Motion Stability Analysis Of Water-based Aircraft In Waves

When water-based aircraft glides in waves,especially in severe sea conditions,it is easy to generate large amplitude swing motion,accompanied by complex nonlinearity.Nonlinear factors play an important role in the motion stability and safety performance of aircraft in waves.Therefore,based on the nonlinear dynamics theory and kinematic stability theory and its analysis method,this paper studied the sliding stability of water-based aircraft in waves,and sought and revealed the internal mechanical mechanism that affects the sliding stability of water-based aircraft in waves.Firstly,on the basis of the differential equation of the linear rolling motion of the aircraft in the regular transverse wave,this paper mainly considered the nonlinearity of damping moment and restoring moment,especially for the calculation of the nonlinear coefficient of restoring moment,put forward a fast formula calculation method which is better than the least square fitting method.By adding the nonlinear factors into the linear differential equation of the aircraft,the mathematical model of the nonlinear rolling motion in the regular transverse wave of the aircraft is established.Secondly,the multi-scale method in nonlinear dynamics theory is used to solve the nonlinear rolling motion differential equation of aircraft under the condition of main resonance in waves,and the second order approximate solution of rolling is given.The second order amplitude-frequency response curve equation of aircraft rolling was obtained by eliminating the secular term condition.The numerical solution of nonlinear rolling of aircraft was obtained by runge-kutta method of Matlab language.The approximate solution obtained by multi-scale method was compared with the numerical solution,and the correctness of the approximate solution based on multi-scale method was verified.Then,the effects of the damping moment model and the restoring moment model on the non-linear rolling motion of aircraft in waves are studied,and the effects of non-linear factors such as the damping coefficient and the restoring torque coefficient on the rolling motion of the aircraft are analyzed in details.The qualitative analysis methods such as time history curve method,phase plane method and Poincare section diagram method are used to determine the motion stability of the aircraft in waves.The qualitative analysis method is easy to cause misjudgment,so this paper uses a quantitative chaotic state identification method,the Lyapunov characteristic exponent method,to accurately calculate the Lyapunov characteristic exponent of the nonlinear system of the aircraft's nonlinear roll motion in waves.According to the stability criterion of Lyapunov characteristic exponent,the aircrafts'motion stability in waves was determined,and the critical value of wave excitation when the aircraft was panning and chaotic motion was determined by the Lyapunov characteristic exponent method.Finally,the differential equation of the parametrically excited rolling motion of the aircraft in the regular head waves is established,and the approximate solutions of the parametrically excited rolling of the aircraft under different damping moment models are solved by a multi-scale method.Starting from the average equation,ignoring the influence of non-linear terms,the stabe region and unstable region boundary curve equation of the trivial solution of the parametrically excited rolling of the aircraft is obtained.The stability of the parametrically excited rolling of the aircraft is analyzed.