The vibrating tube densimeter measures the liquid density based on the relationship between the natural frequency of the resonator and the liquid density in the tube. However, the problem of constructing a complete mathematical model and optimizing the structure size and working mode of the resonator remains unsolved. The paper presents a complete set of working equations of the resonator constructed by Euler Bernoulli beam theory. In addition, the analytical formula of the resonator sensitivity and the Q-factor was deduced. According to the analytical formula, the variation rule of the resonator sensitivity and the Q-factor under different structure sizes and working modes is analyzed, which provides a theoretical basis for optimizing the structure size and working mode of the vibrating tube resonator.
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