Klymenko M.I., Grebenyuk S.M., Boguslavska A.M., Hatsenko A.V. Stress-strained state of rubber and rubber-cord vibroinsulators under condition of temperature and nonlinear deformation

Details

Parent Category: Geo-Technical Mechanics, 2018

Category: Collection of scientific papers «Geotekhnicheskaya Mekhanika» Issue 138

Geoteh. meh. 2018, 138, 196-204

DOI: https://doi.org/10.15407/geotm2018.01.196

Stress-strained state of rubber and rubber-cord vibroinsulators under condition of temperature and nonlinear deformation

Klymenko M.I., Grebenyuk S.M., Boguslavska A.M., Hatsenko A.V.

Authors:

Klimenko M.І., cand. Physics and Mathematics, Associate Professor (ZNU)

Grebenyuk S.M., doctor of technical sciences, head of the department (ZNU)

Boguslavska A.M., graduate student (ZNU)

Gatsenko A.V., graduate student (ZNU)

UDC 539.3

Language:Ukrainian

Abstract.

In the article, stress-strained state of vibroinsulators under of various constructive modifications is determined at axial static load and thermal effect. Two types of vibroinsulators – solid rubber and rubber-cord with composite insertion – are considered. Rubber and rubber-based materials have a number of specific characteristics, and due to this classical methods of calculation are not applicable to them. The approaches to determination of the stress-strained state are based on modification of the finite element method – moment scheme of the finite element, which assumes triple approximation of shift fields, components of deformations tensor, and volume change function. This modification takes into account the rubber poor compressibility. Two problems were solved for the cord vibroinsulator. In the first problem, geometrical non-linearity of cord under deformation is taken into account. The system of the solvable equations is obtained on the basis of variational principle with use of tensor of nonlinear deformations. This problem can be solved through iterative process with use of Newton-Kantorovich method. In the second problem, stress-strained state is determined by taking into account rheological characteristics of rubber. Boltzmann-Volterra’s hereditary theory with Rabotnov’s residual kernel is used for describing mechanical behavior of the material. Finding of the solution of this problem is reduced to the iterative solution of the equation system by Newton-Kantorovich method. Problems of linear elasticity and thermoelasticity were solved while determining stress-strained state of the vibroinsulator modification with composite insertion. In this case, global stiffness matrix is formed for rubber and rubber-cord materials separately because of difference of their elastic constants. In case of combined action of power load and temperature, stress tensor components are determined with the help of Duhamel-Neumann thermoelasticity law. Application of the variation principle reduces this problem to the solution of the system the linear algebraic equations, in which right side models temperature effect. Effect of power and temperature factors and mentioned characteristics on parameters of the vibroinsulator deformation is analyzed.

Keywords:

stress-strained state, vibroinsulator, rubber, nonlinearity, viscoelasticity, thermoelasticity, finite element method.

References:

1. Lavendel, E.E. (1976), Raschot rezino-tekhnicheskikh izdeliy [Calculation of rubber products], Mashinostroyeniye, Moscow.

2. Dymnikov, S.I. (1968), “Calculation of rubber-technical parts at medium deformations”, Mekhanika polimerov [Mechanics of polymers], no. 2, pp. 271-275.

3. Bulat, A.F., Dyrda, V.I., Nemchinov, Yu.I., Lisitsa, N.I., Lisitsa, N.N. and Tymko, N.V. (2010), “Vibration protection of machines and structures using rubber blocks Geo-Technical Mechanics, no. 85, pp. 128-132, Dnipro, Ukraine.

4. Dyrda, V.I., Tverdokhleb, T.E., Leesitca, N.I. and Leesitca, N.N. (2010), “Application b-method for calculation rubber-metallical вибро seismoblocks”, Geo-Technical Mechanics, no. 86, pp. 144-158, Dnipro, Ukraine.

5. Suhova, N.A. and Biderman, V.L. (1962), “To the calculation of rubber shock absorbers, working on compression”, Raschety na prochnost [Strength calculations], no. 8, pp. 200-211.

6. Biderman, V.L. and Suhova, N.A. (1968), “Calculation of cylindrical and rectangular long rubber shock absorbers”, Raschety na prochnost [Strength calculations], no. 13, pp. 55-72.

7. Dyrda, V.I., Grebenyuk, S.N. and Gomenyuk S.I. (2012), Analiticheskiye i chislennyye metody rascheta rezinovykh detaley [Analytical and numerical methods for calculating rubber parts], Zaporizhzhya National University, Dnepropetrovsk-Zaporozhye, Ukraine.

8. Kirichevskiy, V.V., Dokhnyak, B.M., Kozub, Yu.G., Gomenyuk, S.I., Kirichevskiy, R.V. and Grebenyuk, S.N. (2005), Metod konechnykh elementov v vychislitel’nom komplekse “MIRELA+” [Finite Element Method in the MIRELA+ Computing Complex], Naukova dumka, Kyiv, Ukraine.

About the authors

Klimenko Mikhailo Ivanovich, Candidate of Physics and Mathematics (Ph.D), Associate Professor of the Department of Fundamental Mathematics in Zaporizhzhya National University (ZNU), Zaporizhzhya, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it. .

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

Boguslavska Alla Mykhailivna, aspirant in Zaporizhzhya National University (ZNU), Zaporizhzhya, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it. .

Hatsenko Anastasia Vadymivya, aspirant in Zaporizhzhya National University (ZNU), Zaporizhzhya, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it. .

• < Prev
• Next >