Chapters authored
Bifurcation Makes a Wave Resonant Solid-State Gyro Be Stable
A golf ball having special dimples flies better than an analogous smoothed one. A surprise is that there is a range of Reynolds numbers for which the turbulent drag is somewhat less than that in the laminar case. Analogies always meet together and are accomplished themselves in the physics. We have traced an effect similar to the above mentioned in the area of solid mechanics when the nonlinear system passes through a sequence of bifurcations. In mechanical engineering, the role of such a system can play a solid-state wave gyro entering the family of MEMS/NEMS. It is known that a circular Foucault pendulum can serve as an angular sensor. Standing waves in a thin-walled elastic axisymmetric resonator of a solid-state wave gyro, mounted on a rotating platform, can also detect a rotation rate. Because there are no typical mechanical parts there, such wave sensors have advantages for long-term space missions. However, to maintain the functionality and sensitivity of a wave gyro in practice, the driving of standing waves requires a sophisticated feedback control. Nonetheless, we have demonstrated that such a gyro can operate without any feedback at the expense of the natural nonlinearity of the resonator in a postbifurcation regime.
Part of the book: Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems