Keywords: micro-scale resonators, buckling, non-linear phenomena, axial load effects, piezoelectric actuation, Düffing oscillator.

Piezoelectrically actuated micro-scale resonators are attractive for communication and signal-processing applications [1]. Two types of resonators, namely, AlGaAs and PZT resonators are considered here. These resonators are composite structures, with asymmetric cross-sections. In addition, during the fabrication process, residual stresses are also introduced in these resonators. As pointed out in the authors' recent work, they exhibit non-linear characteristics [2,3,4,5]. These characteristics include Düffing oscillator like response during resonance excitations [6], temporal harmonics in the response, and spatial patterns during forced oscillations that cannot be explained by conventional linear analysis.

In the first component of this article, the authors discuss finite element analysis, in which transverse free vibrations of free-free and clamped-clamped resonators subjected to constant axial loads are considered. It is shown that the consideration of axial loads is important to predict the experimentally observed first natural frequencies of different resonators. In a second component of this article, the authors present a non-linear analysis to study dynamic buckling in micro-scale resonators. Through this analysis, it is shown that the experimentally observed spatial patterns during forced oscillations may be interpreted as oscillations about a non-flat equilibrium position caused by buckling. In a third component of this article, it is illustrated as to how non-linear oscillator models of resonators can be developed from experimental data. It is believed that the numerical and analytical efforts presented in this article can be used as a basis to understand non-linear phenomena in micro-scale resonators as well as to develop design tools for such systems.

1

DeVoe, D. L., "Piezoelectric Thin Film Micromechanical Beam Resonators", Sensors and Actuators, 88, 263-272, 2001. doi:10.1016/S0924-4247(00)00518-5

2

Li, H. and Balachandran, B., "Buckling Induced Nonlinear Phenomenon in a Micro-electromechancial Resonator", Proceedings of the ASME International Mechanical Engineering Congress and Exposition, New Orleans, 2002; Paper No. IMECE2002-39010.

3

Balachandran, B. and Li, H., "Nonlinear Phenomena in Microelectromechanical Resonators", Proceedings of IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics, Rome, Italy, June 8-13, 2003.

4

Li, H. and Balachandran, B., "Nonlinear Oscillations of Micromechanical Oscillators", Proceedings of the ASME International Design Engineering Technical Conferences, Chicago, 2003; Paper No. DETC2003/VIB-48520.

5

Preidikman, S., Li, H., and Balachandran, B., "Forced Oscillations of Microelectromechanical Resonators", Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Washington, D. C., 2003; Paper No. IMECE2003-44552.

6

Nayfeh, A. H., and Balachandran, B., "Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods", John Wiley & Sons Inc., New York, 1995.

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