REDUCED ORDER MODEL FOR NON-LINEAR VIBRATIONS OF A PIEZOELECTRIC STRATIFIED PLATE.

matrix of resonating membranes Figure 2. Typical resonance curves for several prestresses and excitation levels. The large amplitude non-linear vibratory behavior of a stratified circular plate with piezoelectric patches 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. The bio-sensor under study is constituted of a 44 × matrix of micromachined stratified circular membranes [2] (Fig. 1). Each membrane can be individually actuated on its fundamental vibration mode by a piezoelectric thin patch. A biorecognition molecule, capable of immobilizing the target molecule, is glued on the top face of the membrane. When the membrane is in contact with a liquid medium that contains the target molecule, the latter is trapped, thus adding mass and lowering the fundamental resonance frequency. By detecting this change of frequency, one is able to detect and measure th