The article is devoted to the search for forms of single-tube resonators of high q-factor for vibration density meters of a liquid. In tube resonators, the source of energy loss is the reactive forces that occur during vibrations in the places where the tube is fixed. Therefore, the search for high-q resonator forms is reduced to finding ways to reduce the loss of mechanical vibration energy in the supports. The existing methods of synthesizing resonator forms – heuristic and electromechanical analogies - are analyzed. The advantage is given to the method of electromechanical analogies, as scientifically justified. An algorithm for synthesizing the shape of a high-q resonator is formed. Using the proposed algorithm, a generalized form of a high-q resonator is synthesized, which is a rigidly pinched tube at the ends, symmetrical with respect to the vertical axis of symmetry, with three sections – the Central one and two identical peripheral ones, differing in their mechanical parameters from the Central one. In particular, the form of a resonator in the form of a tube with a step-variable cross-section is proposed.

This paper is devoted to the current model of vibration-amplitude liquid densimeter developed by the authors. Firstly, the necessity to develop vibration-amplitude liquids densimeters with straigt-flow sensing elements (resonators) belonging to the "low costlow accuracy" category is justified. The resonator structure, developed as the result of the search using the heuristic method, is described. The proposed resonator is a tube rigidly fixed at the ends with additional weights attached symmetrically at the vertical axis at the points of the antinodes of the second fundamental oscillation mode in order to improve the resonator quality-factor by suppressing parasitic harmonics. The structure provides the possibility to restore the resonator natural oscillation frequency (decreased with time) to the primary one. It may be achieved by sequence screwing rods with different lengths into additional masses. The choice of the operating frequency of oscillations equal to 100 Hz is proved. It ensures invariance to the presence of solid inclusions in measured liquid and simplifies the electromagnetic excitation system. There are also theoretical relations obtained as a result of solving a differential equation of natural oscillations of a rigidly fixed tube with additional point masses, which are symmetrically located relatively vertical axis. They allow determining the own resonator oscillations frequencies for given parameters. The description of the operating model of the vibration-amplitude liquids densimeter, obtained experimentally and its calibration characteristic, is given.