GENERALIZED MATHEMATICAL MODEL IN THE CALCULATION METHODS OF VIBRATION INSULATION OF MACHINES

Details

Parent Category: Geo-Technical Mechanics, 2015

Category: Geo-Technical Mechanics, 2015, Issue 121

UDC 678.4.06:621:81

Authors:

Kobets A.S., D. Sc. (Ec.), Professor (DSAEU),

Dyrda V.I., D. Sc. (Tech.), Professor (IGTM NAS of Ukraine),

Kobets A.N., Ph. D. (Tech.), Associate Professor

Tolstenko A.V., Ph. D. (Tech.) (DSAEU)

Abstract.

We consider two mathematical models, mostly compliant with existing physical models, and dynamic processes occurring in real machines. The first model is based on the Fokker-Planck equation and takes into account the non-linearity of vibration insulation system and stationary stochastic fluctuations; it is complex and not quite fully takes into account the rheological characteristics of the material, including the impact of aging and the impact of external aggressive environment. The second model is based on the integral relationships of Boltzmann-Volterra, adequately takes into account the rheological characteristics of the material and non-linearity, and stochastic fluctuations. As an example the dynamics of one-mass system is considered with elastic characteristics varying with time of work; material damage is determined by the method of Walpole. There is a satisfactory agreement between the calculated and experimental results.

Keywords:

Fokker-Planck equation, Boltzmann-Volterra model, rheological characteristics of rubber, dynamics of elastic system

References:

1. Bulat, A.F., Dyrda, V.I., Zviagilskii, E.L. and Kobetc, A.S. (2012), Prikladnaya mekhanika uprugo-nasledstvennykh sred. Tom 2. Metody rascheta elastomernykh detalei [Applied mechanics of elastic-hereditary media. Vol. 2. Design techniques of elastomeric parts], Naukova dumka, Kiev, Ukraine.

2. Samekha, M. and Sankar, T. (1980), “Dynamic acceptance testing of machine tools based on nonlinear model”, Konstruirovaniye, vol. 102, no. 1, pp. 45-51.

3. Smirnov, V.I. (2004), “Seismic isolation for newly designed and strengthening of existing buildings”, Seysmostoykoye stroitel'stvo. Bezopasnost' sooruzheniy, no. 4, pp. 49-54.

About the authors:

Kobets Anatoly Stepanovich, Doctor of Economical Sciences (D. Sc.), Professor, Prex, Dnepropetrovsk State Agrarian and Economic University (DSAEU), Dnepropetrovsk, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.

Dyrda Vitaly Illarionovich, Doctor of Technical Sciences (D. Sc.), Professor, Head of Department of Elastomeric Component Mechanics in Mining Machines, M.S. Polyakov Institute of Geotechnical Mechanics under the National Academy of Science of Ukraine (IGTM, NASU), Dnepropetrovsk, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.

Kobets Aleksandr Nikolaevich, Candidate of Technical Sciences (Ph. D.), Associate Professor, Head of Department of agricultural machinery in Dnepropetrovsk State Agrarian and Economic University (DSAEU), Dnepropetrovsk, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.

Tolstenko Alexandr Vasil’yevich, Candidate of Technical Science (Ph. D.), Associate Professor of Department «Reliability and repair of machinery», Dnepropetrovsk State Agrarian and Economic University (DSAEU), Dnepropetrovsk, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.

 

 

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