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The transmission systems of the differential velocity vane pumps (DVVP) have periodic vibrations under loads. And it is not easy to find the reason. In order to optimize the performance of the pump, the authors proposed DVVP driven by the hybrid Higher-order Fourier non-circular gears and tested it. There were also similar periodic vibrations and noises under loads. Taking into account this phenomenon, the paper proposes fluid mechanics and solid mechanics simulation methodology to analyze the coupling dynamics between fluid and transmission system and reveals the reason. The results show that the pump has the reverse drive phenomenon, which is that the blades drive the non-circular gears when the suction and discharge is alternating. The reverse drive phenomenon leads the sign of the shaft torque to be changed in positive and negative way. So the transmission system produces torsional vibrations. In order to confirm the simulation results, micro strains of the input shaft of the pump impeller are measured by the Wheatstone bridge and wireless sensor technology. The relationships between strain and torque are obtained by experimental calibration, and then the true torque of input shaft is calculated indirectly. The experimental results are consistent to the simulation results. It is proven that the periodic vibrations are mainly caused by fluid solid coupling, which leads to periodic torsional vibration of the transmission system.