ON ONE INTERPRETATION OF THE NON-AUTONOMOUS LINEARIZED HOFF MODEL ON A GEOMETRIC GRAPH

Sophiya A. Zagrebina, Elena I. Nazarova, Minzilia A. Sagadeeva

Abstract


In the article, as an interpretation of the Hoff model on a geometric graph, it is proposed to consider the New York Twin Towers during the terrorist attack on September 11, 2001. Some of the design features of these towers can be well described within the framework of the Hoff model. Studies of the solution of the non-autonomous linearized Hoff model on a geometric graph have shown that such a structure has the property of stability and in the normal state the deflections of the beams from the zero position tend to zero. However, it is clear that as a result of the tragedy of September 11, 2001, conditions in the towers developed such that non-autonomy began to manifest itself in the model, due to which the critical load exceeded the thresholds and the structure lost stability. This was especially evident in the building of the World Trade Center 7, where there was no collision with an airplane and the building collapsed only as a result of a fire.

Keywords


stationary solution; asymptotic stability of solutions; I-beam construction

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References


Hoff N.J. The Analysis of Structures. John Wiley; Chapman and Hall, New York; London, 1956. 493 p.

Sviridyuk G.A. Quasistationary Trajectories of Semilinear Dynamical Equations of Sobolev Type. Russian Acad. Sci. Izv. Math., 1994, vol. 42, no. 3, pp. 601-614. DOI: 10.1070/IM1994v042n03ABEH001547

Sviridyuk G.A., Fedorov V.E. Linear Sobolev Type Equations and Degenerate Semigroups of Operators. VSP, Utrecht, Boston, 2003. 216 p.

Demidenko G.V., Uspenskii S.V. Partial Differential Equations and Systems Not Solvable with Respect to the Highest-Order Derivative. Marcel Dekker, New York, Basel, Hong Kong, 2003. 239 p.

Al'shin A.B., Korpusov M.O., Sveshnikov A.G. Blow-up in Nonlinear Sobolev Type Equations. de Gruyter, Berlin, 2011. 648 p.

Sviridyuk G.A., Zagrebina S.A. Nonclassical Mathematical Physics Models. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2012, no. 40 (299), pp. 7-18.

Sviridyuk G.A. Sobolev Type Equations on a Graph. Non-Classical Equations of Mathematical Physics, coll. of art., 2002, Novosibirsk, pp. 221-225.

Sviridyuk G.A., Shemetova V.V. Hoff Equations on Graphs. Differential Equations, 2006, vol. 42, no. 1, pp. 139-145. DOI: 10.1134/S0012266106010125

Sviridyuk G.A., Bayazitova A.A. On Direct and Inverse Problems for the Hoff Equations on Graph. Journal of Samara State Technical University. Ser. Physical and Mathematical Sciences, 2009, no. 1 (18), pp. 6-17.

Manakova N.A., Dylkov A.G. Optimal Control of the Solutions of the Initial-Finish Problem for the Linear Hoff Model. Mathematical Notes, 2013, vol. 94, issue 2, pp. 220-230. DOI: 10.1134/S0001434613070225

Sagadeeva M.A. Dichotomies of the Solutions for the Linear Sobolev Type Equations. Chelyabinsk, 2012. 139 p.

Zagrebina S.A., Moskvicheva P.O. Stability in Hoff Models. LAMBERT Academic Publishing, Saarbrucken, 2012. 75 p.

Sagadeeva M.A. Investigation of Solutions Stability for Linear Sobolev Type Equations. PhD (Math) Thesis. Chelyabinsk, 2006. 120 p.

Keller A.V., Sagadeeva M.A. The Optimal Measurement Problem for the Measurement Transducer Model with a Deterministic Multiplicative Effect and Inertia. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2014, vol. 7, no. 1, pp. 134-138. DOI: 10.14529/mmp140111

Sagadeeva M.A., Sviridyuk G.A. The Nonautonomous Linear Oskolkov Model on a Geometrical Graph: The Stability of Solutions and the Optimal Control Problem. Semigroups of Operators - Springer Proceedings in Mathematics and Statistics, 2015, vol. 113, pp. 257-271. DOI: 10.1007/978-3-319-12145-116

Sagadeeva M.A. Mathematical Bases of Optimal Measurements Theory in Nonstationary Case. Journal of Computational and Engineering Mathematics, 2016, vol. 3, no. 3, pp. 19-32. DOI: 10.14529/jcem160303

Sagadeeva M.A. Degenerate Flows of Solving Operators for Nonstationary Sobolev Type Equations. Bulletin of the South Ural State University. Series: Mathematics. Mechanics. Physics, 2017, vol. 9, no. 1, pp. 22-30. DOI: 10.14529/mmph170103

Sagadeeva M.A., Generalov A.V. Numerical Solution for Non-Stationary Linearized Hoff Equation Defined on Geometrical Graph. Journal of Computational and Engineering Mathematics, 2018, vol. 5, no. 3, pp.61-74. DOI: 10.14529/jcem180306

Buevich A.V., Sagadeeva M.A., Zagrebina S.A. Stability of a Stationary Solution to one Class of Non-autonomous Sobolev Type Equations. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2023, vol. 16, no. 3, pp. 77-86. DOI: 10.14529/mmp230305

Sagadeeva M.A., Zagrebina S.A. Stability of a Stationary Solution to Non-Autonomous Linearized Hoff Model on a Geometrical Graph. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2024, vol. 17, no. 2, pp. 40-50. DOI: 10.14529/mmp240204

Gross J., McAllister T. Structural Fire Response and Probable Collapse Sequence of the World Trade Center Towers. Federal Building and Fire Safety Investigation of the World Trade Center Disaster (NIST NCSTAR 1-6)}. National Construction Safety Team Act Reports (NIST NCSTAR), National Institute of Standards and Technology, Gaithersburg, MD, 2005. [Electronic resource]. - https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=909181 (Access date: November 15, 2024)

McAllister T., Gann R., Averill J., Gross J., Grosshandler W., Lawson J., McGrattan K., Pitts W., Prasad K., Sadek F., Nelson H. Structural Fire Response and Probable Collapse Sequence of World Trade Center Building 7 (Volume 1). Federal Building and Fire Safety Investigation of the World Trade Center Disaster (NIST NCSTAR 1-9). National Construction Safety Team Act Reports (NIST NCSTAR), National Institute of Standards and Technology, Gaithersburg, MD, 2008. [Electronic resource].- https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=909256 (Access date: November 15, 2024)


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