The resonant shell is fixed on the base by a standard screw. The metallic sealing cap is used to package the resonant shell and isolate any environmental disturbances. The spoke structures on the bottom are designed to decrease the vibration coupling of the operating modes. Piezoelectric electrodes can be glued along the bottom spokes to excite the operating mode. It should be noted that the diameter of the resonant shell in this study is around 20 mm (medium-sized type), and the sealing cap is filled with a gas such as dry air. Despite operating under a non-vacuum condition, the gyroscope can provide tactical accuracy in a range of 1�C5 ��/h [2]. This characteristic makes the vibratory cylinder gyroscope competitive in terms of production cost.Figure 1.Physical structure of the vibratory cylinder gyroscope.

The operating principle of the cylinder gyroscope is well understood. In brief, there is a pair of operating modes in the form of standing waves with a circumferential waves number of 2. The two modes referred to as the exciting mode and sensing mode are circumferentially spaced relative to each other by 45��. The exciting mode of the resonant shell is a standing wave vibration generated by piezoelectric or electrostatic excitation. When the gyroscope rotates, the sensing mode can be detected due to the Coriolis effect, hence the rotation rate of the gyroscope is obtained after circuit demodulation. For more information on the theory of the gyroscope, the reader can refer to the [21�C23].3.

?Theoretical Study of the Acoustic CouplingSince the resonant shell of the vibratory cylinder gyroscope vibrates in the standing wave mode, its circumferential vibration is actually the topic in this study. Based on the elastic shell theory and the acoustic mode theory, a dynamic model is derived to qualitatively analyze the structural-acoustic coupling effect of the gyroscope.The resonant shell has radius R1, thickness h and height L. The resonant shell is enclosed by a sealing cap of radius R2. Let u, v and w be, respectively, the tangential, axial and radial displacement of a point of the shell at the angular position ��, as shown in Figure 2. Let ��r denote the mass density of the resonant shell, and it is assumed that the sealing cap is filled with dry air of density ��g.Figure 2.Schematic representation of the model.

Before the acoustic effect is studied, the air damping should be taken into account. As a matter of experience, the amplitude of the shell vibration can be on the order of micrometers, and the operating frequency is below 20 kHz [2,20,24,25]. Therefore we can conclude that the vibration velocity of the shell is relatively low. Thus only the linear damping Entinostat is introduced in the analysis. The quadratic or cubic damping can also be considered in the analysis, and similar results will be obtained [26,27].