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The paper regarded free vibrations of a plate elastically clamped at  edges with thin-walled open profile rods and pivotally supported on  edges


compressed stretched free vibrations frequency elastic pinching hinged torsional bending reinforced non-reinforced edged stiffness

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How to Cite
N. Melikulov, & А.Otakulov. (2020). Unloaded plates free vibrations, supported by elastic thin-walled rods. International Journal on Orange Technologies, 2(11), 14-16.


  1. The generalized dimensionless elastic pinching coefficients and edges elastic support of the plate presented in the work take into account not only the mechanical and plate geometric parameters and thin-walled rods, but also different boundary conditions at the latter ends, a detailed attaching way the rods to the plate, as well as the longitudinal forces influence transmitted to the ribs. An essential feature of these coefficients is their dependence on the half-wave’ number of the plate curvature.
  2. It is shown that taking into account the constrained torsion in the reinforcing ribs not only significantly increases the load critical parameters, but can also qualitatively change the curvature shape of the middle surface.
  3. The warping restriction of the reinforcing ribs ends, as well as the elastic discrete warping presence bonds located along the rod axis, significantly increases the “plate - ribs” overall rigidity system and its natural vibrations frequency in comparison with free warping case of end sections and the warping connections absence.
  4. References
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  6. A.S. Volmir. Stability of elastic systems. M.Fiz.mat.giz. 1967
  7. A.P. Filippov. Oscillations of elastic systems. K. Publishing House of A.N. Ukrainian SSR 1955
  8. E.A.Beilin, N.M. Melikulov. On the rectangular plates’ stability reinforced with thin-walled rods. –In the book: Construction mechanics and structures calculation: Scientific and technical journal. M. Publishing house of literature on construction. 1980, № 5.р.38-42
  9. N.M. Melikulov. The stability investigation and plates stiffness, reinforced with thin-walled rods, under various loading conditions, - In the book: Structural structures mechanics. Interuniversity, topic collection of tr-L.LISY, 1980. р. 76-85
  10. Muszkowska H. Plyty prostokatne o dwoch krawedziach przeciwleglych swobodnie podparnech i pozostalech sprezyscie zamocowanech. Prace Naykowe Insnytutu Budownictwa Politechniki Wroclawskcy.1973,Nr.11.
  11. Ferachian R.H. Back ling of biaxial le compressed long rectangular plates elastically restrained along the long edges and simply supported along the short edges. Proc. Inst. Engrs. Part 2. Montreal, 1975