The paper proposes an justification of a method of precise calibration (adjustment) of a multidimensional identified differential matrix model (in the form of Lagrange’s equations of the second kind) damped fluctuations of low-supporting super-extended building construction (SEBC) type of the cable-stayed bridge is offered. Results obtained are applied in the mathematical modeling of multi-frequency forced SEBC oscillation, generating theoretical and applied formulation for a synthesis of multi-channel dynamic compensators of critical resonance SEBC oscillations.

oscillation of a large-size building construction, identification of a resonant system, adjustment of the Lagrange’s equations of the second kind.

Received: February 1, 2021; Revised: February 19, 2021; Accepted: February 19, 2021; Published: April 15, 2021

How to cite this article: V. A. Rusanov, A. V. Daneev, A. V. Lakeyev and Yu. É. Linke, Precision calibration of a  differential-matrix model of resonant oscillations of the super-extended building construction, Advances in Differential Equations and Control Processes 24(2) (2021), 199-216. DOI: 10.17654/DE024020199

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] A. A. Baranovsky, Bridges of Big Flights, Design of Suspension and Cable-Stayed Bridges: Course of Lectures, LLC Maksimus Printing House, S-PB, 2005 (in Russian).
[2] A. V. Daneev, A. V. Lakeyev and V. A. Rusanov, Existence of a bilinear differential realization in the constructions of tensor product of Hilbert spaces, WSEAS Transactions on Mathematics 19 (2020), 99-107.
[3] M. E. Stieber, E. M. Petriu and G. Vukovich, Systematic design of instrumentation architecture for control of mechanical systems, IEEE Trans. on Instrument. and Meas 45(2) (1996), 406-412.
[4] A. V. Dmitriyev and E. I. Druzhinin, Identification of the dynamic characteristics of continuous linear models under conditions of complete parametric indeterminacy, Izv. Ross. Akad. Nauk. Teoriya i Sistemy Upravleniya (3) (1999), 44-52 (in Russian).
[5] A. V. Daneev, V. A. Rusanov and M. V. Rusanov, From Kalman-Mesarovic realization to a normal hyperbolic linear model, Cybernetics and Systems Analysis 41(6) (2005), 909-923.
[6] J. C. Willems, System theoretic models for the analysis of physical systems, Ric. Aut. (10) (1979), 71-106.
[7] V. A. Rusanov, A. V. Banshchikov, A. V. Daneev and A. V. Lakeyev, Maximum entropy principle in the differential second-order realization of a nonstationary bilinear system, Advances in Differential Equations and Control Processes 20(2) (2019), 223-248.
[8] A. V. Banshchikov and L. A. Bourlakova, Computer algebra and problems of motion stability, Mathematics and Computer in Simulation 57(3) (2001), 161-174.
[9] N. U. Ahmed, Optimization and Identification of Systems Governed by Evolution Equations on Banach Space, John Wiley and Sons, New York, 1988.
[10] G. Bredon, Introduction to Compact Transformation Groups, Academic Press, New York, 1972; translated under Nauka, Moscow, 1980 (in Russian).
[11] Yu. A. Bakhturin, Main Structures of Modern Algebra, Nauka, Moscow, 1990. (in Russian).
[12] W. M. Wonham, Linear Multivariable Control: a Geometric Approach, Springer-Verlag, New York, 1979; translated under Nauka, Moscow, 1980 (in Russian).
[13] V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, MTsNMO, Moscow, 2012 (in Russian).
[14] V. I. Arnold, On matrices depending on parameters, Russ. Math. Surv. 26(2), (1971), 29-43.
[15] V. V. Prasolov, Elements of Combinatorial and Differentiable Topology, MTsNMO, Moscow, 2014 (in Russian).
[16] L. V. Kantorovich and G. P. Akilov, Functional Analysis, Nauka, Moscow, 1977 (in Russian).
[17] L. Koralov and Y. G. Sinai, Theory of Probability and Random Processes, Springer, New York, 2007; translated under MTsNMO, Moscow, 2013 (in Russian).
[18] V. A. Rusanov, A. V. Banshchikov, A. V. Daneev, A. A. Vetrov and V. A. Voronov, A posteriori simulation of dynamic model of the elastic element of satellite-gyrostat, Far East Journal of Mathematical Sciences (FJMS) 101(9) (2017), 2079-2094.
[19] M. Hazewinkel and R. Kalman, On invariants, canonical forms and moduli for linear, constant, finite dimensional, dynamical systems, Lecture Notes in Econ.-Math. System Theory (131) (1976), 48-60.
[20] R. Hermann and C. F. Mart, Applications of algebraic geometry to systems theory, Part I, IEEE Trans. Autom. Control AC-22 (1977), 19-25.
[21] R. W. Brockett, Some geometric questions in the theory of linear systems, IEEE Trans. Autom. Control AC-21 (1976), 449-455.
[22] V. A. Rusanov and D. Yu. Sharpinskii, The theory of the structural identification of non-linear multidimensional systems, Journal of Applied Mathematics and Mechanics (74) (2010), 84-94.
[23] A. V. Daneev, M. V. Rusanov and V. N. Sizykh, Conceptual schemes of dynamics and computer modeling of spatial motion of large structures, Modern Technologies, System Analysis, Modeling 4 (2016), 17-25.