MMAE Seminar - Dr. Anil K. Bajaj - Nonlinear Resonances and Applications to Micro Electro Mechanical Resonators

Armour College of Engineering's Mechanical, Materials & Aerospace Engineering Department will welcome Dr. Anil K. Bajaj, Alpha P. Jamison Professor and William E. and Florence E. Perry Head of the School of Mechanical Engineering, Purdue University, on Wednesday, April 26th, to present his lecture, Nonlinear Resonances and Applications to Micro Electro Mechanical Resonators.

Abstract

Most micro-electromechanical resonator designs are based on linear resonant operation of micro-structures vibrating in flexural or torsional modes. Novel microresonators that utilize "internal resonance" phenomena and nonlinear interactions in structural modes are described. The focus is on systems with 1:2 internal resonances between two structural modes and their nonlinear interactions in the presence of quadratic nonlinearities. Specifically, two such microresonators, the T-resonator and the pedal resonator, are described. While the T-resonator utilizes modal interactions in two linear flexural modes, the pedal resonator utilizes interactions in flexural and torsional modes. Detailed analytical models for the two resonators, including inertial quadratic nonlinearities, cubic nonlinearities due to mid-plane stretching and curvature of the beam, electrostatic potential, and effects of thermal pre-stress, are developed using a Lagrangian formulation and nonlinear two-mode reduced-order models. These are used to investigate possible static pull-in limits to the resonator's operations, and nonlinear resonant dynamics under bias and harmonic electrostatic actuation. It is shown that the lower frequency mode is activated for actuation levels above a threshold, and generates a response component at half the frequency of resonant actuation. The resonators show high sensitivity to mass perturbations and, thus, hold great potential as RF filter-mixers and mass sensors. The design and fabrication of such resonators involves significant geometric and material parameter uncertainties, and thus Uncertainty Quantification and Sensitivity Analysis techniques are applied to understand the most significant parameters affecting the performance of the resonators. Experiments with a macro sized T-structure with flexural modes tuned to 1:2 resonance verify the basic concept of T-resonator design based.

Biography

Anil K. Bajaj is Alpha P. Jamison Professor and William E. and Florence E. Perry Head of the School of Mechanical Engineering. He joined the Purdue faculty in January 1981, having completed Ph.D. in Mechanics from the University of Minnesota. He obtained, respectively, Bachelor's and Master's degrees in Mechanical Engineering from the Indian Institute of Technology at Kharagpur and at Kanpur. Dr. Bajaj's research and teaching interests are in the areas of Linear and Nonlinear Systems, Analytical Dynamics and Modeling of Multibody Systems, Stability of Elastic Systems, Bifurcations and Chaos in Mechanical Systems, Nonlinear Stability in Fluids and Fluid-Structure Interactions, Dynamics of Seat-occupant Systems, Modeling of Viscoelastic Properties of Foam, and Design of Nonlinear Resonant MEMS. He is a Fellow of the ASME, and has received many Purdue University awards ("Provost's Award for Outstanding Graduate Mentors", Purdue Graduate School, 2006; College of Engineering "Mentorship" Award for Faculty Excellence, "Team" Award for Faculty Excellence, 2009). He has published more than 220 archival journal and conference proceedings papers, and has advised (or co-advised) more than 40 M.S. and Ph.D. students. Dr. Bajaj served as a Contributing Editor of the journal Nonlinear Dynamics till 2015.