Numerical Simulation of Elastic Wave Precession in the Cylindrical Resonator of a Hemispherical Resonator Gyroscope Featuring a Non-Homogeneous Density Distribution

We employ direct numerical simulation to investigate the phenomenon of drift in a hemispherical resonator gyroscope, caused by non-homogeneous density distribution. We described a rotating cylindrical resonator by a system of ordinary differential equations with constant coefficients and found the solution to the system using a matrix exponential. We provide examples that illustrate the drift phenomenon for various values assumed by the non-homogeneity parameter of the density distribution

References

[1] Basarab M.A., Lunin B.S., Matveev V.A., Fomichev A.V., Chumankin E.A., Yurin A.V. Miniature gyroscope based on elastic waves in solids for small spacecraft. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Priborostr. [Herald of the Bauman Moscow State Tech. Univ., Instrum. Eng.], 2014, no. 4, pp. 80–96 (in Russ.).

[2] Matveev V.A., Lunin B.S., Basarab M.A. Navigatsionnye sistemy na volnovykh tverdotelnykh giroskopakh [Navigation system on the wave solid-state gyroscopes]. Moscow, Fizmatlit Publ., 2008. 240 p.

[3] Dzama M.A., Egarmin N.E. Precession of elastic waves during the rotation of certain classes of axisymmetric shells. Izvestiya RAN. Mekhanika tverdogo tela, 1991, no. 1, pp. 170–175 (in Russ.).

[4] Mercuriev I.V., Podalkov V.V. Dinamika mikromekhanicheskogo i volnovogo tverdotel'nogo giroskopov [Dynamics of micromechanical and wave solid-state gyroscopes]. Moscow, Fizmatlit Publ., 2009. 228 p.

[5] Donnik A.S. Vliyanie geometricheskoy neodnorodnosti i uprugoy anizotropii materiala na tochnostnye kharakteristiki volnovogo tverdotel’nogo giroskopa: dis. kand. tekhn. nauk [Influence of material geometrical heterogeneity and elastic anisotropy on the accuracy of the wave solid-state gyroscope characteristics: kand. tech. sci. diss.]. Moscow, MEI Publ., 2006. 131 p.

[6] Vakhlyarskiy D.S., Guskov A.M., Basarab M.A., Matveev V.A. Using a combination of fem and perturbation method in frequency split calculation of a nearly axisymmetric shell with middle surface shape defect. Nauka i obrazovanie: nauchnoe izdanie MGTU im. N.E. Baumana [Science and Education: Scientific Publication of BMSTU], 2016, no. 5, pp. 152–174 (in Russ.). DOI: 10.7463/0516.0839190 Available at: http://technomag.bmstu.ru/doc/839190.html

[7] Kozubnyak S.A. Splitting of natural frequencies of cylindrical resonator gyro due to non-ideal shape. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Priborostr. [Herald of the Bauman Moscow State Tech. Univ., Instrum. Eng.], 2015, no. 3, pp. 39–49 (in Russ.). DOI: 10.18698/0236-3933-2015-3-39-49

[8] Biderman V.L. Mekhanika tonkostennykh konstruktsiy. Statika [Thin-walled structure mechanics. Statics]. Moscow, Mashinostroenie Publ., 1977. 488 p.

[9] Dyakonov V.P. Mathematica 5.1/5.2/6. Programmirovanie i matematicheskie vychisleniya [Mathematica 5.1/5.2/6. Programming and mathematical calculations]. Moscow, DMK-Press Publ, 2008. 574 p.

[10] Matveyev V.A., Basarab M.A., Lunin B.S. Approximation of density distribution of solid-state wave gyro resonator with respect to measured disbalance parameters. Pribory i sistemy. Upravleniye, kontrol’, diagnostika [Instruments and Systems: Monitoring, Control, and Diagnostics], 2015, no. 10, pp. 9–16.

[11] Matveev V.A., Lipatnikov V.I., Alekhin A.V. Proektirovanie volnovogo tverdotelnogo giroskopa [Design of the hemispherical resonator gyro]. Moscow, Bauman MSTU Publ., 1998. 168 p.

[12] Belyaev Yu.N. Methods for computing a transfer matrices of elastic deformations. Vestnik PNIPU. Mekhanika [PNRPU Mechanics Bulletin], 2013, no. 3, pp. 63–110 (in Russ.).