Detecting the mass and position of a particle by the vibration of a cantilevered micro-plate

Abstract Out-of-plane vibrations of a cantilevered micro-plate attached with a particle are analyzed by using the Rayleigh-Ritz method with deflection functions as the product of mode shapes of beams having the boundary conditions of the plate. An inverse model is then proposed to simultaneously identify the mass and position of the attached particle by the vibration of a micro-plate. The identification procedure has been tested on cantilevered Si micro-plates of different length-to-width ratios deposited with a tiny Pt pad atop. The mass and positions (both in length and width directions) of the Pt pad have been extracted from observed changes in the frequency response of both flexural and torsional vibrations of the micro-plate before and after the Pt deposition. The identified results are in good agreement with estimations based on scanning electron microscopy (SEM) observations. It is thus expected that the use of a micro-plate can significantly enhance mass and position sensing capabilities in comparison to the existing slender microcantilever in applications in biology, medicine and chemistry.