Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic Forces

The bifurcation of the periodic response of a micro-machined gyroscope with cubic supporting stiffness and fractional electrostatic forces is investigated. The pull-in phenomenon is analyzed to show that the system can have a stable periodic response when the detecting voltage is kept within a certain range. The method of averaging and the residue theorem are employed to give the averaging equations for the case of primary resonance and 1:1 internal resonance. Transition sets on the driving/detecting voltage plane that divide the parameter plane into 12 persistent regions and the corresponding bifurcation diagrams are obtained via the singularity theory. The results show that multiple solutions of the resonance curves appear with a large driving voltage and a small detecting voltage, which may lead to an uncertain output of the gyroscope. The effects of driving and detecting voltages on mechanical sensitivity and nonlinearity are analyzed for three persistent regions considering the operation requirements of the micro-machined gyroscope. The results indicate that in the region with a small driving voltage, the mechanical sensitivity is much smaller. In the other two regions, the variations in the mechanical sensitivity and nonlinearity are analogous. It is possible that the system has a maximum mechanical sensitivity and minimum nonlinearity for an appropriate range of detecting voltages.

Solar System chaos and the Paleocene–Eocene boundary age constrained by geology and astronomy

Astronomical calculations reveal the Solar System’s dynamical evolution, including its chaoticity, and represent the backbone of cyclostratigraphy and astrochronology. An absolute, fully calibrated astronomical time scale has hitherto been hampered beyond ~50 million years before the present (Ma) because orbital calculations disagree before that age. Here, we present geologic data and a new astronomical solution (ZB18a) showing exceptional agreement from ~58 to 53 Ma. We provide a new absolute astrochronology up to 58 Ma and a new Paleocene–Eocene boundary age (56.01 ± 0.05 Ma). We show that the Paleocene–Eocene Thermal Maximum (PETM) onset occurred near a 405-thousand-year (kyr) eccentricity maximum, suggesting an orbital trigger. We also provide an independent PETM duration (170 ± 30 kyr) from onset to recovery inflection. Our astronomical solution requires a chaotic resonance transition at ~50 Ma in the Solar System’s fundamental frequencies.

Enhanced optical confinement of dielectric nanoparticles by two-photon resonance transition

Two-photon resonance enhances optical confinement of nanoparticles.