Dynamic vibration extinguished on a viscously elastic base

• Autorzy: Ishmamatov M. , Kulmuratov N. , Khalilov S. , Akhmedov N.

Identyfikatory

DOI

10.2478/ijame-2021-0016

• Języki publikacji: EN

Abstrakty

EN

The aim of the work is to develop algorithms and a set of programs for studying the dynamic characteristics of viscoelastic thin plates on a deformable base on which it is installed with several dynamic dampers. The theory of thin plates is used to obtain the equation of motion for the plate. The relationship between the efforts and the stirred plate obeys in the hereditary Boltzmann Voltaire integral. With this, a system of integro-differential equations is obtained which is solved by the method of complex amplitudes. As a result, a transcendental algebraic equation was obtained to determine the resonance frequencies, which is solved numerically by the Muller method. To determine the displacement of the point of the plate with periodic oscillations of the base of the plate, a linear inhomogeneous algebraic equation was obtained, which is solved by the Gauss method. The amplitude - frequency response of the midpoint of the plate is constructed with and without regard to the viscosity of the deformed element. The dependence of the stiffness of a deformed element on the frequency of external action is obtained to ensure optimal damping of vibrational vibrations of the plate.

Słowa kluczowe

EN

dynamic damper; oscillations; viscoelastic plate; integro-differential equation; amplitude-frequency dependence; Boltzmann-Voltaire integral

PL

tłumik dynamiczny; oscylacja; lepkosprężystość

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2021
• Tom: Vol. 26, no. 2
• Strony: 1--10
• Opis fizyczny: Bibliogr. 26 poz., wykr.

Twórcy

autor

Ishmamatov M.

• Navoi State Mining Institute, Higher Mathematics Department, Galaba Shokh Street, Navoi, UZBEKISTAN

autor

Kulmuratov N.

• Navoi State Mining Institute, Mechanical Engineering Department, Galaba Shokh Street, Navoi UZBEKISTAN

autor

Khalilov S.

• Navoi State Mining Institute, Higher Mathematics Department, Galaba Shokh Street, Navoi, UZBEKISTAN

autor

Akhmedov N.

• Navoi State Mining Institute, Higher Mathematics Department, Galaba Shokh Street, Navoi, UZBEKISTAN

Bibliografia

• [1] Frolova KV (ed) (1981): Vibration in Technology: Handbook.– In: Protection from Vibration and Shock, Frolova KV (ed), Mechanical Engineering, Moscow, vol.6.
• [2] Tokarev M.F., Talitskiy E.N. and Frolov V.A. (1984): Mechanical influences and protection of electronic equipment (in Russian).– Moscow, Radio and Communication.
• [3] Nashif A.D., Jones D.I. and Henderson J.P. (1985): Vibration Damping.– John Wiley and Sons.
• [4] Mirsaidov M.M., Safarov I.I. and Teshaev M.Kh. (2019): Oscillations of multilayer viscoelastic composite toroidal pipes.– Journal of the Serbian Society for Computational Mechanics, vol.13, No.2, pp.105-116 10.24874/jsscm.2019.13.02.08.
• [5] Maiboroda V.P., Troyanovskii I.E., Safarov I.I., Vazagashvili M.G. and Katalymova I.V. (1992): Wave attenuation in an elastic medium.– Journal of Soviet Mathematics, vol.60, pp.1379-1382.
• [6] Maiboroda V.P., Safarov I.I. and Troyanovskii I.E. (1983): Free and forced oscillations of a system of rigid bodies on inhomogeneous viscoelastic snubbers.– Soviet Machine Science, pp.25-31.
• [7] Mirsaidov M.M., Safarov I.I., Teshaev M.K. and Boltayev Z.I. (2020): Dynamics of structural - inhomogeneous coaxial-multi-layered systems cylinder-shells.– Journal of Physics: Conference Series, vol.1706, No.1, Article number: 012033.
• [8] Marano G.C., Greco R. and Sgobba S. (2010): A comparison between different robust optimum design approaches: Application to tuned mass dampers.– Probabilistic Engineering Mechanical, vol.25, pp.108-118. https://doi.org/10.1016/j.probengmech.2009.08.004.
• [9] Qiu Z. and Wang X. (2003): Comparison of dynamic response of structures with uncertain-but-bounded parameters using no probabilistic interval analysis method and probabilistic approach.– Int. J. Solids Struct., vol.40, pp.5423-5439. https://doi.org/10.1016/S0020-7683(03)00282-8.
• [10] Muscolino G. and Sofi A. (2013): Bounds for the stationary stochastic response of truss structures with uncertain-but-bounded parameters.– Mech. Syst. Signal Process, vol.37, pp.163-181, https://doi.org/10.1016/j.ymssp.2012.06.016.
• [11] Antoniadis I.A., Kanarachos S.A., Gryllias K. and Sapountzakis I.E. (2018): KDamping: A stiffness based vibration absorption concept.– Journal Vib. Control, vol.24, pp.588-606, https://doi.org/10.1177/1077546316646514.
• [12] Kofanov Yu.N., Shalumov A.S., Goldin V.V. and Zhuravsky V.G. (2000): Mathematical modeling of radio-electronic devices under mechanical influences.– Moscow: Radio and Communication, p.226.
• [13] Capatti M.C., Carbonari S. and Gara F. (2016): Experimental study on instrumented micro piles.– Environmental, Energy and Structural Monitoring Systems (EESMS), 2016 IEEE Workshop, pp.1-6, DOI: 10.1109/EESMS.2016.7504831.
• [14] Adamo F. (2014): Assessment of the uncertainty in human exposure to vibration: an experimental study.– IEEE Sensors Journal, vol.14, No.2, pp.474-481. DOI: 10.1109/JSEN.2013.2284257.
• [15] Palacios-Quiñonero F. and Karimi H.R. (2013): Passive-damping design for vibration control of large structures.– Control and Automation (ICCA), 10th IEEE International Conference, pp.33-38. DOI: 10.1109/ICCA.2013.6565018.
• [16] Zhang X., Sun D., Song Y. and Yan B. (2010): Dynamics characteristic study of the visco-elastic suspension system of construction vehicles.– Technology and Innovation Conference, ITIC 2009, pp.1-4. DOI: 10.1049/cp.2009.1508.
• [17] Sahu S.K. and Datta P.K. (2003). Dynamic stability of laminated composite curved panels with cutouts.– Journal of Engineering Mechanics, vol.29, No.11, pp.1245-1253.
• [18] Korenev B.G. and Reznikov L.M. (1988): Dynamic Vibration Dampers: Theory and Technical Applications.– Science, Fizmatgiz, Moscow.
• [19] Il'yushin A.A. and Pobedrya B.E. (1970): Fundamentals of the Mathematical Theory of Thermoviscoelasticity.– Science, Moscow, p.280.
• [20] Mirsaidov M., Safarov I. and Teshaev M. (2020): Dynamic instability of vibrations of thin-wall composite curvorine viscoelastic tubes under the influence of pulse pressure.– E3S Web of Conferences, pp.164.
• [21] Koltunov A.A. and Maksudov R. (1976): Dynamic stability of a flexible viscoelastic cylindrical shell.– Polymer Mechanics, vol.12, No.5, pp.829-831.
• [22] Safarov I., Teshaev M., Toshmatov E., Boltaev Z. and Homidov F. (2020): Torsional vibrations of a cylindrical shell in a linear viscoelastic medium.– IOP Conference Series: Materials Science and Engineering, vol.883, No.1, Article number 012190.
• [23] Sayfidinov O. and Bognár G.V. (2021): Numerical solutions of the Kardar-Parisi-Zhang interface growing equation with different noise terms.– In: Jármai K. and Voith K. (eds) Vehicle and Automotive Engineering 3, VAE 2020, Lecture Notes in Mechanical Engineering, Springer, Singapore. https://doi.org/10.1007/978-981-15-9529-5_27.
• [24] Mirsaidov M., Safarov I., Boltayev Z. and Teshaev M. (2020): Spread waves in a viscoelastic cylindrical body of a sector cross section with cutouts.– IOP Conference Series: Materials Science and Engineering, vol.869, No.4, Article number 042011.
• [25] Boltaev Z., Safarov I. and Razokov T. (2020): Natural vibrations of spherical inhomogeneity in a viscoelastic medium.– International Journal of Scientific and Technology Research, vol.9, No.1, pp.3674-3680.
• [26] Teshaev M., Safarov I.I. and Mirsaidov M. (2019): Oscillations of multilayer viscoelastic composite toroidal pipes.– J. Serbian Soc. Comput. Mech., vol.13, pp.104-115.