抽油杆柱纵向振动共振条件的质疑与力学模型的修正

在研究抽油杆柱纵向振动特性时，将抽油杆柱简化为上端固定于随悬点运动的基础之上、下端受液体负荷激励的力学模型。研究了单级抽油杆柱纵向自由振动的固有频率以及抽油杆柱对各种激励的稳态响应。建立了单级杆柱第i阶固有频率pi和基频p0之间的关系，即pi=(2i-1)p0，指出了单级抽油杆柱产生共振的条件是激励频率等于基频的奇数倍，证明了APIRPllL有杆抽油系统的设计计算推荐方法中关于激励频率等于偶数倍基频时，单级杆柱将产生共振的结论是错误的，并指出了导致这一错误结论的原因是所采用的力学模型是错误的。通过对抽油杆柱动态特性的计算机仿真，进一步证明了本文结论的正确性。

Doubting the Resonance Condition of the Longitudinal Vibration of the Sucker Rod String Introduced by APIRP11L and Improving of the Mechanical Modeling

A new mechanical model used to study the longitudinal vibration property of the rod string is built, in which the top of the rod string moves with a base and the bottom is excited by a force. The fundamental frequency, the resonance condition and steady response of a single stage rod string are studied. It is proved that the resonance condition of a single stage rod string is that the excitation frequency is equal to odd times of the fundamental frequency. The vibration properties of the rod string are also studied in APIRP11L, and the resonance condition of a single stage rod string is that the exiting frequency is e-qual to the odd or even times of the fundamental frequency. By theoretically analyzing and deducing, it is demonstrated that the even times of the fundamental frequency is not the resonance frequency. It is pointed out that the mechanical model which is used in APIRPllL is incorrect.