Geodesic
Mass Sensing by Symmetry Breaking and Mode
Russian journal of nonlinear dynamics, Tome 20 (2024) no. 2, pp. 231-257

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In this work, we study the nonlinear dynamics of a mode-localized mass detector. A system of equations is obtained for two weakly coupled beam resonators with an alternating electric current flowing through them and taking into account the point mass on one of the resonators. The one-dimensional problem of thermal conductivity is solved, and a steady-state harmonic temperature distribution in the volume of the resonators is obtained. Using the method of multiple scales, a system of equations in slow variables is obtained, on the basis of which instability zones of parametric resonance, amplitude-frequency characteristics, as well as zones of attraction of various branches, are found. It is shown that in a completely symmetrical system (without a deposited particle), the effect of branching of the antiphase branch of the frequency response is observed, which leads to the existence of an oscillation regime with different amplitudes in a certain frequency range. In the presence of a deposited particle, this effect is enhanced, and the branching point and the ratio of the amplitudes of oscillations of the resonators depend on the mass of the deposited particle.
Keywords: nano- and microsystems, nano- and microelectromechanical systems (NEMS/MEMS), sensors of masses of deposited particles, gas detectors, gas concentration sensors, nonlinear dynamics, coupled-field problems, modal localization, weakly coupled systems 
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     author = {N. V. Piskun and A. V. Lukin and I. A. Popov and L. V. Shtukin},
     title = {Mass {Sensing} by {Symmetry} {Breaking} and {Mode}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {231--257},
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N. V. Piskun; A. V. Lukin; I. A. Popov; L. V. Shtukin. Mass Sensing by Symmetry Breaking and Mode. Russian journal of nonlinear dynamics, Tome 20 (2024) no. 2, pp. 231-257. http://geodesic.mathdoc.fr/item/ND_2024_20_2_a3/