Study on the Self-Synchronization and Sommerfeld Effect of Rectangular Thin Plate Vibration System Excited by Double Induction Motors

With the development of vibration equipment towards larger scales and higher frequencies, complex structural vibrations become unavoidable. This paper delves into the Sommerfeld effect and self-synchronization in a system featuring a rectangular thin plate structure excited by two non-ideal induction motors. This research can be applied to the engineering practice of large-scale vibrating machinery such as vibrating platform.

The exploration encompasses theoretical analyses, simulation studies, and experimental investigations. The motion differential equations of the system are established according to the Hamilton’s principle. The semi-inverse method is employed to derive the modal vibration functions and frequency equations for a rectangular thin plate. The finite element method (FEM) analysis is used for verification. The synchronization conditions and stability conditions of the synchronous operation of the system are obtained according to the linear perturbation theory, and the criterion of speed capture is given.

The synchronization state of two induction motors changes from 0° to 180° before and after the natural frequency of the rectangular thin plate. Changing the installation position of the induction motor, two induction motors are on the same waveform of the second-order natural frequency mode shape, and a special phase difference change will occur, that is, the natural frequency will change from 0° to 180° before and after, and again to 0° at higher speeds, and to 180° through the second-order resonance region.

The theoretical results correspond perfectly with the simulation and experiment ones, which proves the correctness of the theoretical results and the feasibility of the theoretical method. The complex interaction between Sommerfeld effect and self-synchronization phenomenon is revealed, and the influence of motor installation position on both is discussed. It is proved that the mode shape of rectangular thin plate has great influence on motor synchronization.