Longitudinal vibration responses of axially functionally graded optimized MEMS gyroscope using Rayleigh-Ritz method, determination of discernible patterns and chaotic regimes

Axial vibration analysis of an optimized MEMS gyroscope is investigated in this paper. For this purpose; a model of rotating, axially functionally graded (tapered) nano-rod is represented. Along with classical continuum mechanics, Eringen's non-local theory is adopted. Using Hamilton's variational approach along with coupled displacement field concept which is derived from Babaei and Yang, governing equations of motion are derived. Rayleigh-Ritz approximate method is used to solve the equation for both clamped-clamped and clamped-free rod model. Verification of current results is ratified by comparison with results available in technical literature. Incorporation of taper parameter, non-local effect and rotation effects reveals predictable patterns along with unpredictable chaotic behavior of the optimized gyroscope. Such outcomes report necessity of precise and case-by-case perusal as for some specific values of taper and non-local parameters; system results unpredictable responses. In such chaotic regimes, pattern detection based on response of the gyroscope is impossible and a kind of real-time monitoring and analysis is required. Excluding critical values of the mentioned parameters of non-locality and taper; generally rotations around a fixed axis leads to lessening the oscillations, enhancing the non-locality yields weak vibrations, and intensifying the taper effects makes the system oscillate with greater frequencies wherein for quite high values of taper parameter, gyroscope model behavior turns out independent. It is good to mention that only case in which increment of taper parameter suppresses vibrations occurs when cross-section area of clamped-free nano-rod model is increasing. Eventually, influential factors of current model are revealed.