Experimental Investigation of Nonlinear Mode Shape in Microscale Beams

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The Ohio State University

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Micro-electro-mechanical-systems (MEMS) have drawn a great interest over last serval decades due to its wide applications including accelerometers and pressure sensors, micro-mirrors, radiofrequency (RF) switches, microphones, and inertia sensors. The moving mechanical element integrated in MEMS devices is typically operating in its resonant mode. Due to its small size and low damping, the micro-beams often exhibit the nonlinear resonance, which is being widely investigated to overcome the limitations of linear mode in term of its levels of sensitivity and reliability. This work covers an experimental study of the dynamic responses of micro-beams, including the nonlinear mode shape and resonances by improving the experimental tool and accuracy. The characterization is performed on a silicon-polymer micro-beam that is excited near its fundamental mode frequency by a piezoelectric shaker. The nonlinearity of this micro-beam originates geometrically from the elongation of the polymer part during large flexural oscillations of the silicon part. Its amplitude of oscillation is detected by Laser Doppler Vibrometer (LDV) while the excitation frequency is varied. To study the nonlinear mode shape, the points of measurement are scanned along the longitudinal direction of the micro-beam located on a 2-axis piezoelectric stage. Established a custom LabVIEW program which can precisely control the movable stage and collect the vibration amplitude data at different locations is necessary. The measurement establishes a nonlinear behavior of micro-beam revealed by its nonlinear mode shape and frequency response. Further comparison between the experimental nonlinear mode shape and FEM simulation results validates the experimental characterization. The experimental measurement provides the most realistic mode shape of the micro-beam and gives a better understanding of the vibration behavior of MEMS resonators.


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Nonlinear Mode shape of micro-beam