BUCKLING AND NON-LINEAR VIBRATIONS OF A MEMS BIOSENSOR

The large amplitude non-linear vibratory behavior of a stratified circular plate with a piezoelectric patch is addressed in this study. The goal is to build an efficient model of a resonating MEMS (Micro Electro Mechanical System) bio-sensor whose function is to detect in real-time the presence of a given molecule (the so called target molecule) in a liquid medium. This study introduces the plate equations of motion, that includes the effects thermal-like prestresses, the piezoelectric material, its stratified structure with two annular regions and the geometrical non-linearities stemming from large deflections. Their resolution by an expansion onto the eigenmodes of the unstressed system gives the first insights in the buckling phenomena and the nonlinear vibrations.

[1]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[2]  F. Bloom,et al.  Handbook of Thin Plate Buckling and Postbuckling , 2000 .

[3]  Stefan Bilbao,et al.  Geometrically nonlinear flexural vibrations of plates: In-plane boundary conditions and some symmetry properties , 2008 .

[4]  Cyril Touzé,et al.  ASYMMETRIC NON-LINEAR FORCED VIBRATIONS OF FREE-EDGE CIRCULAR PLATES. PART 1: THEORY , 2002 .

[5]  Bruno Cochelin,et al.  Two methods for the computation of nonlinear modes of vibrating systems at large amplitudes , 2006 .

[6]  B. Balachandran,et al.  Buckling and free oscillations of composite microresonators , 2006, Journal of Microelectromechanical Systems.

[7]  R. Arquier,et al.  Manlab - logiciel de continuation intéractif , 2005 .

[8]  Liviu Nicu,et al.  Micromachined piezoelectric membranes with high nominal quality factors in newtonian liquid media : A Lamb's model validation at the microscale , 2007 .

[9]  Cyril Touzé.  A normal form approach for nonlinear normal modes , 2003 .

[10]  Marco Amabili,et al.  Nonlinear normal modes for damped geometrically nonlinear systems: Application to reduced-order modelling of harmonically forced structures , 2006 .

[11]  Bruno Cochelin,et al.  Asymptotic-numerical methods and pade approximants for non-linear elastic structures , 1994 .

[12]  C. Chia.  Nonlinear analysis of plates , 1980 .

[13]  Cyril Touzé,et al.  Non-linear vibrations of free-edge thin spherical shells: modal interaction rules and 1:1:2 internal resonance , 2005 .