Abstract
The mathematical modeling method is used to study the flutter of an arbitrary shaped plate in a plane. For the numerical simulation of unstable vibrations of the plate, an effective numerical algorithm without saturation is proposed, which makes it possible to obtain an acceptable accuracy in the approximate solution on a sparse grid. As a standard, the critical flutter speed is sought on two grids 9 × 15 and 15 × 31; the criterion for the correctness of the calculation is the proximity of the obtained values; it is possible to set an arbitrary grid. Calculations are made for an elliptical aluminum plate for two thicknesses h = 0.003 and h = 0.005 at different directions of the flow velocity vector. The coincidence of calculations on the two grids is satisfactory.
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REFERENCES
K. I. Babenko, Fundamentals of Numerical Analysis, 2nd ed. (RChD, Moscow and Izhevsk, 2002) [in Russian].
A. A. Il’yushin and I. A. Kiiko, “A new formulation of the problem of the flutter of a hollow shell,” J. Appl. Mat. Mech. 58 (3), 545–549 (1994). https://doi.org/10.1016/0021-8928(94)90104-X
S. D Algazin and I. A Kiiko, “A numerical-analytic investigation of the flutter of a plate of arbitrary shape in the plane,” J. Appl. Mat. Mech. 61 (1), 169–172 (1997). https://doi.org/10.1016/S0021-8928(97)00021-X
S. D. Algazin, P K. I. Babenko, Fundamentals of Numerical Analysis, 2nd ed. (RChD, Moscow and Izhevsk, 2002) [in Russian].
A. A. Il’yushin and I. A. Kiiko, “A new formulation of the problem of the flutter of a hollow shell,” J. Appl. Mat. Mech. 58 (3), 545–549 (1994). https://doi.org/10.1016/0021-8928(94)90104-X
S. D Algazin and I. A Kiiko, “A numerical-analytic investigation of the flutter of a plate of arbitrary shape in the plane,” J. Appl. Mat. Mech. 61 (1), 169–172 (1997). https://doi.org/10.1016/S0021-8928(97)00021-X
S. D. Algazin, Preprint No. 678, IPMekh RAN (Inst. of Applied Mechanics, RAS, Moscow, 2001).
E. P. Kazandjan, Preprint No. 82, IPM RAN (Keldysh Institute of Applied Mathematics RAS, Moscow, 1977).
S. D. Algasin and I. A. Kiiko, Flutter of Plates and Shells, 2d ed. (URSS, Moscow, 2016) [in Russian].
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The work was carried out on the topic of the state assignment of the IPMech RAS no. AAAA-A20-120011690132-4.
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Translated by M. K. Katuev
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Algazin, S.D. FLUTTER OF AN ARBITRARY SHAPED PLATE WITH MIXED BOUNDARY CONDITIONS IN A PLANE. Mech. Solids 57, 128–131 (2022). https://doi.org/10.3103/S0025654422010083
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DOI: https://doi.org/10.3103/S0025654422010083