Bulat A.F., Dyrda V.I., Novikova A.V., Grebenyuk S.M., Lapin V.A., Marienkov M.H. Calculation of thin-layer rubber-metal elements of machines and buildings considering the compressibility of the material

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Parent Category: Geo-Technical Mechanics, 2021

Category: Geo-Technical Mechanics, 2021, № 157

Geoteh. meh. 2021, 157, 19-28

https://doi.org/10.15407/geotm2021.157.019doi.org/10.15407/geotm2021.157.019

 

CALCULATION OF THIN-LAYER RUBBER-METAL ELEMENTS OF MACHINES AND BUILDINGS CONSIDERING THE COMPRESSIBILITY OF THE MATERIAL

¹Bulat A.F., ¹Dyrda V.I., ¹Novikova A.V., ²Grebenyuk S.M., ³Lapin V.A., ⁴Marienkov M.H.

¹Institute of Geotechnical Mechanics named by N. Poljakov of NAS of Ukraine, ²Zaporizhzhia National University, ³Kazakh Research and Design Institute of Construction and Architecture, ⁴SE “State Scientific-Research Institute of Building Constructions”

UDC 678.4.06:621.81

Language: Ukrainian

Abstract. In some constructions with rubber-metal elements, the rubber is loaded in such a way that the hydrostatic stress is tens of times greater than the shear stress. In this case, ignoring the compressibility of rubber can lead to large errors in calculating the elastic and strength parameters of rubber parts. The elastic elements, for which consideration of the material compressibility is essential, include thin-layer rubber-metal elements, whose dimensions in plan are much larger than the thickness. Such rubber-metal elements are used for vibration and seismic protection of heavy machines, buildings and structures.
In this paper, the compression of a thin-layer cylindrical rubber-metal element is considered with taking into account the compressibility of the material. In the calculation, it was assumed that the hydrostatic stress is constant over the thickness of the rubber layer, and also that the rate of change of the displacement components in the middle surface of the layer can be neglected in comparison with the corresponding speed in the direction normal to the layer. These assumptions were substantiated as a result of the analysis of the geometry of deformation and equilibrium conditions of a thin layer of rubber bonded to metal reinforcement.
As a result of applying these assumptions to the solution of the problem set, a boundary value problem is obtained for an ordinary inhomogeneous linear differential equation of the second order. The corresponding homogeneous equation is solved using a power series, the coefficients of which are expressed in terms of the previous ones using a recurrent formula. Finally, a formula with a modified Bessel function of the first kind is obtained for the hydrostatic stress. The analysis of the obtained formula leads to some simplifications for different values of the dimensionless parameter, which connects the bulk modulus and shear modulus, and the radius of the cylindrical element and its thickness.
The resulting axial load on the rubber element is represented by the force that would be perceived by the element in case of uniaxial deformation, i.e. if displacements in cross-sections were prohibited and compression would be performed only due to the change in volume, multiplied by a certain coefficient less than one, which takes into account the decrease in the stiffness of the element due to shear deformation.
The paper also presents the results of experimental studies carried out by the authors for thin-layer cylindrical rubber-metal elements made of medium-filled rubber 2959. An example of calculating the axial load on a thin-layer element considering the compressibility of rubber is given. The obtained axial load value coincides with the experimental results with a sufficient accuracy value.
Keywords: thin-layer rubber-metal element, rubber compressibility, hydrostatic stress, axial load.

REFERENCES:

1. Biderman, V.L. and Mart’yanova, G.V. (1962), “Compression of low rubber shock absorbers and spacers”, Izvestiya AN SSSR. Ser. Mekhanika i mashinostroyeniye, no. 3, pp. 154-158.

2. Dyrda, V.I., Tverdokhleb, T.Ye., Lisitsa, N.I., Lisitsa, N.N., Ryzhkov, I.Ye., Il’yushonok, V.V. and Tymko, N.V. (2005), “Some features of calculation of rubber-metal elements in view of effect of volume compression”, Geo-Technical Mechanics, no. 60, pp. 152-158.

3. Dyrda, V.I., Kalhankov, Ye.V., Tsanidi, I.M., Cherniy, O.A., Tolstenko, O.V., Derkach, O.D. and Kabat, O.S. (2018), “Specificity of rubber-metal elements calculation with taking into account effect of bulk compression”, Geo-Technical Mechanics, no. 138, pp. 160-168. https://doi.org/10.15407/geotm2018.01.160

About the authors:

Bulat Anatolii Fedorovych, Academician of the National Academy of Science of Ukraine, Doctor of Technical Sciences (D.Sc.), Professor, Director of the Institute, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Science of Ukraine, Dnipro, Ukraine,  This email address is being protected from spambots. You need JavaScript enabled to view it.

Dyrda Vitalii Illarionovych, Doctor of Technical Sciences (D. Sc.), Professor, Head of Department of Elastomeric Component Mechanics in Mining Machines, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Science of Ukraine, Dnipro, Ukraine,  This email address is being protected from spambots. You need JavaScript enabled to view it.

Novikova Alina Viacheslavivna, Master of Science, Junior Researcher of Department of Elastomeric Component Mechanics in Mining Machines, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Science of Ukraine, Dnipro, Ukraine,  This email address is being protected from spambots. You need JavaScript enabled to view it.

Grebenyuk Serhii Mykolaiovych, Doctor of Technical Sciences (D. Sc.), Head of the Department of Fundamental Mathematics in Zaporizhzhya National University, Zaporizhzhya, Ukraine,  This email address is being protected from spambots. You need JavaScript enabled to view it.

Lapin Vladimir Alekseevich, Candidate of Technical Sciences (Ph.D.), Director of Center for Scientific Research in Building Industry, Corresponding Member of International Engineering Academy and National Engineering Academy of the Republic of Kazakhstan, Kazakh Research and Design Institute of Construction and Architecture, Almaty, Kazakhstan,  This email address is being protected from spambots. You need JavaScript enabled to view it.

Marienkov Mykola Hryhorovych, Doctor of Technical Sciences (D. Sc.), Head of the Department, State Enterprise “State Research Institute of Building Constructions”, Kyiv, Ukraine,  This email address is being protected from spambots. You need JavaScript enabled to view it.

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