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motion equations of hemispherical resonator and analysis of frequency split caused by slight mass non-uniformity

Chinese Journal of Aeronautics 2020年第10期33卷 2660-2669页

作者： Yan HUO Shunqing REN Guoxing YI Changhong WANG Space Control and Inertial Technology Research Centre Harbin Institute of TechnologyHarbin 150080China

The mass non-uniformity of hemispherical resonator is one of reasons for frequency split,and frequency split can cause gyroscope to ***,it is of great significance to analyze the relationship between mass non-uniformity and frequency split,which can provide a theoretical basis for mass balance of imperfect *** starting point of error mechanism analysis for gyroscope is the motion equations of ***,based on the Kirchhoff-Love hypothesis in the elastic thin shell theory,the geometric deformation equations of resonator are ***,the deformation energy equation of resonator is derived according to the vibration mode and relationship between the stress and strain of hemispherical thin ***,the kinetic energy equation of resonator is deduced by the Coriolis ***,the motion equations of resonator are established by the Lagrange mechanics *** theoretical values of precession factor and natural frequency are calculated by the motion equations,which are substantially consistent with the ones by the finite element method and practical measurement,the errors are within a reasonable ***,the varying trend of natural frequency with respect to the geometrical and physical parameters of resonator by the motion equations is consistent with that by the finite element *** above conclusions prove the correctness and rationality of motion ***,the motion equations of resonator with mass non-uniformity are established by the same modeling method in case of ignoring the input angular rate and damping,and the state equations with respect to the velocity and displacement of vibration system are derived,then twonatural frequencies are solved by the characteristic *** is concluded that one of reasons for frequency split is the 4 th harmonic of mass non-uniformity,and thus much attention should be paid to minimizing the 4 th harmonic of mass non-uniformity in the course o

关键词： Hemispherical resonator Lagrange mechanics principle Theory of elastic thin shell motion equations Mass non-uniformity Frequency split

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Standing wave drift of hemispherical resonator with quality factor non-uniformity under a ring electrode excitation

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Chinese Journal of Aeronautics 2022年第1期35卷 160-172页

作者： Yan HUO Zeyu WANG Shunqing REN Zhennan WEI Guoxing YI Changhong WANG Space Cotrol and Inertial Technology Research Centre Harbin Institute of TechnologyHarbin 150080China HIT(Anshan)Institute of Industrial Technology Anshan 114000China

Hemispherical Resonator Gyroscope(HRG)is a classical high precision Coriolis Vibration Gyroscope(CVG),which performs attitude estimation of carrier by detecting the precession of standing wave of resonator,thus,the drift of standing wave of resonator has a great influence on the output accuracy of gyroscope,where the quality factor non-uniformity of resonator is one of main error *** electrode is a classical excitation structure of HRG because the standing wave can precess freely under its excitation,which makes the gyroscope have more accurate scale factor,larger measurement range and better dynamic *** this paper,the equations of motion of an ideal resonator excited by a ring electrode are derived by the elastic thin shell theory and Lagrange mechanical principle,then the corresponding equivalent mechanical model is *** to the“average method”,it can be seen that the ideal resonator excited by the ring electrode works in integral mode,and any position in the circumferential direction of resonator can be a working point,which means that the quality factor non-uniformity has a great effect on the drift of standing ***,the equations of motion of resonator with quality factor non-uniformity under the ring electrode excitation are deduced by the equivalent mechanical model,and the drift model of standing wave is established by the“average method”,it can be found that both the amplitude of quality factor non-uniformity and angle between the“inherent damping axis”and antinode axis of standing wave can affect the drift rate of standing ***,the drift model indicates that if the input angular rate does not reach the threshold,the precession angular rate of standing wave will appear“self-locking”phenomenon,that is,the gyroscope will lose the integral effect.

关键词： Hemispherical resonator Theory of elastic thin shell motion equations Average method Quality factor non-uniformity “Self-locking”phenomenon

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THEORETICAL AND COMPUTATIONAL INVESTIGATIONS OF NONLINEAR WAVE PROPAGATIONS IN ARTERIES(Ⅰ)——A THEORETICAL MODEL OF NONLINEAR PULSE WAVE PROPAGATIONS

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Science China Chemistry 1989年第6期32卷 711-728页

作者：伍时桂李兆治 Beijing Polytechnic University State University of New York BuffaloN Y 14260U.S.A.

In this paper, a new theoretical model of nonlinear wave propagations in arteries with surrounding tissues was put forward. The equations of motion for the blood vessels and their peripheral tissues as a system have been derived. These equations were expressed in terms of the stresses of the vessel wall and fluid, and the geometry of the blood vessel. They can be used to solve numerically the problems for the propagations of nonlinear pulse waves in arteries together with the momentum and continuity equations of incompressible-viscous flow, as well as the constitutive equations of fluid and vessel wall. The numerical solutions can involve pressure, velocities and flowrate of the blood flow, as well as displacements, velocities and stresses of the vessel wall. These physical variables of propagations of pulse waves in arteries are all of significance physiologically and clinically.

关键词： nonlinear waves theoretical model blood flow arterial walls surrounding tissue motion equations constitutive equation

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Method of Earthquake Prediction Based on the Soliton Mechanisms of Some Shocks

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Journal of Environmental Science and Engineering(B) 2014年第3期3卷 151-155页

作者： Mariana Turbal Yuriy Turbal Andriy Bomba Radoveniuk Olena Department of Applied Mathematics National University of Water Management and Nature Resourses Use Rivne 33022 Ukraine

In this paper, a new method of earthquakes prediction taking into account the influence of strain solitary waves as a ＂trigger＂ of some shocks is presented. Methods of forecasting are based on evaluating trajectories of individual solitons and clarification of shocks probability. Solitary waves are considered in solid anisotropic elastic medium and proved that there exist the motion equations solutions in the form of solitary waves. Predicting the trajectories of solitary waves related to the moment problem for the special case of Chebyshev system of functions or exponential problem. This problem is solved using special bijective mapping. Seismic process in the region of Japanese Islands, March 11,2011 is analyzed as an example.

关键词： Solitons solids motion equations anisotropic earthquake.

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