An Improved Formulation for Structural Optimization of Nonlinear Dynamic Response

Abstract

Nonlinear dynamics is widely exploited in micro-mechanical resonators with a number of applications. One of the crucial issues in these applications is to intentionally tailor the intrinsic nonlinearity in these structures. In this study, a structural optimization methodology is improved for tailoring the intrinsic nonlinearity in these resonators by manipulating their structural geometry. In the optimization, the objective function is defined based on the nonlinear modal coupling coefficients as well as eigenfrequencies and modal shapes of the vibration modes. A preliminary study shows that the improved formulation of the optimization problem enables better designs.

Maximizing the rate sensitivity of resonating gyroscopes using nonlinear shape optimization

“…In the light of these results, future efforts can be focused on (i) experimental implementation of these ideas on a ring resonator and (ii) adapting the tuning methods presented here for application in more general ring/disk geometries in an attempt to improve their angular rate sensitivity. These approaches will likely involve detailed computational approaches such as those described in [32][33][34][35].…”

“…In this work we examine ways in which one can use simple design alterations to systematically manipulate the mechanical and/or electrostatic contributions to the aforementioned nonlinear effects in order to improve, and even optimize, gyroscope sensitivity. The approach taken is a simplified version of the shape optimization techniques described in [32][33][34]. Specifically, since the devices of interest have circular symmetry and mode degeneracy must be maintained, non-uniform shapes can be easily expressed in terms of Fourier coefficients, making the approach less computationally intensive, even analytical for some geometrical modifications.…”