Compliant structures with time-varying moment of inertia and non-zero averaged momentum and their application in angular rate microsensors

In this work we introduce a new class of fully compliant structures performing vibratory motion, yet characterized by non-zero averaged momentum, appearing due to time-dependency of the inertial parameters. The work is motivated by microelectromechancial systems (MEMS) applications, where an implementation of unidirectional, non-vibratory motion involving relative motion of parts is not desirable for reliability reasons. Instead of changing the mass, which is challenging on the microscale, the moment of inertia of the proof mass performing tilting vibrations is controlled in such a way that it is higher or lower depending on the sign of the velocity. This results in a non-zero angular momentum averaged over the period. The equations describing the dynamics of a generic structure with a time-varying inertia and in a rotating coordinate frame are derived by using a variational principle. Simple approximate expressions for the averaged momentum and steady tilting angle are obtained and validated numerically. Based on the model results for different operational scenarios, we demonstrate that these devices can be efficiently used in fully compliant actuators and vibratory angular rate sensors (microgyros) with a steady response in a sensing mode (pseudospinning disk gyros), as well as in a parametrically excited gyro. The structure can be viewed also as a first step toward the realization of dynamic materials (DM) which are substances with material properties that may change in space and time.