Dynamic stability behavior of a beam-type vibratory structure, for applications in a class of vibratory angular rate sensors is investigated. A suitable mathematical model for a rotating beam perturbed by periodic velocity fluctuations is developed. The natural frequency variations due to the gyroscopic coupling present in the system are characterized. When the system is considered to be under an influence of periodic perturbations in the input angular speed, the dynamic stability is investigated. The method of averaging is employed for this purpose, and closed-form stability conditions are obtained. The analytical results are verified by direct numerical integration of the system equations.
Ariaratnam, S.T. and Sri Namachchivaya, N.1986. ``Periodically Perturbed Linear Gyroscopic Systems,''Journal of Structural Mechanics , 14(2):153-176.
2.
Asokanthan, S.F. and Cho, J.2005. ``Dynamic Stability of Beam-type Angular Rate Sensors Subjected to Rate Fluctuations'' Proceedings of International Conference on Smart Materials Structures and Systems, July 28-30, 2005, Bangalore, India, pp. 167-174.
3.
Bogoliubov, N.N. and Mitropolsky, Y.A.1961. Asymptotic Methods in the Theory of Non-linear Oscillations, Hindustan Publishing Corp, Delhi-6, India.
4.
Cho, J.2005. ``Dynamic Response and Stability of Ring-based Vibratory Angular Rate Sensors,'' M.E.Sc. Thesis, The University of Western Ontario, London, Ontario, Canada.
5.
Kammer, D.C. and Schlack Jr, A.L.1987. ``Effects of Nonconstant Spin Rate on the Vibration of a Rotating Beam,''Journal of Applied Mechanics, 54:305-310.
6.
Kane, T.R., Ryan, R.R. and Banerjee, A.K.1987. ``Dynamics of a Cantilever Beam Attached to a Moving Base ,'' AIAA Journal of Guidance, Control, and Dyanmics, 10(2):139-151.
7.
Lawrence, A.1992. Modern Inertial Technology, Navigation, Guidance, and Control, Springer-Verlag, New York .
8.
Maluf, N.2000. An Introduction to Microelectromechanical System Engineering , Artech House Inc., Boston and London.
9.
Nayfeh, A.L.1973. Perturbation Methods, John Wiley & Sons. Inc., New York.
10.
Van Doorn, E. and Asokanthan, S.F.1996. ``Attitude Stability of Dual-spin Asymmetric Spacecraft,'' The Journal of the Astronautical Sciences, 44(2):149-165.
11.
Valeev, K.G.1963. ``On the Danger of Combination Resonances,'' Journal of Applied Mathematics and Mechanics, (PMM)27(6): 1745-1759.
12.
Yoo, H.H., Ryan, R.R. and Scott, R.A.1995. ``Dynamics of Flexible Beam Undergoing Overall Motions ,'' Journal of Sound and Vibration, 181(2):261-278.
