Nonlinear Dynamics : міжнародна конференція
Постійне посилання на розділhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/24521
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Документ Investigation of the Parametric Vibrations of Laminated Plates by RFM(NTU "KhPI", 2016) Kurpa, Lidiya; Mazur, Olga; Tkachenko, VictoriaThe R-functions theory is applied to study free vibration and dynamic instability of the symmetrically laminated plates subjected to combined static and periodic axial forces. It is assumed that subcritical state of the plate may be inhomogeneous. Theoretical formulation is made on the classical plate theory (CTP). The developed approach is based on combined application of Ritz’s method, Galerkin procedure, R-functions theory and Bolotin’s method. The buckling, instability zones and response curves for laminated plate with different external cutouts are presented and discussed. Effects of plate geometrical parameters, parking of layers, mechanical characteristics of the material on buckling, natural frequencies and parametric resonance are also studied.Документ Application of the Variational-Structural Method to Investigate the Elasto-Plastic Bending of Thin Shells and Plates(NTU "KhPI", 2016) Morachkovska, Irina; Timchenko, Galina; Lyubitska, KaterynaThe effective method basing on theory of R-functions and variational structural method is developedfor solving non-linear boundary problems. Elastic-plastic bending of thin shallow shells is considered. The problems are reduced to finding stationary points of suggested mixed variational functionals according to the initial linearization due to usage of subsequent loading and Newton-Kantorovich jointly with method of varying elastic parameters. The method is used for automatic calculations in «POLE» programming system for investigations of shell structural elements. The numerical justification of the method is given. New laws of nonlinear deformation of shallow shells and plates with complex shapes in plane are established.Документ Application of the R-Functions Theory to Problems of Nonlinear Dynamics of Laminated Composite Shallow Shells and Plates: Review(NTU "KhPI", 2016) Kurpa, LidiyaA review of studies performed using the R-functions theory to solve problems of nonlinear dynamics of plates and shallow shells is presented. The systematization of results and studies for the problems of free and parametric vibrations and for problems of static and dynamic stability is fulfilled. Expansion of the developed original method of discretization for nonlinear movement equations on new classes of nonlinear problems is shown. These problems include researches of vibrations of antisymmetric laminated cylindrical and spherical panels; laminated composite shallow shells with variable thicknesss of the layers; functionally graded (FG) shallow shells and others. The basic issues that arise when using RFM are described. The future prospects of using the theory of R-functions for solving problems of nonlinear dynamics of plates and shallow shells with complex form are formulated. First of all this is an algorithms development and creation of the associated software to apply multi-modes approximations; improvement of approximation tools for nonlinear problems; investigation of the cracked functionally graded shallow shells; FG panels under thermal environments; parametric vibrations, static and dynamical stability of the multilayered and FG plates and shells.