Research On Aeroelastic Stability Of Aircraft Panel In Supersonic Flow

Panels are very important structure units on an aircraft.Panel flutter is a phenomenon of self-exciting vibrations at high speeds,resulting from the interaction between the elastic force,aerodynamic load of aircraft surface skin and inertia force in the supersonic flow.Nonlinear panel flutter usually interprets as a limit cycle oscillation(LCO).Such structural instability may leads to fatigue damage,but maybe catastrophic structural failure sometimes.The curvature of aircraft panel always exists in the engineering practice of supersonic aircraft structure design.The aerodynamic heating effect of supersonic airflow is more significant in large Mach number flight.Therefore,researches on aeroelastic stability of aircraft panel is helpful for deeply understanding the mechanism of panel flutter,and finding the behavior law of relevant design parameters effect on the flutter boundary.Furthermore,some research results will provide basic data for estimating the fatigue life of aircraft panel.This work has both the academic significance and engineering background.In this thesis,thermal aeroelastic differential equations of aircraft panels in supersonic airflow are achieved on basis of von Kármán nonlinear strain-displacement relation and aerodynamic piston theory.Further study of aeroelastic stability of aircraft panel is carried out by means of Galerkin method.Flutter boundary characteristics of thermal aeroelastic system,as well as effects of different parameter combinations on critical dynamic pressure and stability,are analysed.The main research work and achievements in this thesis are as follows:(1)Panel motion in supersonic airflow is governed by a partial differential equation.This partial differential equation is transformed to a nonlinear ordinary equation by means of Galerkin method.Hurwitz determinant is obtained on basis of the coefficients of the characteristic equation,which belong to the Jacobi matrix at the equilibrium point of the nonlinear system.Then,with the aid of Hopf bifurcation algebraic criteria,the problem of finding bifurcation point of the nonlinear system is transformed to one solution the roots of a real coefficient algebraic equation.The relationship,between pure imaginary zeros of a real coefficient algebraic equation and each order Hurwitz determinant,is proved also.Furthermore,the analytical solutions of critical conditions of Hopf bifurcations and pitchfork bifurcations are obtained.And the number and the stabilities of the equilibrium points in the different regions of parameter plane are analyzed.Numerical simulations are carried out by using the Runge-Kutta method and eigenvalue theory.Then the nonlinear effect of aerodynamic piston theory on flutter characteristics of flat panel is studied.(2)The curvature of aircraft skin panel always exists.The nonlinear aeroelastic partial differential equation for two-dimensional heated curved panels is established on basis of von Kármán strain-displacement relationship and curvature modified piston theory.Hopf bifurcations of two-dimensional heated curved panels in supersonic airflow is investigated with the aid of Hopf bifurcation algebraic criteria.So analytical expressions of critical dynamic pressure and flutter frequency are proposed.The effect of initial curvature and temperature changing on critical dynamic pressure is evaluated.(3)There exists two static load terms,which relate to the initial curvature but time,in the nonlinear aeroelastic equation of curved panels in supersonic airflow.The static load results in the static aeroelastic deformation of the panel.Distribution law of static load along aerodynamic chord is analysed.Solving the steady state equations of aeroelastic deformation by means of Newton iteration method,the properties of static aeroelastic deformation are obtained.Then the effect of static aerodynamic load on static aeroelastic deformation is studied.So do static thermal load and both.Furthermore,the number and the stabilities of the equilibrium points,which belong to the nonlinear algebraic equation set,in the different regions of parameter plane are analyzed.The analytical solutions of critical conditions of Hopf bifurcations and static bifurcations are obtained.(4)Note that material parameters change in real time as the temperature rises.Young's modulus decreases with the increase of temperature and thermal expansion coefficient increases with the increase of temperature.It is assumed that both the Young's modulus and thermal expansion coefficient are linear functions of temperature increasing.The nonlinear aeroelastic partial differential equation in supersonic airflow is established,with Young's modulus and thermal expansion coefficient changing.The analytical solutions of critical conditions of Hopf bifurcations and static bifurcations are obtained.And the number and the stabilities of the equilibrium points in the different regions of parameter plane are analyzed.In order to compare with critical flutter pressure in steady tempreture field,one of the elastic modulus and thermal expansion coefficient can be set as a constant,which are chosen as matched groups.Secondly,note that panel elastic deformation affects aerodynamic heating.These local airflow properties are computed using oblique shock relations and third-order position theory.Aerodynamic heating is computed using Eckert's reference enthalpy method.The transient temperature distribution is computed using finite difference solution.Therefore,aerothermal aeroelastic coupling method and frame for supersonic panel flutter is obtained.Wind tunnel test is an important means to test the aeroelastic stability.Shock waves are compressed in different denonation modes to produce high temperature and high-pressure flow.A method of ignition and initiation is proposed on basis of delay double-head initiation mode.The mutual interference and influence of blast wave formed by detonation products can be reduced.