Experimental Study on Variation of Surface Roughness and Q Factors of Fused Silica Cylindrical Resonators with Different Grinding Speeds

For the axisymmetric shell resonator gyroscopes, the quality factor (Q factor) of the resonator is one of the core parameters limiting their performances. Surface loss is one of the dominating losses, which is related to the subsurface damage (SSD) that is influenced by the grinding parameters. This paper experimentally studies the surface roughness and Q factor variation of six resonators ground by three different grinding speeds. The results suggest that the removal of the SSD cannot improve the Q factor continuously, and the variation of surface roughness is not the dominant reason to affect the Q factor. The measurement results indicate that an appropriate increase in the grinding speed can significantly improve the surface quality and Q factor. This study also demonstrates that a 20 million Q factor for fused silica cylindrical resonators is achievable using appropriate manufacturing processes combined with post-processing etching, which offers possibilities for developing high-precision and low-cost cylindrical resonator gyroscopes.

A Weak Form Implementation of Nonlinear Axisymmetric Shell Equations With Examples

We present a weak form implementation of the nonlinear axisymmetric shell equations. This implementation is suitable to study the nonlinear deformations of axisymmetric shells, with the capability of considering a general mid-surface shape, non-homogeneous (axisymmetric) mechanical properties and thickness variations. Moreover, given that the weak balance equations are arrived to naturally, any external load that can be expressed in terms of an energy potential can, therefore, be easily included and modeled. We validate our approach with existing results from the literature, in a variety of settings, including buckling of imperfect spherical shells, indentation of spherical and ellipsoidal shells, and geometry-induced rigidity (GIR) of pressurized ellipsoidal shells. Whereas the fundamental basis of our approach is classic and well established, from a methodological view point, we hope that this brief note will be of both technical and pedagogical value to the growing and dynamic community that is revisiting these canonical but still challenging class of problems in shell mechanics.

Size-dependent two-node axisymmetric shell element for buckling analysis with couple stress theory

In this paper, two-node size-dependent axisymmetric shell element formulation is developed by using thin conical shell model in the place of the beam model, which is used in previous research and using the modified couple stress theory in the place of the classical continuum theory. Since classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have become quite popular. The mass stiffness matrix and geometric stiffness matrix for axisymmetric shell element are developed in this paper, and by means of size-dependent finite element formulation it is extended to more precisely account for nanotube buckling. The results have indicated using the two-node axisymmetric shell element, where the rigidity of the nano-shell is greater than that in the classical, and the critical axial buckling loads obtained from couple stress theory are greater than that of classical, which is due to the presence of one size parameter in couple stress theory. The findings also indicate that the developed size-dependent axisymmetric shell element is able to analyze the buckling of cylindrical and conical shells and also circular plate, which is reliable for simulating micro/nanostructures and can be used for the analysis of size effect and has desirable convergence characteristic. Besides, in addition to reducing the number of elements required, using axisymmetric shell element also increases convergence speed and accuracy.

Calculation of structural-inhomogeneous multiply connected shell structures with viscoelastic elements

Using the basic relationships of the hereditary theory of viscoelasticity and asymptotic methods, the problem of natural oscillations of structural-inhomogeneous, multiply connected, axisymmetric shell structures is reduced to an effectively solvable mathematical problem of complex eigenvalues, in which approximate engineering methods are proposed.