Application of uncertainty quantification techniques for a nonlinear 1:2 internal resonance system

Rajat Goyal, Purdue University

Abstract

Nonlinear phenomena based resonating devices offer a very promising role as efficient and accurate MEMS devices in a rapidly growing and improving area of MEMS based sensing and actuation. The requirement of high reliability and accuracy stipulates very strict performance metrics of these devices. In order to understand the effects of any input variability on the output, a robust modeling and simulation technique should be developed which predicts the device behavior sufficiently accurately, while at the same time considering the computational complexity associated with complete nonlinear analytical modeling. This works deals with a nonlinear T-shaped 1:2 internal resonance autoparametric resonator and looks into the uncertainty quantification aspect of it. The aleatoric uncertainties of material and geometric properties are considered and their quantification problem is addressed. The solution of the system, which is a two stepped process considering linear modeshapes and frequencies and nonlinear averaged Lagrangian, is modified for piezoelectric actuation. Simulation for uncertainties is done for the linear and nonlinear parts separately and effects of parameter variation on the final output are brought out. Several techniques of efficient simulation are presented and sensitivity of the device towards tuning is established. An attempt of experimental uncertainty quantification is presented with a macro-scale model built to replicate the functionality of the MEMS device. Various issues related to its operation in the macro domain are brought out and suggestions for further improvements are made based on the current observations. Future research on developing the MEMS device for characterization and uncertainty studies is suggested.

Degree

M.S.M.E.

Advisors

Bajaj, Purdue University.

Subject Area

Mechanical engineering

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