Advanced Mathematical Models & Applications

The aim of the article is to develop a mathematical model for the resonator of a vibration-frequency liquid densitometer with additional movable supports. The resonator, which has double symmetry, is two parallel tubes rigidly fastened at the ends, connected to each other by a pair of elastic crosspieces with respect to transverse and angular movements, which perform antiphase free oscillations. An analytical expression is derived that relates the frequency of natural oscillations of the resonator with the liquid under study with its mechanical and geometric parameters. The developed mathematical model of the resonator of the vibration-frequency liquid densitometer with movable supports allows at the design stage to determine its main dimensions, which allow ensuring the required initial natural frequency of the resonator, and therefore ensure the required measurement sensitivity.