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前全苏钻井所A.H.Mirzajanzade近来提出用Duffing方程作为油井涡轮枢轴运行的数学模型,并用它说明钻井过程在一定条件下会产生浑沌现象。本文详细分析了Duffing方程的近似解、周期解的稳定性、分频、倍频共振、振幅突变现象及系统进入浑沌状态的条件。 本文还分析了非线性系统浑沌状态的几个性质,并根据仿真结果及理论分析对Mirzajanznde等人提出的钻井过程的数学模型提出修正:在Duffing方程中增加具有浑沌状态的随机扰动项,使其更加符合实际,更能说明油井涡轮枢轴运动进入浑沌状态的原因。
A.H.Mirzajanzade of the former All-Soviet drilling institute recently proposed to use the Duffing equation as a mathematical model for the operation of oil well turbine pivots and to show that the drilling process can produce chaos under certain conditions. This paper analyzes in detail the approximate solutions of Duffing equations, the stability of periodic solutions, the crossover, multiplier resonance, the phenomenon of amplitude abrupt change and the conditions for the system to enter the chaotic state. In this paper, we also analyze several properties of the chaos state of nonlinear systems. Based on the simulation results and theoretical analysis, we propose a modification to the mathematical model of drilling process proposed by Mirzajanznde et al .: Adding random perturbation terms with chaos in the Duffing equation, Make it more realistic, can explain the reason that oil well turbine pivot movement enters chaos state.