Застосування в автоматиці підкріплених еліпсоїдальних оболонок під дією нестаціонарного навантаження

Authors

  • Н. В. Майбородіна
  • В. П. Герасименко

Abstract

USE IN AUTOMATION SUPPORTED ELLIPSOIDAL SHELLS UNDER NONSTATIONARY LOAD

N. Mayborodina, V. Gerasymenko

 

Design of thin-walled shell-type are a wide class of objects, which are used in modern automation, electrical engineering, radio, radar, and other branches of modern technology. The most studied are the problem of harmonic oscillations of reinforced shells of simple geometry (cylindrical, conical, spherical). Needs theory and modern technology: the study of dynamic behavior of reinforced shells of complicated geometry.

The purpose of the research is to analyze the problem of forced vibrations of discretely supported by cross ribs ellipsoidal shell under a nonstationary load.

The process of forced vibrations of ellipsoidal shell are discussed in the framework of hyperbolic systems of nonlinear differential equations of shell theory of the Timoshenko type. For deformations and stresses used variant of geometrically nonlinear theory of shells Timoshenko type in a quadratic approximation.

At construction of mathematical model of deformation of the first reinforcing ribs directed will proceed from hypotheses not deformed cross-sectional reinforcing element. The deformation ratio for th reinforcing rib is set in the framework of the geometrically nonlinear version of the theory of Timoshenko type in a quadratic approximation. Conditions hard contact between the components of the displacement vector of the center of gravity of the cross section of the ribs and the components of the generalized displacement vector of the middle surface.

Dealt with the problem of forced vibrations of a transversely reinforced part of the ellipsoidal shell. Supported on the shell operates a distributed normal load , ; . Conditions    for the generalized displacement vector is zero.

Geometric design parameters:

, , , , , , .

Transverse reinforcing elements were placed: , .

Physic-mechanical parameters of construction:

, , , , .

In this case   take the values:

1.;     2.;

3.;      4. ;

5..

Physic-mechanical parameters of ribs: ,  , .

The calculations were performed on a time interval . In Fig. 1 shows the curves for the value  at time  for the above five cases, the values of the parameters. Considered the time to reach the maximum value  in absolute value. From the above graphics, you can visually determine the location of ribs and their influence on the strain state of the structure.

 

Fig.1.

For the third option graph close to the graph of the second option. This means that the second option orthotropy corresponds to the isotropic case. The maximum value of the deformation module for the fifth option takes a value 6,5 and isotropic for the third option 3,6, that approximately in 2 times more.

Conclusions

The physical-mechanical parameters significantly affect the strain state elfadel orthotropic discretely reinforced shells under nonstationary loads.

References

Свободные колебания элементов оболочечных конструкций / [Григоренко Я. М., Беспалова Е. ?., Китайгородский А. Б., Шинкарь А. ?.]. – К. : Наук. думка, 1986. – 172 с.

Мейш В. Ф. К расчету неосесимметричных колеба¬ний дискретно подкрепленных поперечными ребрами гибких эллипсои¬дальных оболочек при нестационарных нагрузках / В. Ф. Мейш, Н. В. Майбородина // Прикл. механика. – 2008. – № 10. – С. 63–73.

Самарский А. А. Теория разностных схем / А. А. Самарский. – М. : Наука, 1977. – 656 с.

Mohamad S. Q. Recent research advances in the dynamic behavior of shells: 1989–2000, Part 2: Homogeneous shells // Appl. Mech. Rev. – September 2002. – Volume 55, Issue 5. P. 415–435.

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Published

2017-02-24

Issue

No. 242 (2016)

Section

Статті

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