Determination of biconical cavity eigenfrequencies using method of partial intersecting regions and approximation by rational fractions

M. V. Andreev; Oleg O. Drobakhin; D. Yu. Saltykov; N. B. Gorev; I. F. Kodzhespirova

doi:10.3103/S0735272719120033

Authors

M. V. Andreev Oles Honchar Dnipro National University, Ukraine https://orcid.org/0000-0001-7360-8058
Oleg O. Drobakhin Oles Honchar Dnipro National University, Ukraine https://orcid.org/0000-0003-2624-9122
D. Yu. Saltykov Oles Honchar Dnipro National University, Ukraine https://orcid.org/0000-0001-5403-4773
N. B. Gorev Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Dnipro, Ukraine https://orcid.org/0000-0001-6739-5172
I. F. Kodzhespirova Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Dnipro, Ukraine https://orcid.org/0000-0001-8975-712X

DOI:

https://doi.org/10.3103/S0735272719120033

Keywords:

biconical cavity, eigenfrequency, method of partial intersecting regions, collocation method, quasisolution, fractionally rational approximation

Abstract

The paper considers the problem of determining the eigenfrequencies of biconical cavity making it possible to simplify the eigenfrequency-based design of devices. We used the solving of the excitation problem for biconical cavity using the method of partial intersecting regions in combination with the collocation method. Based on the concept of the search of quasisolution for determining eigenfrequencies, it was proposed to apply the fractionally rational approximation of cavity response obtained as a result of solving the problem of resonator excitation. The efficiency of finding eigenfrequencies of biconical cavity was substantiated by using the fractionally rational approximation based on the chain fraction interpolation of cavity response calculated only at collocation points. Using the above approach, we have obtained the relationship of eigenfrequencies of azimuth-symmetric oscillations of biconical cavity as a function of the aperture angle, and the typing of lower azimuth-symmetric transverse electric modes of biconical cavity has been performed.

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