Abstract. Considering the influence of variable equivalent stiffness on system response, the equivalent stiffness is defined as a step function, and a mathematical model of nonlinear longitudinal vibration of sucker rod string (SRS) is built. The dynamic response under displacement and load force excitation is solved by fourth-order Runge-Kutta method with zero initial condition. The results show the steady-state responses under the displacement and load force excitation of different function forms are different. The response curves of both displacement and velocity under the displacement and load force excitation of cosine function form have larger fluctuation than it under the displacement and load force excitation of sine function form. Therefore, the characteristic analysis of SRS plays an important role in understanding the influence of the excitation form and sensitive parameters on steady response.
InstructionThe SRS is a slender rod of several kilometres, which transmits the movement from mechanical rotary motion to plunger linear motion [1][2]. And, the characteristic analysis of longitudinal vibration of SRS is very important for the parameters optimization of sucker rod pumping system (SRPS) [3]. Therefore, the dynamic simulation of SRS is studied by domestic and foreign scholars. After wave equation of Gibbs [4], an improved model of SRPS is built by Dale Russel Doty and S.D. . Recently, I.N.Shardakov, Luan Guo-hua and M.M Xing etal [7][8][9] analyse boundary conditions effecting rod law of motion and correct the excitation forces of rod longitudinal vibration. However, the most of aforementioned approaches have not been studied sufficiently. Relevant references [9][10] shows that the equivalent stiffness is a function of time, when the influence of the helical buckling of SRS on the equivalent stiffness is taken into consideration, which affects the characteristic of longitudinal vibration of SRS. Therefore, with non-constant equivalent stiffness, the dynamic Characteristic of SRS with Variable Equivalent Stiffness is necessary to be analysed.In this paper, the dynamic model and nonlinear second-order differential equations are built, and the entire equilibrium equation is given in section 2. In section 3, the system equations of nonlinear longitudinal vibration of SRS are solved by fourth-order Runge-Kutta method with zero intimal conditional. In section 4, the dynamic responses under different function forms of load force excitation as well as the load force and displacement excitation are given, and the effects of different function forms of load force excitation as well as displacement excitation on the amplitude-frequency curves are analysed. In section 5, the significance of dynamic characteristic of SRS and conclusions are summarized.
Dynamic model and nonlinear second-order differential equationsIn order to establish mechanical model of nonlinear longitudinal vibration for SRS, the fundamental assumptions are as follows: (1)The tubing string is anchored; (2)The viscous damping of liquid is c...