Random Response Analysis Of Rolling Motion Of A Delta Wing With Gaussian White Noise And Poisson White Noise

In the actual flight,the aircraft will encounter the interference of various random factors brought by the external environment and internal motivation.These interferences will aggravate the rolling motion of the aircraft,destroy the flight stability of the aircraft.In order to study the random response of the roll motion of the delta wing vehicle under the random excitation,this thesis introduces the external excitation and the velocity parameter on the general roll model,and studies the problems of the steady probability density,the first crossing,the random stability and the random bifurcation,and the control of the roll motion under the excitation of Gaussian white noise and Poisson white noise.The main contents of the paper are as follows:In Chapter 1,the research status and results of the problems related to the roll motion of delta-wing aircraft at home and abroad,as well as the research background and significance of this article are introduced.In Chapter 2,the related concepts of stochastic differential equations,Ito differential rules,and the basic knowledge of Gaussian white noise and Poisson white noise are introduced.In Chapter 3,a roll motion model of delta wing vehicle is established considering the external excitation and the velocity parameter excitation.The dissipation energy balance method,the amplitude envelope random average method,and the energy envelope random average method are used to obtain the approximate stationary probability density functions of the system.The accuracy of the three methods is compared by numerical simulation,and the correctness of the theoretical results is verified.Due to the existence of external excitation,the trivial solution of the system is unstable.The stochastic stability and bifurcation of the parametric excitation system are studied by using the three index method.In Chapter 4,the reliability and first passage of delta wing vehicle under random excitation are studied by considering the influence of random external excitation and parametric excitation of Gaussian white noise.The average first crossing time of the system is obtained by using the generalized Pound Lyugin equation,and the average first crossing time of the system with bang bang control is discussed by using the stochastic optimal control theory.In Chapter 5,a rolling motion model of a delta wing aircraft under Poisson white noise is established.The vander Pol transform is used to transform the system into equations of motion regarding amplitude and phase.Based on the standard form of non-linear dynamic system and the basic theory of time averaging,the FPK equation under non-Gaussian excitation under non-Gaussian random excitation is obtained.The perturbation method is used to expand it,and the higher-order terms are truncated to obtain the approximate probability density of the system with Poisson white noise.Finally,it is numerically simulated.In Chapter 6,the main results of this article and the ideas for the next work are briefly summarized.