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Explicit Formulas for Optimum Parameters of Viscoelastic-type Tuned Mass Dampers

Yıl 2024, , 346 - 357, 24.03.2024
https://doi.org/10.17798/bitlisfen.1412550

Öz

Tuned mass dampers (TMDs) are passive vibration control devices that are attached to a primary system to reduce the dynamic vibrations under exciting motion. The Voigt-type TMD, which is the most widely used one, is known as a standard model of dynamic vibration absorber (DVA). The purpose of this study is to improve the vibration control performance of passive control devices by using viscoelastic-type tuned mass dampers (V-TMDs). The study adopts the Zener model to represent the viscoelastic behavior of V-TMD. In this study, the fixed-point method is used to determine the optimum parameters of a V-TMD. The displacement amplification factor (DAF) of the coupled system is obtained in the frequency domain. The optimal parameters of the V-TMD system attached to an undamped single degree-of-freedom (sdof) main system are obtained by minimizing the DAF (symbolized with 𝛽) under the effect of base excitation. The optimum parameters, such as damping ratio (ξ) and stiffness ratio (𝜅) of the coupled system are derived, and explicit expressions corresponding to the optimum parameters are presented for engineering designs. Moreover, the change in DAF values for different mass ratios (µ) is also discussed. It is proven that V-TMD is very effective in reducing the amplitudes of vibration. The study also provides valuable insights for engineering practitioners who want to design and implement V-TMDs for vibration control applications because accurate expressions, which are simple and easy to use, are derived in order to obtain optimum parameters, and step-by-step procedures are explained.

Kaynakça

  • [1] H. Frahm, Device for Damping Vibrations of Bodies. US Patent No. 989, 958, 1911.
  • [2] J. Ormondroyd and J. P. Den Hartog, "The Theory of Dynamic Vibration Absorber," Journal of Applied Mechanics, vol.50, pp. 9-22, 1928.
  • [3] J. P. Den Hartog, Mechanical Vibrations. New York. McGraw-Hill, 1956.
  • [4] S.V. Bakre and R. S. Jangid, "Optimum Parameters of Tuned Mass Damper for Damped Main System, " Structural Control Health Monitoring, vol. 14, no. 3, pp. 448-470, 2007.
  • [5] G. B. Warburton, "Optimum Absorber Parameters for Minimizing Vibration Response," Earthquake Engineering Structural Dynamics, vol. 9, no. 3, pp. 251-262, 1981.
  • [6] G. B. Warburton, "Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters, " Earthquake Engineering Structural Dynamics, vol.10, no. 3, pp. 381-401, 1982.
  • [7] H-C. Tsai and G-C. Lin, "Optimum Tuned-Mass Dampers for Minimizing Steady State Response of Support-Excited and Damped Systems, " Earthquake Engineering Structural Dynamics, vol. 22, no. 11, pp. 957-973, 1993.
  • [8] H-C. Tsai and G-C. Lin, "Explicit Formulae for Optimum Absorber Parameters for Force-Excited and Viscously Damped System, "Journal of Sound and Vibration, vol.176, no. 5, pp. 585-596, 1994.
  • [9] F. Sadek, B. Mohraz, A. W. Taylor and R. M. Chung, "A Method of Estimating the Parameters of Tuned Mass Dampers for Seismic Applications" Earthquake Engineering and Structural Dynamics, vol. 26, no.6, pp. 617-635, 1997.
  • [10] O. Nishihara and T. Asami, "Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers (Minimizations of the Maximum Amplitude Magnification Factors), " Trans. ASME, Journal of Vibration and Acoustics, vol.124, no. 4, pp.576-582, 2002.
  • [11] J. Štěpánek, and J. Máca, "Optimization of Tuned Mass Dampers Attached to Damped Structures - Minimization of Maximum Displacement and Acceleration," Acta Polytechnica CTU Proceedings, vol.30, pp. 98-103, 2021.
  • [12] A.Y.T. Leung and H. Zhang, "Particle Swarm Optimization of Tuned Mass Dampers, " Engineering Structures, vol.31, no.3, pp. 715-728, 2009.
  • [13] H. Cetin, E. Aydin and B. Ozturk, "Optimal Damper Allocation in Shear Buildings with Tuned Mass Dampers and Viscous Dampers, " International Journal of Earthquake and Impact Engineering (IJEIE), vol. 2, no.2, pp. 89-120, 2017.
  • [14] A. Batou and S. Adhikari, "Optimum Parameters of Viscoelastic Tuned-Mass Dampers, " Journal of Sound and Vibration, vol. 445, pp. 17-28, 2019.
  • [15] O. Nishihara, "Exact Optimization of a Three-Element Dynamic Vibration Absorber: Minimization of the Maximum Amplitude Magnification Factor" Journal of Vibration and Acoustics, vol. 141, no. 1, p.011001, 2019.
  • [16] T. Asami and O. Nishihara, "Analytical and Experimental Evaluation of an Air Damped Dynamic Vibration Absorber: Design Optimizations of the Three-Element Type Model, " Journal of Vibration and Acoustics, vol.121, no. 3, pp. 334-342,1999.
  • [17] T. Asami and O. Nishihara, "H2 Optimization of the Three-Element Type Dynamic Vibration Absorbers," Journal of Vibration and Acoustics, vol. 124, no. 4, pp.583-592, 2002.
  • [18] N. D. Anh, N. X. Nguyen and L.T. Hoa, "Design of Three-Element Dynamic Vibration Absorber for Damped Linear Structures," Journal of Sound and Vibration, vol. 332, no. 19, pp. 4482-4495, 2013.
  • [19] O. Araz, "Optimization of Three-Element Tuned Mass Damper for Single Degree of Freedom Structures under Ground Acceleration," El-Cezerî Journal of Science and Engineering, vol. 8, no. 3, pp.1264-1271, 2021.
  • [20] N. W. Tschoegl, The Phenomenological Theory of Linear Viscoelastic Behavior. Berlin Heidelberg. Springer-Verlag ,1989.
Yıl 2024, , 346 - 357, 24.03.2024
https://doi.org/10.17798/bitlisfen.1412550

Öz

Kaynakça

  • [1] H. Frahm, Device for Damping Vibrations of Bodies. US Patent No. 989, 958, 1911.
  • [2] J. Ormondroyd and J. P. Den Hartog, "The Theory of Dynamic Vibration Absorber," Journal of Applied Mechanics, vol.50, pp. 9-22, 1928.
  • [3] J. P. Den Hartog, Mechanical Vibrations. New York. McGraw-Hill, 1956.
  • [4] S.V. Bakre and R. S. Jangid, "Optimum Parameters of Tuned Mass Damper for Damped Main System, " Structural Control Health Monitoring, vol. 14, no. 3, pp. 448-470, 2007.
  • [5] G. B. Warburton, "Optimum Absorber Parameters for Minimizing Vibration Response," Earthquake Engineering Structural Dynamics, vol. 9, no. 3, pp. 251-262, 1981.
  • [6] G. B. Warburton, "Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters, " Earthquake Engineering Structural Dynamics, vol.10, no. 3, pp. 381-401, 1982.
  • [7] H-C. Tsai and G-C. Lin, "Optimum Tuned-Mass Dampers for Minimizing Steady State Response of Support-Excited and Damped Systems, " Earthquake Engineering Structural Dynamics, vol. 22, no. 11, pp. 957-973, 1993.
  • [8] H-C. Tsai and G-C. Lin, "Explicit Formulae for Optimum Absorber Parameters for Force-Excited and Viscously Damped System, "Journal of Sound and Vibration, vol.176, no. 5, pp. 585-596, 1994.
  • [9] F. Sadek, B. Mohraz, A. W. Taylor and R. M. Chung, "A Method of Estimating the Parameters of Tuned Mass Dampers for Seismic Applications" Earthquake Engineering and Structural Dynamics, vol. 26, no.6, pp. 617-635, 1997.
  • [10] O. Nishihara and T. Asami, "Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers (Minimizations of the Maximum Amplitude Magnification Factors), " Trans. ASME, Journal of Vibration and Acoustics, vol.124, no. 4, pp.576-582, 2002.
  • [11] J. Štěpánek, and J. Máca, "Optimization of Tuned Mass Dampers Attached to Damped Structures - Minimization of Maximum Displacement and Acceleration," Acta Polytechnica CTU Proceedings, vol.30, pp. 98-103, 2021.
  • [12] A.Y.T. Leung and H. Zhang, "Particle Swarm Optimization of Tuned Mass Dampers, " Engineering Structures, vol.31, no.3, pp. 715-728, 2009.
  • [13] H. Cetin, E. Aydin and B. Ozturk, "Optimal Damper Allocation in Shear Buildings with Tuned Mass Dampers and Viscous Dampers, " International Journal of Earthquake and Impact Engineering (IJEIE), vol. 2, no.2, pp. 89-120, 2017.
  • [14] A. Batou and S. Adhikari, "Optimum Parameters of Viscoelastic Tuned-Mass Dampers, " Journal of Sound and Vibration, vol. 445, pp. 17-28, 2019.
  • [15] O. Nishihara, "Exact Optimization of a Three-Element Dynamic Vibration Absorber: Minimization of the Maximum Amplitude Magnification Factor" Journal of Vibration and Acoustics, vol. 141, no. 1, p.011001, 2019.
  • [16] T. Asami and O. Nishihara, "Analytical and Experimental Evaluation of an Air Damped Dynamic Vibration Absorber: Design Optimizations of the Three-Element Type Model, " Journal of Vibration and Acoustics, vol.121, no. 3, pp. 334-342,1999.
  • [17] T. Asami and O. Nishihara, "H2 Optimization of the Three-Element Type Dynamic Vibration Absorbers," Journal of Vibration and Acoustics, vol. 124, no. 4, pp.583-592, 2002.
  • [18] N. D. Anh, N. X. Nguyen and L.T. Hoa, "Design of Three-Element Dynamic Vibration Absorber for Damped Linear Structures," Journal of Sound and Vibration, vol. 332, no. 19, pp. 4482-4495, 2013.
  • [19] O. Araz, "Optimization of Three-Element Tuned Mass Damper for Single Degree of Freedom Structures under Ground Acceleration," El-Cezerî Journal of Science and Engineering, vol. 8, no. 3, pp.1264-1271, 2021.
  • [20] N. W. Tschoegl, The Phenomenological Theory of Linear Viscoelastic Behavior. Berlin Heidelberg. Springer-Verlag ,1989.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Yapı Dinamiği
Bölüm Araştırma Makalesi
Yazarlar

Mehmet Ali Kösen 0009-0002-8823-7944

Gülçin Tekin 0000-0003-0207-4305

Erken Görünüm Tarihi 21 Mart 2024
Yayımlanma Tarihi 24 Mart 2024
Gönderilme Tarihi 31 Aralık 2023
Kabul Tarihi 28 Şubat 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

IEEE M. A. Kösen ve G. Tekin, “Explicit Formulas for Optimum Parameters of Viscoelastic-type Tuned Mass Dampers”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, c. 13, sy. 1, ss. 346–357, 2024, doi: 10.17798/bitlisfen.1412550.



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