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Постійне посилання на розділhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/35393
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Документ Application of R-Functions Theory to Study Parametric Vibrations and Dynamical Stability of Laminated Plates(Точка, 2013) Kurpa, Lidiya; Mazur, Olga; Tsukanov, IgorThe problem of nonlinear parametric vibrations and stability analysis of the symmetric laminated plates is considered. The proposed method is based on multimode approximation of displacements and solving series auxiliary linear tasks. The main feature of the work is the application of the R-functions theory, which allows investigating parametric vibrations of plates with complex shape and different boundary conditions.Документ Dynamical instability of laminated plates with external cutout(Elsevier Inc., 2016) Awrejcewicz, Jan; Kurpa, Lidiya; Mazur, OlgaA method to study dynamical instability and non-linear parametric vibrations of symmetrically laminated plates of complex shapes and having different cutouts is proposed. The first-order shear deformation theory (FSDT) and the classical plate theory (CPT) are used to formulate a mathematical statement of the given problem. The presence of cutoutses sentially complicates the solution of buckling problem, since the stress field is non-uniform. At first, a plane stress analysis is carried out using the variational Ritz method and the R-functions theory. The obtained results are applied to investigate buckling and parametric vibrations of laminated plates. The developed method uses the R-functions theory, and it may be directly employed to study laminated plates of arbitrary forms and different boundary conditions. Besides, the proposed method is numerical-analytical, what greatly facilitates a solution of similar-like non-linear problems. In order to show the advantage of the developed approach, instability zones and response curves for the layered cross- and angle-ply plates with external cutouts are constructed and discussed.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.