Dynamics of a nonlinear microresonator based on resonantly interacting flexural-torsional modes

A novel microresonator operating on the principle of nonlinear modal interactions due to autoparametric 1:2 internal resonance is introduced. Specifically, an electrostatically actuated pedal-microresonator design, utilizing internal resonance between an out-of-plane torsional mode and a flexural in-plane vibrating mode is considered. The two modes have their natural frequencies in 1:2 ratio, and the design ensures that the higher frequency flexural mode excites the lower frequency torsional mode in an autoparametric way. A Lagrangian formulation is used to develop the dynamic model of the system. The dynamics of the system is modeled by a two degrees of freedom reduced-order model that retains the essential quadratic inertial nonlinearities coupling the two modes. Retention of higher-order model for electrostatic forces allows for the study of static equilibrium positions and static pull-in phenomenon as a function of the bias voltages. Then for the case when the higher frequency flexural mode is resonantly actuated by a harmonically varying AC voltage, a comprehensive study of the response of the microresonator is presented and the effects of damping, and mass and structural perturbations from nominal design specifications are considered. Results show that for excitation levels above a threshold, the torsional mode is activated and it oscillates at half the frequency of excitation. This unique feature of the microresonator makes it an excellent candidate for a filter as well as a mixer in RF MEMS devices.

[1]  A. H. Nayfeh,et al.  Nonlinear motions of beam-mass structure , 1990 .

[2]  Anil K. Bajaj,et al.  Amplitude modulated dynamics of a resonantly excited autoparametric two degree-of-freedom system , 1994 .

[3]  O. Degani,et al.  Pull-in study of an electrostatic torsion microactuator , 1998 .

[4]  Kimberly L. Turner,et al.  Institute of Physics Publishing Journal of Micromechanics and Microengineering Mechanical Domain Coupled Mode Parametric Resonance and Amplification in a Torsional Mode Micro Electro Mechanical Oscillator , 2022 .

[5]  Clark T.-C. Nguyen,et al.  Vibrating RF MEMS for next generation wireless applications , 2004, Proceedings of the IEEE 2004 Custom Integrated Circuits Conference (IEEE Cat. No.04CH37571).

[6]  H. Craighead,et al.  Mechanical resonant immunospecific biological detector , 2000 .

[7]  M. Younis,et al.  A Study of the Nonlinear Response of a Resonant Microbeam to an Electric Actuation , 2003 .

[8]  Amit K. Gupta,et al.  Single virus particle mass detection using microresonators with nanoscale thickness , 2004 .

[9]  Robert Puers,et al.  Pull-in voltage analysis of electrostatically actuated beam structures with fixed–fixed and fixed–free end conditions , 2002 .

[10]  R. L. Edwards,et al.  Measurements of Young's modulus, Poisson's ratio, and tensile strength of polysilicon , 1997, Proceedings IEEE The Tenth Annual International Workshop on Micro Electro Mechanical Systems. An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots.

[11]  Eric Beyne,et al.  MEMS for wireless communications: ‘from RF-MEMS components to RF-MEMS-SiP’ , 2003 .

[12]  M. R. Silva.  Non-linear flexural-flexural-torsional-extensional dynamics of beams—I. Formulation , 1988 .

[13]  Anil K. Bajaj,et al.  Resonant dynamics of an autoparametric system : A study using higher-order averaging , 1996 .

[14]  C. L. Zaretzky,et al.  Nonlinear flexural-flexural-torsional interactions in beams including the effect of torsional dynamics. I: Primary resonance , 1994, Nonlinear Dynamics.

[15]  Ali H. Nayfeh,et al.  Modal interactions in resonant microscanners , 2006 .

[16]  A. D. S. Barr,et al.  The Autoparametric Vibration Absorber , 1972 .

[17]  Sebastian Rützel,et al.  Nonlinear dynamics of atomic–force–microscope probes driven in Lennard–Jones potentials , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[18]  Kimberly L. Turner,et al.  Tuning the dynamic behavior of parametric resonance in a micromechanical oscillator , 2003 .

[19]  J. Murdock.  Perturbations: Theory and Methods , 1987 .

[20]  Anil K. Bajaj,et al.  Microresonators Based on 1:2 Internal Resonance , 2005 .

[21]  Maxim Zalalutdinov,et al.  Optically pumped parametric amplification for micromechanical oscillators , 2001 .

[22]  Mohammed F. Daqaq,et al.  Adaptation of Nontraditional Control Techniques to Nonlinear Micro and Macro Mechanical Systems , 2006 .

[23]  A. Bajaj,et al.  Amplitude modulated chaos in two degree-of-freedom systems with quadratic nonlinearities , 1997 .

[24]  G. Stemme,et al.  Gas damping of electrostatically excited resonators , 1997 .

[25]  A. Nayfeh,et al.  Linear and Nonlinear Structural Mechanics , 2002 .

[26]  Lidija Sekaric,et al.  Parametric amplification in a torsional microresonator , 2000 .

[27]  N. C. MacDonald,et al.  Five parametric resonances in a microelectromechanical system , 1998, Nature.

[28]  Kimberly L. Turner,et al.  Application of parametric resonance amplification in a single-crystal silicon micro-oscillator based mass sensor , 2005 .