Unified nonlinear dynamic model for shells of revolution with arbitrary shaped meridians

Xu, Jie; Yuan, Xuegang; Wang, Yan Qing

doi:10.1016/j.ast.2024.108910

Cited by 3 publications

(2 citation statements)

References 47 publications

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“…As can be seen from Figure 8a, ignoring the nonlinear terms affecting the square of the angular velocity and the angular acceleration results in zero error for the ideal resonator, which is also consistent with the results of Equation (22). From Figure 8b, it can be seen that for a non-ideal resonator, the difference in the standing wave precession angle caused by ignoring the nonlinear terms becomes more and more significant as the angular velocity changes more and more sharply.…”

Section: High-intensity Dynamicsupporting

confidence: 81%

“…Due to the complexity of the nonlinear models, in reference [21] a precise low-order model was studied by perturbation analysis with the Galerkin method (or Ritz method), accounting for modal coupling and interactions. In reference [22], which discussed the von Karman nonlinearity, a high-dimensional nonlinear dynamical equation for the shell of revolution was formulated based on Love's theory, and the influence of meridian geometry on natural frequency was studied. The above references are crucial resources for researching nonlinear dynamic models of hemispherical resonators.…”

Section: Introductionmentioning

confidence: 99%

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The Influence of Nonlinear High-Intensity Dynamic Processes on the Standing Wave Precession of a Non-Ideal Hemispherical Resonator

Cheng,

Ren,

et al. 2024

Sensors

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The properties of small size, low noise, high performance and no wear-out have made the hemispherical resonator gyroscope a good choice for high-value space missions. To enhance the precision of the hemispherical resonator gyroscope for use in tasks with large angular velocities and angular accelerations, this paper investigates the standing wave precession of a non-ideal hemispherical resonator under nonlinear high-intensity dynamic conditions. Based on the thin shell theory of elasticity, a dynamic model of a hemispherical resonator is established by using Lagrange’s second kind equation. Then, the dynamic model is equivalently transformed into a simple harmonic vibration model of a point mass in two-dimensional space, which is analyzed using a method of averaging that separates the slow variables from the fast variables. The results reveal that taking the nonlinear terms about the square of the angular velocity and the angular acceleration in the dynamic equation into account can weaken the influence of the 4th harmonic component of a mass defect on standing wave drift, and the extent of this weakening effect varies with the dimensions of the mass defects, which is very important for steering the development of the high-precision hemispherical resonator gyroscope.

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Section: High-intensity Dynamicsupporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%