For the elastic connecting rod vibration machine driven by AC motor， the Sommerfeld effect of this non-ideal vibration system is studied. Based on Lagrange equation， the electromechanical coupling dynamic equation of the vibration system is established by introducing the mathematical model of AC motor. By using the average method， the first approximate analytical solution of the system and the steady state motion equation of motor are derived. Three stability conditions of the system are obtained according to the first stability criterion. The numerical analysis of the theoretical results show that the electromechanical coupling must be considered in the non-ideal vibration system driven by AC motor， because its amplitude-frequency characteristic curve also has the rigid nonlinear property. By analyzing the cases of the jump phenomenon， it is found that the motor motion equation is a transcendental equation， which leads to the phenomenon of multiple roots. As for which state is stable， it is necessary to substitute the parameter into the stability condition to judge. The above theoretical results are verified by time domain simulation. Finally， the system parameters such as mass， vibration stiffness， transmission stiffness， eccentric radius and motor damping are quantitatively discussed， which can provide a basis for the design of parameters of this kind of vibration machine.