Structural Mechanics of Engineering Constructions and BuildingsStructural Mechanics of Engineering Constructions and Buildings1815-52352587-8700Peoples’ Friendship University of Russia (RUDN University)1864810.22363/1815-5235-2018-14-2-132-141Research ArticleThe dynamic stability of physically nonlinear plate systems under biaxial compressionIvanovSergey Pavlovich<p>Doctor of Science, Professor, Head of Department of Strength of Materials and Applied Mechanics, the Volga State University of Technology; Professor of Department of Electro-Mechanics, the Mari State University. He is the author of 147 scientific articles, 2 monographs, 4 textbooks, 20 names of educational literature. General research interests: strength, stability and vibrations analyses of the physically and geometric nonlinear rods, plates and plate systems</p>sp-ivanov@mail.ruIvanovOleg Gennadevich<p>Cand. Sc, Assistant Professor, Associate Professor of the Department of Strength of Materials and Applied Mechanics, the Volga State University of Technology. He is the author of 35 scientific articles, 1 monograph, 6 names of educational literature. General research interests: strength and stability analyses of the physically nonlinear plates and plate systems resting on elastic foundation</p>IvanovOG@volgatech.netIvanovaAnastasia Sergeevna<p>Aspirant, Senior Lecturer of the Department of Strength of Materials and Applied Mechanics, the Volga State University of Technology. At the present time she works on the Candidate's dissertation «The dynamic stability of physically nonlinear rods, plates and plate systems» in the specialty 05.23.17 - Structural Mechanics. She is the author of 15 scientific articles, 1 name of educational literature. General research interests: stability analyses of the physically nonlinear rods, plates and plate systems</p>ivanova-a-s@list.ruVolga State University of TechnologyMari State University1512201814213214106062018Copyright © 2018, Ivanov S.P., Ivanov O.G., Ivanova A.S.2018<p>The article presents the method of dynamic stability analysis of plate systems with nonshifting ribs. A plate system under the biaxial dynamic compression loads is considered. The Kirchhoff - Love hypotheses, the nonlinear-elastic body hypothesis are considered the basis of the calculations. The material of the plate system is assumed to be physically nonlinear, stress-deformation diagram is approximated in the form of a cubic polynomial. The displacement of points in normal direction to middle plane of plates is presented in the form of Vlasov expansion. To derive the basic differential equations of stability, the strainenergy method and Vlasov's variation method are used. The extreme value of total energy of the system is defined using Euler - Lagrange equation, after solving of which the set of basic nonlinear differential equations of buckling of the plate system with non-shifting ribs under dynamic compression loads is given. As an example, the stability calculation of physically nonlinear T-shaped plate system hinge-supported along the contour is carried out. Buckling of the plate system occurs longitudinally on one half-wave of sinusoid. At the solution of a task in the first approximation, a nonlinear differential equation is derived, the numerical integration of which was carried out by the Runge - Kutta method. Based on the results of the calculations, graphs of the relative magnitude of deflection against the dynamic coefficient are plotted. The influence of the degree of physical nonlinearity of the material, the rate of change of the dynamic compressive load on the dynamic criterion of buckling of the plate system was studied.</p>dynamic stabilityphysical nonlinearityplateplate systemcompression loadstrain-energy methodvariation method of Vlasovдинамическая устойчивостьфизическая нелинейностьпластинапластинчатая системасжимающая нагрузкаэнергетический методвариационный метод Власова[Volmir, A.S. (1967). Stability of deformable systems, Moscow: Science, 984 p. (In Russ.)][Trushin, S.I., Zhuravleva, T.A., Sysoeva, E.V. (2016). Dynamic buckling of nonlinearly deformable reticulate plates from composite material with different lattice configurations, Nauchnoe Obozrenie, No 4, p. 44–51. (In Russ.)][Vescovini, R., Dozio, L. (2015). Exact refined buckling solutions for laminated plates under uniaxial and biaxial loads, Composite Structures, Vol. 127, p. 356–368.][Nazarimofrad, E., Barkhordar, A. (2016). 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Vlasova k resheniyu nelinejnykh zadach plastinchatykh system: Monographiya, Yoshkar-Ola: PGTU, 248 p. (In Russ.)][Lukash, P.A. (1978). Osnovy nelinejnoj stroitel’noj mekhaniki, Moscow: Strojizdat, 204 p. (In Russ.)][Vlasov, V.Z. (1958). Tonkostennye prostranstvennye sistemy, Moscow: Gosstrojizdat, 502 p. (In Russ.)][Ivanov, S.P., Ivanova, A.S. (2015). The static stability of plates and plate systems with nonshifting ribs under biaxial compression, Structural Mechanics of Engineering Constructions and Buildings, No 4, p. 63–67. (In Russ.)]