Abstract—
The problem of active suppression of vibrations of an elastic panel moving longitudinally in an ideal fluid flow is considered. The dynamics equation of the panel includes the fluid response and external mechanical action that serves to implement the damping process. The conditions of extremality of lateral vibration damping are derived and the efficiency of the optimal distribution of the forces applied to the panel and the optimal time program of the external influence functioning are estimated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
V. V. Bolotin, Dynamic Stability of Elastic Systems (Gostekhizdat, Moscow, 1956) [in Russian].
V. V. Bolotin, Nonconservative Problems of the Theory of Elastic Stability (Fizmatlit, Moscow, 1961; Pergamon Press, London, 1963).
N. V. Banichuk, S. Y. Ivanova, and A.V. Sharanyuk, Structures Dynamics. Analysis and Optimization (Nauka, Moscow, 1989) [in Russian].
A. B. Movchan, “On stability of a panel moving in a gas,” Prikl. Mat. Mekh. 21 (2), 231–243 (1957).
R. L. Bisplinghoff, H. Ashley, and R. Halfman, Aeroelasticity (Addison-Wesley, Cambridge, 1955).
V. V. Bolotin, Yu. V. Gavrilov, B. P. Makarov, and Yu. Yu. Shveiko, “Nonlinear problems of the stability of plane panels at hypersonic speeds,” Izv. Akad. Nauk SSSR, OTN, Mekh. Mashinostr., No. 3, 3–14 (1959).
N. V. Banichuk and A. A. Mironov, “Optimization problems for plates oscillating in an ideal fluid,” J. Appl. Math. Mech. 40 (3), 474–481 (1976).
N. V. Banichuk, Shape Optimization for Elastic Bodies (Nauka, Moscow, 1980) [in Russian].
H. Ashley and M. Landahl, Aerodynamics of Wings and Bodies. (Dover Publ., New York, 1965).
J. Lighthill, An Informal Introduction to Theoretical Fluid Mechanics (Oxford University Press, Oxford, 1986).
N. Banichuk, J. Jeronen, P. Neittaanmäki, et al., Mechanics of Moving Materials (Springer, Cham, 2014).
N. Banichuk, A. Barsuk, J. Jeronen, et al., Stability of Axially Moving Materials (Springer, Cham, 2020).
H. Ashley, “On making things the best aeronautical uses of optimization,” J. Aircr. 19 (1), 5–28 (1982).
N. V. Banichuk, Problems and Methods of Optimal Structural Design (Plenum Press, New York, 1983).
N. V. Banichuk and S. Y. Ivanova, “The suppression of transverse vibrations of an elastic panel moving axially in a fluid flow,” Dokl. Phys. 65, 186–189 (2020). https://doi.org/10.1134/S1028335820040023
N. V. Banichuk, Introduction to Optimization of Structures (Nauka, Moscow, 1986; Springer, New York, 1990) [in Russian].
S. G. Mikhlin, Variational Methods in Mathematical Physics (Nauka, Moscow,1970) [in Russian].
M. I. Vishik, “The problem of Cauchy with operators as coefficients, the mixed boundary problem for systems of differential equations and an approximate method of their solution”, Mat. Sborn. Nov. Ser. 39 (1), 51–148 (1956).
I. V. Svirskii, Methods of the Bubnov-Galerkin Type and Successive Approximations (Nauka, Moscow, 1968) [in Russian].
Funding
The research was carried out on the topic of the State Assignment (state registration number AAAA-A20-120011690132-4) and with partial financial support from the Russian Foundation for Basic Research (project no. 20-08-00082a).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by M. K. Katuev
About this article
Cite this article
Banichuk, N.V., Ivanova, S.Y. ON THE OPTIMAL METHODS OF DAMPING HYDROELASTIC VIBRATIONS. Mech. Solids 56, 505–512 (2021). https://doi.org/10.3103/S0025654421040038
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0025654421040038