Linear,nonlinear dynamics,and sensitivity analysis of a vibratory ring gyroscope

The linear and nonlinear dynamic responses of a vibratory ring gyroscope are investigated in this study focusing on the response mechanism of such a vibratory gyroscope. It is found that the nonlinear equations governing the drive and sense directions are coupled through both inertial linear and geometric nonlinear terms. Nonlinear responses are studied based on the full coupled nonlinear dynamic equations. The varying amplitude on the sense direction is analyzed for different input angular rates. The effect of nonlinearity on the ring gyroscope system is performed by comparing the results of nonlinear responses to those of linear responses. The contributions of some parameters to the amplitude responses and gyroscope sensitivity are analyzed, the conclusions of which provide guidelines to improve the sensitivity of the vibratory ring gyroscopes.

Synthesis of O6-Corona[3]arene[3]pyridazines and Their Molecular Recognition Property in Organic and Aqueous Media

O6-Corona[3]arene[3]pyridazines were synthesized from the one-pot macrocyclic condensation reaction of 3,6-dichlorotetrazine with 1,4-dihydroquinone derivatives followed by the inverse electron demand Diels-Alder reaction of the tetrazine rings with a cyclopentanone-derived enamine. Conversion of six ester groups within macrocycle into all sodium acetate moieties afforded a water soluble O6-corona[3]arene[3]pyridazine. The coronary macrocycle host formed complexes selectively with organic ammoniums and dinitrile guests in a 1 ： 1 stoichiometric ratio in organic solvents with association constants ranging from （2.96± 0.10）× 10^1 to （2.53±0.33）× 10^5 L·mol^-1. Water soluble O6-corona[3]arene[3]pyridazine was also able to complex strongly with organic ammoniums in water to give an association constant up to （2.67 ± 0.21） × 10^4 L·mol^-1. The pseudo-rotaxane and inclusion structures of the host-guest complexes were revealed by the X-ray crystallography.

Nonlinear Performance of MEMS Vibratory Ring Gyroscope

Micro-electro-mechanical system(MEMS)gyroscopes are an important sort of inertial sensor for identifying parameters of spinning structures,such as the spinning speed and angular deviation,based on the Coriolis effect.In this paper,the nonlinear mechanism of MEMS vibratory ring gyroscopes is analyzed by applying a fully coupled nonlinear model,in which the gyroscopic coupling and geometrically and structurally nonlinear couplings are all taken into account.The coupled differential equations governing the drive and sense motions are established via the Lagrangian equations.Numerical simulation is conducted,and the key nonlinear components and energy transfer behaviors between the drive and sense modes are elucidated.It is revealed that the cubic rigidity nonlinearity is another significant factor leading to the coupling between the drive and sense modes other than the gyroscopic coupling.Perturbation analysis is also carried out by using the method of multiple scales.The nonlinear frequency-amplitude responses of the drive and sense vibrations are obtained,and comprehensive parametric studies are performed.The significant effects of system damping,excitation amplitude,drive amplitude and spinning speed on the responses are discussed,which will facilitate to improve the nonlinear performance and sensitivity of the gyroscope.