sensitivities is used to predict the variation of flutter speed with respect to shape variables. Comparison of these results with those from reanalysis indicates that Taylor approximation based on analytic sensitivities can precisely predict trends of flutter characteristics near the baseline configuration, but the applied neighborhood is small for sweep and area. The method can help designers make a judicious choice of wing shape parameters for preventing flutter in the preliminary design phase of aircraft.

A high-efficiency aerothermoelastic analysis method

In this paper,a high-efficiency aerothermoelastic analysis method based on unified hypersonic lifting surface theory is established.The method adopts a two-way coupling form that couples the structure,aerodynamic force,and aerodynamic thermo and heat conduction.The aerodynamic force is first calculated based on unified hypersonic lifting surface theory,and then the Eckert reference temperature method is used to solve the temperature field,where the transient heat conduction is solved using Fourier’s law,and the modal method is used for the aeroelastic correction.Finally,flutter is analyzed based on the p-k method.The aerothermoelastic behavior of a typical hypersonic low-aspect ratio wing is then analyzed,and the results indicate the following:(1)the combined effects of the aerodynamic load and thermal load both deform the wing,which would increase if the flexibility,size,and flight time of the hypersonic aircraft increase;(2)the effect of heat accumulation should be noted,and therefore,the trajectory parameters should be considered in the design of hypersonic flight vehicles to avoid hazardous conditions,such as flutter.