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A multimodal approach for simultaneous mass and rotary inertia sensing from vibrating cantilevers
Physica E: Low-dimensional Systems and Nanostructures, Volume: 125, Start page: 114366
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Nano and micromechanical mass sensing using cantilever oscillators of different length-scales has been an established approach. The main principle underpinning this technique is the shift in the resonance frequency caused by the additional mass in the dynamic system. While the mass of an object to b...
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Nano and micromechanical mass sensing using cantilever oscillators of different length-scales has been an established approach. The main principle underpinning this technique is the shift in the resonance frequency caused by the additional mass in the dynamic system. While the mass of an object to be sensed is useful information, some idea about the shape of the object would be an additional benefit. The shape information may be used to make a distinction between two different objects of the same mass. This paper establishes the conceptual framework for simultaneous sensing of the mass as well as the rotary inertia of an object attached to a vibrating cantilever beam. The rotary inertia of an object gives additional insight into its shape, which is a key motivation of this work. It is shown that by using two modes it is possible to formulate two coupled nonlinear equations, which in turn can be solved to obtain the mass and the rotary inertia simultaneously from the frequency shifts of first two vibration modes. Euler-Bernoulli beam theory and an energy approach are used to derive closed-form expressions for the identified mass and rotary inertia from the measured frequency shifts. Analytical expressions are validated using high fidelity finite element simulation results.
Nanomechanical sensor, Frequency shift, Mass sensing, Rotary inertia, Cantilever beam
College of Engineering