DETERMINING PARAMETERS OF DYNAMIC IMPACT IN THE PLATE OF BALLASTLESS TRACK
Authors: Vinogradov V. V. , Bykov Y. A. , Kovalenko N. I. 
Published: October 2022

[For the English abstract and full text of the article please see the attached PDF-File (English version follows Russian version)].ABSTRACT A mathematical model of wave surface propagation in the flat element, which is a carrier plate of ballastless track under dynamic action of wheel set, is demonstrated. An algorithm of accounting different rheological properties of interacting bodies, based on the analytical method of representation of unknown quantities in the form of expansions in terms of spatial coordinates and time, initial and boundary conditions, is offered. The method of constructing a wave pattern in the plate is based on the principle of superposition of two separate tasks: contact problem of initial dynamic load application and wave plate deformation problem over time, including through the dissemination of elastic waves with finite speeds. In the article the wave problem is solved in an analytical form for displacement functions. Keywords: dynamic impact, plate Uflyand-Mindlin-Reissner, elastic waves, orthotropic properties, spherical functions, ballastless railway track. REFERENCES 1.Abrate, S.Localized impact on sandwich structures with laminated facing.Applied Mechanics Reviews, 1997, Vol.50, Iss.2, pp.69-82. 2.Sycheva, A.V., Loktev, A.A., Zaletdinov, A. V.Calculation of depression in the subgrade surface [Raschet osadki polotna zheleznodorozhnogo puti ot dejstvija dinamicheskoj nagruzki s pomoshh’ju luchevogo metoda].Nelinejnyj mir, 2013, Iss.11, pp.67-76. 3.Loktev, A. A.Dynamic contact of a spherical indenter and a prestressed orthotropic Uflyand-Mindlin plate.Acta Mechanica, 2011, Vol.222, Iss.1-2, pp.17-25. 4.Olsson, R., Donadon, M.V., Falzon, B. G.Delamination threshold load for dynamic impact on plates.International Journal of Solids and Structures, 2006, Vol. 43, pp. 3124-3141. 5.Thomas, T. Y.Plastic Flow and Fracture in Solids.N.Y.; L.: Acad.Press, 1961. 6.Achenbach, J.D., Reddy, D. P.Note on wave propagation in linear viscoelastic media.Zeitschrift für angewandte Mathmetik and Physik, 1967, Vol.18, pp.141-144. 7.Biryukov, D.G., Kadomtsev, I. G.Elastic plastic nonaxisymmetric impact of parabolic body on a spherical shell [Uprugoplasticheskij neosesimmetrichnyj udar parabolicheskogo tela po sfericheskoj obolochke].Prikladnaja matematika i teoreticheskaja fizika, 2005, Vol.46, Iss.1, pp.181-186. 8.Zaletdinov, A.V., Loktev, A. A.Defining interaction points of direct and reflected waves in a plate [Opredelenie tochek vzaimodejstvija prjamyh i otrazhennyh voln v plastinke].Vestnik MGSU, 2010, Iss.4, pp.92-98. 9.Malekzadeh, K., Khalili, M.R., Olsson, R., Jafari, A.Higher-order dynamic response of composite sandwich panels with flexible core under simultaneous low-velocity impacts of multiple small masses.International Journal of Solids and Structures, 2006, Vol.43, pp.6667-6687. 10.Agostinacchio, M., Ciampa, D., Diomedi, M., Olita, S.Parametrical analysis of the railways dynamic response at high speed moving loads.Journal of Modern Transportation, 2013, Vol.21, Iss.3, pp.169-181. 11.Abrate, S.Modelling of impact on composite structures.Compos Structures, 2001, Vol.51, pp.129-138.