Influence of Pressure on the Frequency Spectrum of Micro and ‎Nanoresonators on Hinged Supports

Document Type : Research Paper


1 Mavlyutov Institute of Mechanics, Ufa, 450054, Russia

2 Blagonravov Institute of Mechanical Engineering, Moscow, 101990, Russia


Eigenfrequencies of bending oscillations are determined for a resonator with rectangular cross-sections mounted on hinged supports. Consideration is given to the surface effect caused by the interaction between gas pressure and the difference in the areas of the resonator’s convex and concave surfaces. Changes in the frequency spectrum are examined at the presence of both concentrated and uniformly distributed masses attached to the resonator’s surface. The solution of the inverse problem enables the identification of attached masses using changes of eigenfrequencies.


Main Subjects

[1] O’Connell, A.D., Hofheinz, M., Ansmann, M., Bialczak,R.C., Lenander, M., Lucero, E., Neeley, M., Sank, D., Wang, H., Weides, M., Wenner, J., Martinis, J.M., Cleland, A.N., Quantum ground state and single-phonon control of a mechanical resonator, Nature, 464, 2010, 697–703, DOI: 10.1038/nature08967.
[2] Burg, T.P., Godin, M., Knudsen, S.M., Shen, W., Carlson, G., Foster, J.S., Babcock, K., Manalis, S.R., Weighing of biomolecules, single cells and single nanoparticles in fluid, Nature, 446, 2007, 1066–1069, DOI: 10.1038/nature05741.
[3] Husale, S., Persson, H.H.J., Sahin, O., DNA nanomechanics allows direct digital detection of complementary DNA and microRNA targets, Nature, 462, 2009, 1075–1078, DOI: 10.1038/nature08626.
[4] Raman, A., Melcher, J., Tung, R., Cantilever dynamics in atomic force microscopy, Nano Today, 3(1−2), 2008, 20–27, DOI: 10.1016/S1748-0132(08)70012-4.
[5] Eom, K., Park, H. S., Yoon, D. S., Kwon, T., Nanomechanical resonators and their applications in biological/chemical detection: Nanomechanics principles, Physics Reports-Review Section of Physics Letters, 503 (4−5), 2011, 115–163, DOI: 10.1016/j.physrep.2011.03.002.
[6] Elnathan, R., Kwiat, M., Patolsky, F., Voelcker, N. H., Engineering vertically aligned semiconductor nanowire arrays for applications in the life sciences, Nano Today, 9(2), 2014, 172–196, DOI: 10.1016/j.nantod.2014.04.001. 
[7] Stassi, S., Marini, M., Allione, M., Lopatin, S., Marson, D., Laurini, E., Pricl, S., Pirri, C. F., Ricciardi, C., Fabrizio, E. D., Nanomechanical DNA resonators for sensing and structural analysis of DNA-ligand complexes, Nature Communications, 10, 2019, 1–10, DOI: 10.1038/s41467-019-09612-0.
[8] Jaber, N., Hafiz, M. A. A., Kazmi, S. N. R., Hasan, M. H., Alsaleem, F., Ilyas, S., Younis, M. I., Efficient excitation of micro/nano resonators and their higher order modes, Scientific Reports, 9(319), 2019, DOI:10.1038/s41598-018-36482-1. 
[9] SoltanRezaee, M., Bodaghi, M., Simulation of an electrically actuated cantilever as a novel biosensor, Scientific Reports, 10(3385), 2020, DOI: 10.1038/s41598-020-60296-9.
[10] Tavakolian, F., Farrokhabadi, A., SoltanRezaee, M., Rahmanian, S., Dynamic pull-in of thermal cantilever nanoswitches subjected to dispersion and axial forces using nonlocal elasticity theory, Microsystem Technologies, 25(3), 2019, 19–30, DOI: 10.1007/s00542-018-3926-y.
[11] He, J., Lilley, C. M., Surface stress effect on bending resonance of nanowires with different boundary conditions, Applied Physics Letters, 93, 2008, 263108, DOI: 10.1063/1.3050108.
[12] He, J., Lilley, C. M., Surface effect on the elastic behavior of static bending nanowires, Nano Letters, 8, 2008, 1798–1802, DOI: 10.1021/nl0733233.
[13] Wu, J. X., Li, X. F., Tang, A. Y., Lee, K. Y., Free and forced transverse vibration of nanowires with surface effects, Journal of Vibration and Control, 23, 2017, 2064–2077, DOI: 10.1177/1077546315610302.
[14] Wang, F., Abedini, A., Alghamdi, T., Onsorynezhad, S., Bimodal approach of a frequency-up-conversion piezoelectric energy harvester, International Journal of Structural Stability and Dynamics, 4, 2019, DOI:10.1142/S0219455419500901.
[15] Ilgamov, M. A., Flexural vibrations of a plate under changes in the mean pressure on its surfaces, Acoustical Physics, 64(5), 2018, 605–611, DOI: 10.1134/S1063771018050032.
[16] Ilgamov, M. A., Influence of surface effects on bending and buckling of nanowires, Doklady Physics, 64(9), 2019, 345–348, DOI: 10.1134/S1028335819090040.
[17] Ilgamov, M. A., The influence of surface effects on bending and vibrations of nanofilms, Physics of the Solid State, 61(10), 2019, 1825–1830, DOI: 10.1134/S1063783419100172.
[18] Morassi, A., Fernandez-Saez, J., Zaera, R., Loya, J.A., Resonator-based detection in nanorods, Mechanical Systems and Signal Processing, 93, 2017, 645–660, DOI: 10.1016/j.ymssp.2017.02.019.
[19] Dilena, M., Dell'Oste, M. F., Fernandez-Saez, J., Morassi, A., Zaera, R., Mass detection in nanobeams from bending resonant frequency shifts, Mechanical Systems and Signal Processing, 116, 2019, 261–276, DOI: 10.1016/j.ymssp.2018.06.022.
[20] Khakimov, A. G., Review of studies on the computational diagnosis of local defects of structural elements, Multiphase Systems, 14(1), 2019, 1–9, DOI: 10.21662/mfs2019.1.001.
[21] He, Q., Lilley, C. M., Resonant frequency analysis of Timoshenko nanowires with surface stress for different boundary conditions, Journal of Applied Physics, 112, 074322, 2012, DOI: 10.1063/1.4757593.
[22] Olsson, P. A., T., Park, H. S., Lidstrom, P. C., The influence of shearing and rotary inertia on the resonant properties of gold nanowires, Journal of Applied Physics, 108, 2010, 104312, DOI: 10.1063/1.3510584.
[23] Timoshenko, S. P., Young, D. H., Weaver, W., Vibration Problems in Engineering, John Wiley & Sons, New York, 1974.
[24] Rayleigh, J. W., The Theory of Sound, Macmillan and Company, London, 1894.
[25] Dowell, E. A., Ilgamov, M. A., Studies in Nonlinear Aeroelasticity, SV. N.Y., London, Tokyo, 1988.