Zega Valentina

Assistant Professor


+39 0223996213
Department of Civil and Environmental Engineering (DICA) - Politecnico di Milano

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Nonlinear Dynamics in MEMS

Nonlinear Dynamics in MEMS resonators

People involved: V. Zega, A. Frangi

Numerical modelling of MicroElectroMechanical Systems (MEMS) resonators is attracting increasing interest from the sensors community especially when the nonlinear regime is activated by challenging applications of the device.
The dynamic response of a double-ended tuning fork MEMS resonator is studied both in the linear and nonlinear regime.


Figure 1: DETF MEMS resonator – first flexural mode. The contour of the displacement field is shown in color.

A one Degree Of Freedom (1 dof) model able to predict the frequency response of the device is proposed. Geometric and electrostatic nonlinearities are simulated through a Finite Element Method (FEM) and a Boundary Element Method (BEM) code, respectively. The total damping of the resonator is computed by taking into account both the thermoelastic and the nonlinear fluid contributions (http://intranet.dica.polimi.it/pub/fileadmin/user_upload/docenti_file/10069907/damping/damping.html). Experimental measurements performed on
resonators fabricated in polysilicon and single crystal silicon validate the proposed model showing a very good agreement with theoretical predictions.

Figure 2: Frequency response of a DETF resonator. Numerical predictions and experimental measurements are reported in solid and dotted lines, respectively. The frequency responses correspond to a dc voltage of 3.6V on the mechanical structure and to different amplitudes of the time dependent signal on the driving electrodes: 100 mV, 155 mV and 223 mV. The pressure inside the package is assumed equal to 30 ubar.

[1] V. Zega, A. Frangi, G. Gattere, ‘Nonlinear Dynamics of MEMS resonators: numerical modelling and experiments’ IEEE Sensors 2019, Montreal, Canada, October 27-30, 2019.
[2] V. Zega, G. Gattere, S. Koppaka, A. Alter, G.D. Vukasin, A. Frangi, T.W. Kenny ‘Numerical modelling of Non-Linearities in MEMS resonators’ J. Microelectromech. Syst., 26(6), (2020), 1443-1453.