scholarly journals Standing Wave Binding of Hemispherical Resonator Containing First–Third Harmonics of Mass Imperfection under Linear Vibration Excitation

Sensors ◽  
2020 ◽  
Vol 20 (19) ◽  
pp. 5454
Author(s):  
Yan Huo ◽  
Shunqing Ren ◽  
Zhennan Wei ◽  
Guoxing Yi
Keyword(s):  
Standing Wave ◽  
Equations Of Motion ◽  
Theoretical Method ◽  
Fused Silica ◽  
Mechanism Analysis ◽  
Linear Vibration ◽  
Vibration Excitation ◽  
Hemispherical Resonator ◽  
Parasitic Components ◽  
Thin Shell Theory

Due to complicated processing technology, the mass distribution of a hemispherical resonator made of fused silica is not uniform, which can affect the azimuth of the standing wave of a resonator under the linear vibration excitation. Therefore, the analysis of standing wave evolution of a resonator with mass imperfection under linear vibration excitation is of significance for the improvement of the output accuracy of a gyroscope. In this paper, it is assumed that the resonator containing the first–third harmonics of mass imperfection is excited by horizontal and vertical linear vibration, respectively; then, the equations of motion of an imperfect resonator under the second-order vibration mode are established by the elastic thin shell theory and Lagrange mechanics principle. Through error mechanism analysis, it is found that, when the frequency of linear vibration is equal to the natural frequency of resonator, the standing wave is bound in the azimuth of different harmonics of mass imperfection with the change in vibration excitation direction. In other words, there are parasitic components in the azimuth of the standing wave of a resonator under linear vibration excitation, which can cause distortion of the output signal of a gyroscope. On the other hand, according to the standing wave binding phenomenon, the azimuths of the first–third harmonics of mass imperfection of a resonator can also be identified under linear vibration excitation, which can provide a theoretical method for the mass balance of an imperfect resonator.

scholarly journals Modeling of Acceleration Influence on Hemispherical Resonator Gyro Forcing System

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Guoxing Yi ◽  
Yangguang Xie ◽  
Ziyang Qi ◽  
Boqi Xi
Keyword(s):  
Dynamic Model ◽  
Thin Shell ◽  
Shell Theory ◽  
Electrostatic Force ◽  
Inertial Load ◽  
Negative Effects ◽  
Hemispherical Resonator ◽  
Negative Effect ◽  
Simulation Results ◽  
Thin Shell Theory

Acceleration adds negative effect to Hemispherical Resonator Gyro (HRG) output; therefore, it is important to model the influence and then make necessary compensations, accordingly. Based on the elastic thin-shell theory under the Kirchhoff-Love assumption, the acceleration influence on HRG forcing system is modeled and then schemes for incentive are suggested. Firstly, the dynamic model of resonator is introduced. Then, inertial load and electrostatic force are calculated to obtain the deformation of resonator. At last, schemes for pickoff incentive are proposed to weaken the effect of acceleration on HRG forcer. The simulation results illustrate that acceleration has negative effects on the exciting confidents of forcers and the proposed scheme can eliminate the acceleration influence on forcing system.

Mechanism Analysis Using Implicit Constraints

2008 ◽  
Author(s):  
George H. Sutherland
Keyword(s):  
Equations Of Motion ◽  
Reaction Force ◽  
Mechanism Analysis ◽  
Kinematic Parameters ◽  
Joint Reaction Force ◽  
Dynamic Mechanisms ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Mechanism Kinematic ◽  
Joint Reaction

This paper introduces an approach to kinematic and dynamic mechanisms analysis where one or more joints are modeled using joint component relative displacements that approximate real joint behavior. This approach allows for the simultaneous nonrecursive solution for both mechanism kinematic parameters and selected dynamic joint reaction forces. Also, for closed loop mechanisms, the approach eliminates the need for forming explicit loop closure constraint equations, so that the dynamic equations of motion, derived using either the Newtonian or Lagrangian method, have a simplified unconstrained form. The key element underlying the approach is the formation of axioms for the standard mechanism joint types that describe the form of the joint reaction force and/or moment in terms of a virtual (or real) displacement between the joint components.

The dynamics and design of a non-linear vibration absorber

1993 ◽  
Vol 207 (6) ◽  
pp. 363-374 ◽  
Author(s):  
D H Gonsalves ◽  
R D Neilson ◽  
A D S Barr
Keyword(s):  
Numerical Simulation ◽  
Equations Of Motion ◽  
Resonance Peak ◽  
Vibration Absorber ◽  
Linear Vibration ◽  
Frequency Range ◽  
Non Linear ◽  
Experimental Rig ◽  
Auxiliary Mass

This paper presents the design of an efficient non-linear vibration absorber. The system comprises a linear absorber with the addition of a spring between the two masses, which contacts the absorber mass when its displacement exceeds a certain value. The addition of this snubber stiffness facilitates a reduction in the amplitude of the second resonance peak of the linear absorber, which therefore enables the system to be operated over a wider frequency range without reaching larger amplitudes. The modification also has the effect of attenuating the response of the auxiliary mass. The equations of motion for the system are presented and optimization is carried out. A description of an experimental rig that was built follows. The results from the rig are compared with those from numerical simulation and show good correlation.

Mechanism Analysis of Thermal/Electric Field Poling in Fused Silica

2002 ◽  
Vol 41 (Part 1, No. 5A) ◽  
pp. 2958-2961 ◽  
Author(s):  
Xueming Liu ◽  
Hanyi Zhang
Keyword(s):  
Electric Field ◽  
Fused Silica ◽  
Mechanism Analysis ◽  
Electric Field Poling

Dynamic Analysis of Multi-Rigid-Body Systems

1974 ◽  
Vol 96 (3) ◽  
pp. 886-892 ◽  
Author(s):  
V. K. Gupta
Keyword(s):  
Digital Simulation ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Mechanism Analysis ◽  
Spatial Mechanism ◽  
Higher Derivatives ◽  
Reaction Forces ◽  
Representative Problem ◽  
Classical Vector ◽  
Vector Approach

A method is presented for formulating and solving the Newton-Euler equations of motion of a system of interconnected rigid bodies. The digital simulation may involve numerical integration of the kinematic equations as well as the dynamic equations. The reaction forces and torques resulting from rigid constraints imposed at the connecting joints are also determined. The derivation of kinematic expressions for first and higher derivatives is demonstrated based on direct differentiation of the rotation matrix in the spirit of the classical vector approach. A representative problem in spatial mechanism analysis is solved and illustrated with numerical results.

scholarly journals Двумерные кулоновские плазмон-экситоны: релаксация возбуждений

2021 ◽  
Vol 63 (8) ◽  
pp. 1157
Author(s):  
В.А. Кособукин
Keyword(s):  
Near Field ◽  
Equations Of Motion ◽  
Harmonic Oscillators ◽  
Classical Electrodynamics ◽  
Two Dimensional ◽  
Linear Vibration ◽  
Coupled Harmonic Oscillators ◽  
Vibration Theory ◽  
Mechanical Oscillators ◽  
External Polarization

A theory is developed for the relaxation of two-dimensional non-radiative (Coulomb) plasmon-excitons in thin closely located layers of a metal and a semiconductor. In the framework of classical electrodynamics, the equations of motion are formulated for the polarization waves of non-radiative plasmons and excitons with taking into account the Coulomb coupling and the near-field of external polarization. In the model of coupled harmonic oscillators represented by the polarization fields of excitations, the problem of relaxation is solved for Coulomb plasmons, excitons and plasmon-excitons. It is shown that the two dispersion branches of normal plasmon-exciton modes undergo anticrossing (mutual repulsion) at the resonance between plasmon and exciton. With dissipative damping and power interchange between the excitations taken into account, the process of plasmon-exciton relaxation depending on time is investigated. The theory displays the principal analogies between dynamics of plasmon-excitons and of excitations in other objects of linear vibration theory, such as mechanical oscillators, resonant electric chains, etc.

The Gyroscopic Vibration Absorber

1967 ◽  
Vol 89 (4) ◽  
pp. 706-712
Author(s):  
Robert Jones
Keyword(s):  
Linear Function ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Vibration Absorber ◽  
Variable Frequency ◽  
Equivalent Weight ◽  
Support Structure ◽  
Linearized Equations ◽  
Vibration Excitation ◽  
Analytical Results

The linearized equations of motion of the gyroscopic vibration absorber are derived showing that the antiresonant frequency is a linear function of the speed of the gyroscopic disk; thus the gyroscopic vibration absorber (GVA) can be easily synchronized and therefore applied to vehicles and machinery having variable frequency vibration excitation. The effects on the antiresonant frequency from elastic restraint about the pivots and flexibility in the support structure are also examined. The bandwidth of the GVA is compared to a Frahm absorber of equivalent weight. Experimental results confirm the analytical results and show the feasibility of the GVA as a synchronous absorber.

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