Analysis of Nonlinear Cyclically Symmetric Isolation Sistem of a Cargo in a Container under Plane Harmonic Vibrations

Authors: Belkin A.E., Dashtiev I.Z., Nikitin E.A. Published: 20.12.2021
Published in issue: #4(139)/2021  

DOI: 10.18698/0236-3941-2021-4-32-50

Category: Mechanical Engineering and Machine Science | Chapter: Machine Science  
Keywords: vibration isolation, isolation ring, polyure-thane shock absorbers, mathematical model, nonlinear vibration theory, harmonic linearization

The problem of calculating the system of a cylindrical shaped load transverse damping installed in a coaxial container is considered. This system has several annular belts of insulation with a cyclically symmetric arrangement of shock absorbers along the circumferential direction. A simple dynamic model of one insulation belt formed by polyurethane tunnel-type shock absorbers is investigated. Such shock absorbers have a high energy absorption coefficient and can operate at very high drafts comparable to their height, which is important when the space between the cargo and the container wall is limited. Within the proposed model framework, a harmonic nonlinear analysis of cargo plane oscillations under kinematic excitation coming from the container is considered. A method for reducing a nonlinear cyclically symmetric system with discrete elastic elements, which allows limiting the analysis to the calculation of a vibration isolation system with one degree of freedom, is proposed. Using the harmonic linearization procedure, the amplitude-frequency characteristics of oscillations and plots of vibration isolation coefficients of cargo at different values of excitation amplitude have been obtained. The results are verified by comparing the analytical solution with the results of numerical integration for a non-reduced nonlinear system with two degrees of freedom. The obtained solution allows choosing the vibration isolation belt parameters, in particular the number of shock absorbers and their stiffness, depending on the conditions of kinematic excitation and permissible overload


[1] Mendelsohn M.A., Rudd G.E., Rosenblatt G.B. Chemical and engineering properties of polyurethane isolator pads. Ind. Eng. Chem. Prod. Res. Dev., 1975, vol. 14, no. 3, pp. 181--189. DOI: https://doi.org/10.1021/i360055a011

[2] Zhao V., Wang M.J. Size effect on load bearing force of rubber isolator with pre-buckled struts. 2nd Int. Conf. Comp. Eng. Technol., 2010, vol. 5, pp. 522--526. DOI: https://doi.org/10.1109/ICCET.2010.5486177

[3] Alasheev V.I., Belkin A.E., Bobrov A.V., et al. The analysis of a polyurethane tunnel-type shock absorber operating under shock loading. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [BMSTU Journal of Mechanical Engineering], 2017, no. 5, pp. 4--13 (in Russ.). DOI: http://dx.doi.org/10.18698/0536-1044-2017-5-4-13

[4] Bek M., Betjes J., von Bernstorff B.S., et al. Viscoelasticity of new generation thermoplastic polyurethane vibration isolators. Phys. Fluids, 2017, vol. 29, no. 12. DOI: https://doi.org/10.1063/1.5000413

[5] Wu J.H., Li C.H., Chiu H.T., et al. Anti-vibration and vibration isolator performance of poly (styrene-butadiene-styrene) / ester-type polyurethane thermoplastic elastomers. Polym. Adv. Technol., 2010, vol. 21, no. 3, pp. 164--178. DOI: https://doi.org/10.1002/pat.1411

[6] Lv Z.Q., Shu L.H. Shock mechanics model and characteristic analysis of polyurethane isolator with displacement restrictor. Adv. Mat. Res., 2012, vol. 503-504, pp. 972--977. DOI: https://doi.org/10.4028/www.scientific.net/AMR.503-504.972

[7] Ragul᾿skis K.M., ed. Vibrozashchitnye sistemy s kvazinulevoy zhestkost᾿yu [Vibration isolation systems with quasi-zero stiffness]. Leningrad, Mashinostroenie Publ., 1986.

[8] Kruglov Yu.A., Khramov B.A., Kabanov E.N. Sistemy udarovibrozashchity raket, apparatury i oborudovaniya [Shock and vibration isolation systems of missiles, equipment and rigs]. St. Petersburg, BGTU "Voenmekh" Publ., 2010.

[9] Atzrodt H., Mayer D., Melz T. Reduction of bearing vibrations with shunt damping. Proc. 16th ICSV, 2009, p. 7.

[10] Dutt J.K., Toi T. Rotor vibration reduction with polymeric sectors. J. Sound Vib., 2003, vol. 262, no. 4, pp. 769--793. DOI: https://doi.org/10.1016/S0022-460X(02)01081-7

[11] Belkin A.E., Dashtiev I.Z., Nikitin E.A., et al. Physical and mathematical modeling of vibration isolation for cargo in a container with polyurethane shock absorbers. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [BMSTU Journal of Mechanical Engineering], 2018, no. 7, pp. 11 --19 (in Russ.). DOI: http://dx.doi.org/10.18698/0536-1044-2018-7-11-19

[12] Belkin A.E., Dashtiev I.Z., Nikitin E.A. Nonlinear analysis of vibration isolation of a cargo, mounted in a container on tunnel-type polyurethane shock absorbers. Problemy mashinostroeniya i nadezhnosti mashin [Journal of Machinery Manufacture and Reliability], 2019, no. 7, pp. 88--96 (in Russ.).

[13] Panovko Ya.G. Vnutrennee trenie pri kolebaniyakh uprugikh system [Internal friction in vibrating elastic systems]. Moscow, FIZMATGIZ Publ., 1960.

[14] Kolovskiy M.Z. Nelineynaya teoriya vibrozashchitnykh system [Nonlinear theory of vibration protection systems]. Moscow, Nauka Publ., 1966.

[15] Biderman V.L. Teoriya mekhanicheskikh kolebaniy [Mechanical vibrations theory]. Moscow, URSS Publ., 2017.