DOI: 10.14489/td.2021.06.pp.058-064
Ilgamov M. A., Khakimov A. G. DEPENDENCE OF THE FREQUENCY SPECTRUM OF MICRO- AND NANO- RESONATORS ON PRESSURE AND ATTACHED MASS (pp. 58-64)
Abstract. An elastic rod of circular or rectangular section is rigidly fixed on both ends. The applicability of classical equations for the deformation of thin elements like rods, plates and shells to describe the stated problem is assessed using such integral characteristics, as eigenfrequencies. The assembly pressure is uniform, specifically atmospheric, and acts also on the areas of strip edges. It is assumed that there are no strains in this case. Excess pressures act only on the strip’s surface. The self-weight of the strip is neglected. Accounting for the attached mass of the surrounding medium and radiation penetrating into it shows that pressures in the upper and lower parts of the rod differ. But these factors are not taken into account, which can be justified in case of light gases. Since the relative axial lengthening at the boundaries equals zero in case of rigid clamping, it will also equal zero along the entire length in the absence of external axial forces. Frequency equations have been derived in case of the action of the surrounding pressure and also uniformly distributed and attached point masses. The influence of the excess pressure of the surrounding medium on the frequency spectrum of the rod oscillations is determined by the non-dimensional parameter that increases with an increase in pressure and the rod length and decreases with an increase of bending rigidity. At the negative excess pressure (vacuuming) this parameter reverses its sign, and the frequencies become lower. With an increase in both distributed and attached point mass the eigenfrequencies of oscillations decrease due to the rod invariable bending rigidity. The displacement of the point mass towards the center results in a decrease in odd eigenfrequencies, while even eigenfrequencies remain the same. Using the first frequency measured we can determine the excess pressure acting on the rod’s surface. Using two frequencies of bending oscillations we can determine the attached point mass and its coordinate. These results can be used when simulating the performance of resonators, including micro and nano ones.
Keywords: resonator, surface effect, bending vibrations, natural frequencies, primal and inverse problems.
M. A. Ilgamov, A. G. Khakimov (Mavlyutov Institute of Mechanics – Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences (Mavlyutov Institute of Mechanics UFRC RAS, Ufa, Russia) Е-mail:
ilgamov@anrb.ruДанный адрес e-mail защищен от спам-ботов, Вам необходимо включить Javascript для его просмотра.
,
hakimov@anrb.ruДанный адрес e-mail защищен от спам-ботов, Вам необходимо включить Javascript для его просмотра.
1. Raman A., Melcher J., Tung R. (2008). Cantilever dynamics in atomic force microscopy. Nano Today, Vol. 3, (1−2), pp. 20 – 27. 2. Eom K., Park H. S., Yoon D. S., Kwon T. (2011). Nanomechanical resonators and their applications in biological/chemical detection: Nanomechanics principles. Physics Reports–Review Section of Physics Letters, Vol. 503, (4−5), pp. 115 – 163. 3. Elnathan R., Kwiat M., Patolsky F., Voelcker N. H. (2014). Engineering vertically aligned semiconductor nanowire arrays for applications in the life sciences. Nano Today, Vol. 9, (2), pp. 172 – 196. 4. He J., Lilley C. M. (2008). Surface stress effect on bending resonance of nanowires with different boundary conditions. Applied Physics Letters, 93. 5. He J., Lilley C. (2008). M. Surface effect on the elastic behavior of static bending nanowires. Nano Letters, (8), pp. 1798 – 1802. 6. Wu J. Х., Li X. F., Tang A. Y., Lee K. Y. (2017). Free and forced transverse vibration of nanowires with surface effects. Journal of Vibration and Control, Vol. 23, pp. 2064 – 2077. 7. Wang F., Abedini A., Alghamdi T., Onsorynezhad S. (2019). Bimodal Approach of a Frequency-Up-Conversion Piezoelectric Energy Harvester. International Journal of Structural Stability and Dynamics, Vol. 19, (08). 8. Ilgamov M. A. (1998). Static Problems of Hydroelasticity. Moscow: Nauka. 9. Il'gamov M. A. (2019). Influence of surface effects on bending and stability of nanowires. Doklady Akademii nauk, Vol. 488, (2), pp. 137 – 141. [in Russian language] 10. Il'gamov M. A. (2019). Influence of surface effects on bending and vibrations of nanofilms. Fizika tverdogo tela, Vol. 61, (10), pp. 1825 – 1830. [in Russian language] 11. Il'gamov M. A. (2020). Frequency spectrum of wire micro- and nanocavity. Doklady Rossiyskoy akademii nauk. Fizika, tekhnicheskie nauki, Vol. 494, (1), pp. 21 – 24. [in Russian language] 12. Morassi A., Fernandez-Saez J., Zaera R., Loya J. A. (2017). Resonator-based detection in nanorods. Mechanical Systems and Signal Processing, Vol. 93, pp. 645 – 660. 13. Dilena M., Dell'Oste M. F., Fernandez-Saez J. et al. (2019). Mass detection in nanobeams from bending resonant frequency shifts. Mechanical Systems and Signal Processing, Vol. 116, pp. 261 – 276. 14. Hakimov A. G. (2019). Review of Research on Computational Diagnostics of Local Defects of Structural Elements. Mnogofaznye sistemy, Vol. 14, (1), pp. 1 – 9. [in Russian language] 15. Timoshenko S. P., Yang D. H., Uiver. U. (1985). Fluctuations in engineering. Moscow: Mashinostroenie. [in Russian language] 16. Rayleigh J. W. (1984). The Theory of Sound. London: Macmillan and Company. 17. Dowell E. H. (1975). Aeroelasticity of Plates and Shells. Leyden: NIP. 18. Landau L. D., Lifshits E. M. (1987). The theory of elasticity. Moscow: Nauka. [in Russian language] 19. Il'gamov M. A. (2016). Interaction of instabilities in a hydroelastic system. Prikladnaya matematika i mekhanika, Vol. 80, (5), pp. 566 – 579. [in Russian language] 20. Il'gamov M. A. (2017). Influence of ambient pressure on the bending of a thin plate and film. Doklady Akademii nauk, Vol. 476, (4), pp. 402 – 405. [in Russian language] 21. Olsson P. A. T., Park H. S., Lidstrom P. C. (2010). The Influence of shearing and rotary inertia on the resonant properties of gold nanowires. Journal of Applied Physics, Vol. 108.
This article is available in electronic format (PDF).
The cost of a single article is 450 rubles. (including VAT 18%). After you place an order within a few days, you will receive following documents to your specified e-mail: account on payment and receipt to pay in the bank.
After depositing your payment on our bank account we send you file of the article by e-mail.
To order articles please copy the article doi:
10.14489/td.2021.06.pp.058-064
and fill out the form
|