Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Archive of Applied Mechanics
Published in: Archive of Applied Mechanics 2/2020

12-10-2019 | Original

Passive vibration suppression of plate using multiple optimal dynamic vibration absorbers

Authors: M. Ari, R. T. Faal

Published in: Archive of Applied Mechanics | Issue 2/2020

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In the present paper, the optimization problem of the dynamic vibration absorbers (DVAs) for suppressing vibrations in thin plates within the wide frequency band is investigated. It is considered that the plate has simply supported edges and is subjected to a concentrated harmonic force. The vibration suppression is accomplished by the implementation of multiple mass–spring absorbers in order to minimize the plate deflection at the natural frequencies of the plate without absorbers. The governing equations of the plate equipped with DVAs for both isotropic and FG plates are derived and solved numerically and analytically. The formulation of the problem is capable of optimizing the \(L_{2}\) norm of the plate deflection at the wide frequency band with respect to mass, stiffness and position of each absorber attachment point. In this study, the possibility of simultaneous absorption of one or multiple natural frequencies of the plate without any absorbers is also studied. Some numerical results are also presented.
previous article Surface Zener–Stroh crack model to slip band due to contact
next article Two-dimensional elasticity solution for free vibration of simple-supported beams with arbitrarily and continuously varying thickness

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Appendix
Available only for authorised users
Literature
1.
Sun, J.Q., Jolly, M.R., Norris, M.A.: Passive, adaptive and active tuned vibration absorbers—a survey. J. Mech. Des. 117, 234–242 (1995)
2.
Ishida, Y.: Recent development of the passive vibration control method. Mech. Syst. Signal Process. 29, 2–18 (2012)
3.
Kolovsky, M.Z.: Nonlinear Dynamics of Active and Passive Systems of Vibration Protection. Springer, Berlin (2013)
4.
Mahadevaswamy, P., Suresh, B.S.: Optimal mass ratio of vibratory flap for vibration control of clamped rectangular plate. Ain Shams Eng. J. 7, 335–345 (2016)
5.
Megahed, S.M., El-Razik, A.K.A.: Vibration control of two degrees of freedom system using variable inertia vibration absorbers: modeling and simulation. J. Sound Vib. 329, 4841–4865 (2010)
6.
Tursun, M., Eşkinat, E.: H2 optimization of damped-vibration absorbers for suppressing vibrations in beams with constrained minimization. J. Vib. Acoust. 136, 21012 (2014)
7.
Frahm, H.: Device for damping vibrations of bodies. U.S. Patent No. 989,958. U.S. Patent and Trademark Office, Washington, DC (1911)
8.
Ormondroyd, J.: The theory of the dynamic vibration absorber. Trans. ASME Appl. Mech. 50, 9–22 (1928)
9.
Hahnkamm, E.: The damping of the foundation vibrations at varying excitation frequency. Master Archit. 4, 192–201 (1932)
10.
Den Hartog, J.P.: Mechanical Vibrations. Courier Corporation, North Chelmsford (1985)MATH
11.
Vu, X.-T., Nguyen, D.-C., Khong, D.-D., Tong, V.-C.: Closed-form solutions to the optimization of dynamic vibration absorber attached to multi-degrees-of-freedom damped linear systems under torsional excitation using the fixed-point theory. Inst. Mech. Eng. Part K J. Multi-body Dyn. 232, 237–252 (2018)
12.
Hua, Y., Wong, W., Cheng, L.: Optimal design of a beam-based dynamic vibration absorber using fixed-points theory. J. Sound Vib. 421, 111–131 (2018)
13.
14.
Kalehsar, H.E., Khodaie, N.: Optimization of response of a dynamic vibration absorber forming part of the main system by the fixed-point theory. KSCE J. Civ. Eng. 22, 2354–2361 (2018)
15.
Noori, B., Farshidianfar, A.: Optimum design of dynamic vibration absorbers for a beam, based on H\(\infty \) and H2 optimization. Arch. Appl. Mech. 83, 1773–1787 (2013)MATH
16.
Nishihara, O.: Exact optimization of a three-element dynamic vibration absorber: minimization of the maximum amplitude magnification factor. J. Vib. Acoust. 141, 11001 (2019)
17.
Cheung, Y.L., Wong, W.O.: H\(\infty \) and H2 optimizations of a dynamic vibration absorber for suppressing vibrations in plates. J. Sound Vib. 320, 29–42 (2009)
18.
Moradi, H., Sadighi, M., Bakhtiari-Nejad, F.: Optimum design of a tuneable vibration absorber with variable position to suppress vibration of a cantilever plate. Int. J. Acoust. Vib. 16, 55 (2011)
19.
Jacquot, R.G.: Suppression of random vibration in plates using vibration absorbers. J. Sound Vib. 248, 585–596 (2001)
20.
Faal, R.T., Amiri, M.B., Pirmohammadi, A.A., Milani, A.S.: Vibration analysis of undamped, suspended multi-beam absorber systems. Meccanica 47, 1059–1078 (2012)MathSciNetMATH
21.
Yamaguchi, H.: Damping of transient vibration by a dynamic absorber. Trans. Jpn. Soc. Mech. Eng. 54, 561 (1988)
22.
Nishihara, O., Matsuhisa, H.: Design of a dynamic vibration absorber for minimization of maximum amplitude magnification factor (derivation of algebraic exact solution). Trans. Jpn. Soc. Mech. Eng. Ser. C. 63, 3438–3445 (1997)
23.
Esmailzadeh, E., Jalili, N.: Optimum design of vibration absorbers for structurally damped Timoshenko beams. J. Vib. Acoust. 120, 833–841 (1998)
24.
Brown, B., Singh, T.: Minimax design of vibration absorbers for linear damped systems. J. Sound Vib. 330, 2437–2448 (2011)
25.
Fang, J., Wang, S.-M., Wang, Q.: Optimal design of vibration absorber using minimax criterion with simplified constraints. Acta Mech. Sin. 28, 848–853 (2012)MathSciNet
26.
Fang, J., Wang, Q., Wang, S., Wang, Q.: Min-max criterion to the optimal design of vibration absorber in a system with Coulomb friction and viscous damping. Nonlinear Dyn. 70, 393–400 (2012)MathSciNet
27.
Anh, N.D., Nguyen, N.X.: Design of non-traditional dynamic vibration absorber for damped linear structures. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 228, 45–55 (2014)
28.
Zilletti, M., Elliott, S.J., Rustighi, E.: Optimisation of dynamic vibration absorbers to minimise kinetic energy and maximise internal power dissipation. J. Sound Vib. 331, 4093–4100 (2012)
29.
Yang, C., Li, D., Cheng, L.: Dynamic vibration absorbers for vibration control within a frequency band. J. Sound Vib. 330, 1582–1598 (2011)
30.
Wang, Y.Z., Wang, K.S.: The optimal design of a dynamic absorber for an arbitrary planar structure. Appl. Acoust. 23, 85–98 (1988)
31.
Viana, F.A.C., Kotinda, G.I., Rade, D.A., Steffen Jr., V.: Tuning dynamic vibration absorbers by using ant colony optimization. Comput. Struct. 86, 1539–1549 (2008)
32.
Wong, W.O., Tang, S.L., Cheung, Y.L., Cheng, L.: Design of a dynamic vibration absorber for vibration isolation of beams under point or distributed loading. J. Sound Vib. 301, 898–908 (2007)
33.
Issa, J.S.: Vibration absorbers for simply supported beams subjected to constant moving loads. Proc. Inst. Mech. Eng. Part K J. Multi-body Dyn. 226, 398–404 (2012)
34.
Febbo, M., Vera, S.A.: Optimization of a two degree of freedom system acting as a dynamic vibration absorber. J. Vib. Acoust. 130, 11013 (2008)
35.
Moghaddas, M., Esmailzadeh, E., Sedaghati, R., Khosravi, P.: Vibration control of Timoshenko beam traversed by moving vehicle using optimized tuned mass damper. J. Vib. Control 18, 757–773 (2012)MathSciNetMATH
36.
Kukla, S.: Frequency analysis of a rectangular plate with attached discrete systems. J. Sound Vib. 264, 225–234 (2003)
37.
Kukla, S., Szewczyk, M.: Frequency analysis of annular plates with elastic concentric supports by Green’s function method. J. Sound Vib. 300, 387–393 (2007)
38.
Zur, K.K.: Green’s function for frequency analysis of thin annular plates with nonlinear variable thickness. Appl. Math. Model. 40, 3601–3619 (2016)MathSciNetMATH
39.
Żur, K.K.: Quasi-Green’s function approach to free vibration analysis of elastically supported functionally graded circular plates. Compos. Struct. 183, 600–610 (2018)
40.
Żur, K.K.: Free vibration analysis of elastically supported functionally graded annular plates via quasi-Green’s function method. Compos. Part B Eng. 144, 37–55 (2018)
41.
Żur, K.K.: Quasi-Green’s function approach to fundamental frequency analysis of elastically supported thin circular and annular plates with elastic constraints. J. Theor. Appl. Mech. 55, 87–101 (2017)
42.
Hou, P.-F., Chen, J.-Y.: A refined analysis for the transversely isotropic plate under tangential loads by the 3D Green’s function. Eng. Anal. Bound. Elem. 93, 10–20 (2018)MathSciNetMATH
43.
Rao, S.S.: Vibration of Continuous Systems. Wiley, New York (2007)
44.
Baferani, A.H., Saidi, A.R., Jomehzadeh, E.: An exact solution for free vibration of thin functionally graded rectangular plates. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 225, 526–536 (2011)MATH
Metadata
Title
Passive vibration suppression of plate using multiple optimal dynamic vibration absorbers
Authors
M. Ari
R. T. Faal
Publication date
12-10-2019
Publisher
Springer Berlin Heidelberg
Published in
Archive of Applied Mechanics / Issue 2/2020
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-019-01607-z

Other articles of this Issue 2/2020

Archive of Applied Mechanics 2/2020 Go to the issue

Original

Steady-state thermomechanical analysis of composite laminated plate with damage based on extended layerwise method

Original

Anisotropic multiferroic ellipsoidal particulate composites

Original

The lowest vibration modes of an elastic beam composed of alternating stiff and soft components

Original

Finite-form solution for anti-plane problem of nanoscale crack

Editorial

Thanks to our reviewers

Original

Two-dimensional elasticity solution for free vibration of simple-supported beams with arbitrarily and continuously varying thickness

Premium Partners

    Image Credits