10.14489/td.2021.06.pp.058-064

2021, 06 June

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.

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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: Данный адрес e-mail защищен от спам-ботов, Вам необходимо включить Javascript для его просмотра. , Данный адрес e-mail защищен от спам-ботов, Вам необходимо включить Javascript для его просмотра.

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