Closed form expression for self-sensing microcantilever-based mass sensing

Abstract

The dynamics of a self-sensing microcantilever beam for mass sensing applications are presented. The microcantilever is assumed to be uniform and obeying the Euler-Bernoulli beam theory assumptions. The beam possesses an unknown tip mass to be measured and a piezoelectric patch actuator deposited on the cantilever surface. The actuator is operated in a self-sensing mode, in the sense that the same piezoelectric patch is used to simultaneously actuate the beam and sense the voltage induced due to beam vibrations. A balanced impedance bridge is used to supply voltage to the piezoelectric actuator and to read the induced voltage. Mathematical models for this mechatronic system actuated through a pure capacitive and a resistive-capacitive bridge network are derived. Equations of motion are obtained using the Hamilton's principle by considering the microcantilever as a distributed-parameters system. A technique to estimate the unknown tip mass, based on the inverse solution to the characteristic equation problem is presented along with sensitivity analysis of the unknown mass with respect to the characteristic equation parameters. A closed-form solution for the determination of unknown tip mass is obtained which has many advantages over numerical estimation methods in a widespread mass sensing application.