Research Papers

Tuning the Dissipation in Friction Dampers Excited by Depolarized Waves Across Patterned Surfaces

[+] Author and Article Information
Melih Eriten

Department of Mechanical Engineering,
University of Wisconsin–Madison,
1513 University Avenue,
Madison, WI 53706
e-mail: eriten@wisc.edu

Ahmet D. Usta, Lejie Liu

Department of Mechanical Engineering,
University of Wisconsin–Madison,
1513 University Avenue,
Madison, WI 53706

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 2, 2016; final manuscript received March 29, 2016; published online May 26, 2016. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 138(5), 051004 (May 26, 2016) (8 pages) Paper No: VIB-16-1062; doi: 10.1115/1.4033343 History: Received February 02, 2016; Revised March 29, 2016

Recently, patterned surfaces (elastodynamic meta-surfaces) were shown to cause mechanical wave depolarization resulting in conversion of uniaxial waves to multiaxial vibrations. Frictional oscillators loaded in multiple directions provide more tailorable damping scheme when compared to uniaxially loaded equivalents. This paper utilizes wave depolarization properties of patterned surfaces in tuning frictional damping. In particular, two-dimensional (2D) motion achieved by anisotropic wave reflection and depolarization across patterned surfaces is exerted on a simple friction oscillator; and frictional energy dissipation is studied using the homogenization theory and mechanics of a simple friction oscillator under macro and microslip conditions. The degree of depolarization is shown to control the extent of frictional shakedown (no-dissipation) zones and magnitude of energy dissipation for different incident wave frequencies and amplitudes. Transmission of the depolarized waves from the patterned surface to the friction oscillator enables higher and more uniform frictional damping for broader loading conditions. Uniform damping facilitates predictive linear dynamic models, and tuning the magnitude of damping permits efficient and robust wave attenuation, and energy transfer and localization in dynamic applications. A discussion on modeling assumptions and practical utilization of this potential is also provided. The presented potential of tuning frictional dissipation from very low to high values by simple surface patterns suggests that more sophisticated surface patterns can be designed for spatially varying frequency-dependent wave attenuation.

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Kim, E. , and Yang, J. , 2014, “ Wave Propagation in Single Column Woodpile Phononic Crystals: Formation of Tunable Band Gaps,” J. Mech. Phys. Solids, 71, pp. 33–45. [CrossRef]
Kim, E. , Kim, Y. H. N. , and Yang, J. , 2015, “ Nonlinear Stress Wave Propagation in 3D Woodpile Elastic Metamaterials,” Int. J. Solids Struct., 58, pp. 128–135. [CrossRef]
Kim, E. , Li, F. , Chong, C. , Theocharis, G. , Yang, J. , and Kevrekidis, P. G. , 2015, “ Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures,” Phys. Rev. Lett., 114(11), p. 118002. [CrossRef] [PubMed]
Guarín-Zapata, N. , Gomez, J. , Yaraghi, N. , Kisailus, D. , and Zavattieri, P. D. , 2015, “ Shear Wave Filtering in Naturally-Occurring Bouligand Structures,” Acta Biomater., 23, pp. 11–20. [CrossRef] [PubMed]
Wang, P. , Shim, J. , and Bertoldi, K. , 2013, “ Effects of Geometric and Material Nonlinearities on Tunable Band Gaps and Low-Frequency Directionality of Phononic Crystals,” Phys. Rev. B, 88(1), p. 014304. [CrossRef]
Boechler, N. , Yang, J. , Theocharis, G. , Kevrekidis, P. G. , and Daraio, C. , 2011, “ Tunable Vibrational Band Gaps in One-Dimensional Diatomic Granular Crystals With Three-Particle Unit Cells,” J. Appl. Phys., 109(7), p. 074906. [CrossRef]
Boechler, N. , Eliason, J. K. , Kumar, A. , Maznev, A. A. , Nelson, K. A. , and Fang, N. , 2013, “ Interaction of a Contact Resonance of Microspheres With Surface Acoustic Waves,” Phys. Rev. Lett., 111(3), p. 036103. [CrossRef] [PubMed]
Boechler, N. S. , 2011, “ Granular Crystals: Controlling Mechanical Energy With Nonlinearity and Discreteness,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
Liu, Z. , Zhang, X. , Mao, Y. , Zhu, Y. Y. , Yang, Z. , Chan, C. T. , and Sheng, P. , 2000, “ Locally Resonant Sonic Materials,” Science, 289(5485), pp. 1734–1736. [CrossRef] [PubMed]
Bonanomi, L. , Theocharis, G. , and Daraio, C. , 2015, “ Wave Propagation in Granular Chains With Local Resonances,” Phys. Rev. E, 91(3), p. 033208. [CrossRef]
Gantzounis, G. , Serra-Garcia, M. , Homma, K. , Mendoza, J. M. , and Daraio, C. , 2013, “ Granular Metamaterials for Vibration Mitigation,” J. Appl. Phys., 114(9), p. 093514. [CrossRef]
Herbold, E. B. , Kim, J. , Nesterenko, V. F. , Wang, S. Y. , and Daraio, C. , 2009, “ Pulse Propagation in a Linear and Nonlinear Diatomic Periodic Chain: Effects of Acoustic Frequency Band-Gap,” Acta Mech., 205(1–4), pp. 85–103. [CrossRef]
Wang, P. , Casadei, F. , Kang, S. H. , and Bertoldi, K. , 2015, “ Locally Resonant Band Gaps in Periodic Beam Lattices by Tuning Connectivity,” Phys. Rev. B, 91(2), p. 020103. [CrossRef]
Khanolkar, A. , Wallen, S. , Ghanem, M. A. , Jenks, J. , Vogel, N. , and Boechler, N. , 2015, “ A Self-Assembled Metamaterial for Lamb Waves,” Appl. Phys. Lett., 107(7), p. 071903.
Schwan, L. , and Boutin, C. , 2013, “ Unconventional Wave Reflection Due to ‘Resonant Surface’,” Wave Motion, 50(4), pp. 852–868. [CrossRef]
Boutin, C. , Schwan, L. , and Dietz, M. S. , 2015, “ Elastodynamic Metasurface: Depolarization of Mechanical Waves and Time Effects,” J. Appl. Phys., 117(6), p. 064902. [CrossRef]
Boutin, C. , and Roussillon, P. , 2006, “ Wave Propagation in Presence of Oscillators on the Free Surface,” Int. J. Eng. Sci., 44(3–4), pp. 180–204. [CrossRef]
Lazan, B. J. , Damping of Materials and Members in Structural Mechanics, Pergamon Press, Oxford, NY.
Hartog, J. P. D. , 1930, “ LXXIII. Forced Vibrations With Combined Viscous and Coulomb Damping,” Philos. Mag. Ser. 7, 9(59), pp. 801–817. [CrossRef]
Cattaneo, C. , 1938, “ Sul Contatto di Due Corpo Elastici,” Atti Accad. Naz. Lincei, Cl. Sci. Fis., Mat. Nat., 27, pp. 342–348.
Mindlin, R. , 1949, “ Compliance of Elastic Bodies in Contact,” ASME J. Appl. Mech., 16, pp. 259–268.
Williams, E. J. , and Earles, S. W. E. , 1974, “ Optimization of the Response of Frictionally Damped Beam Type Structures With Reference to Gas Turbine Compressor Blading,” ASME J. Manuf. Sci. Eng., 96(2), pp. 471–476.
Beards, C. F. , and Woowat, A. , 1985, “ The Control of Frame Vibration by Friction Damping in Joints,” ASME J. Vib. Acoust., 107(1), pp. 26–32. [CrossRef]
Gaul, L. , and Nitsche, R. , 2000, “ Friction Control for Vibration Suppression,” Mech. Syst. Signal Process., 14(2), pp. 139–150. [CrossRef]
Beards, C. F. , 1983, “ The Damping of Structural Vibration by Controlled Interfacial Slip in Joints,” ASME J. Vib. Acoust., 105(3), pp. 369–373. [CrossRef]
Griffin, J. H. , and Menq, C.-H. , 1991, “ Friction Damping of Circular Motion and Its Implications to Vibration Control,” ASME J. Vib. Acoust., 113(2), pp. 225–229. [CrossRef]
Menq, C.-H. , Chidamparam, P. , and Griffin, J. H. , 1991, “ Friction Damping of Two-Dimensional Motion and Its Application in Vibration Control,” J. Sound Vib., 144(3), pp. 427–447. [CrossRef]
Jang, Y. H. , and Barber, J. R. , 2011, “ Effect of Phase on the Frictional Dissipation in Systems Subjected to Harmonically Varying Loads,” Eur. J. Mech. A/Solids, 30(3), pp. 269–274. [CrossRef]
Putignano, C. , Ciavarella, M. , and Barber, J. R. , 2011, “ Frictional Energy Dissipation in Contact of Nominally Flat Rough Surfaces Under Harmonically Varying Loads,” J. Mech. Phys. Solids, 59(12), pp. 2442–2454. [CrossRef]
Papangelo, A. , and Ciavarella, M. , 2015, “ Effect of Normal Load Variation on the Frictional Behavior of a Simple Coulomb Frictional Oscillator,” J. Sound Vib., 348, pp. 282–293. [CrossRef]
Davies, M. , Barber, J. R. , and Hills, D. A. , 2012, “ Energy Dissipation in a Frictional Incomplete Contact With Varying Normal Load,” Int. J. Mech. Sci., 55(1), pp. 13–21. [CrossRef]
Barber, J. R. , Davies, M. , and Hills, D. A. , 2011, “ Frictional Elastic Contact With Periodic Loading,” Int. J. Solids Struct., 48(13), pp. 2041–2047. [CrossRef]
Patil, D. B. , and Eriten, M. , 2015, “ Effect of Roughness on Frictional Energy Dissipation in Presliding Contacts,” ASME J. Tribol., 138(1), p. 011401. [CrossRef]
Klarbring, A. , Ciavarella, M. , and Barber, J. R. , 2007, “ Shakedown in Elastic Contact Problems With Coulomb Friction,” Int. J. Solids Struct., 44(25–26), pp. 8355–8365. [CrossRef]
Ponter, A. R. S. , Hearle, A. D. , and Johnson, K. L. , 1985, “ Application of the Kinematical Shakedown Theorem to Rolling and Sliding Point Contacts,” J. Mech. Phys. Solids, 33(4), pp. 339–362. [CrossRef]


Grahic Jump Location
Fig. 1

Frictional oscillator attached to a meta-surface containing SDOF resonators

Grahic Jump Location
Fig. 2

Normalized surface displacements U1/USH and U2/USH for misalignment angles of α={1/40,1/8,1/4,3/8}π and γ=1, ζ=0.05

Grahic Jump Location
Fig. 4

The normalized energy dissipation ζs on Ω-η plane for misalignment angles of α={1/40,1/8,1/4,3/8}π and Λ=0.5

Grahic Jump Location
Fig. 5

Shakedown boundaries on Ω - η plane for misalignment angles of α={1/40,1/8,1/4,3/8}π and Λ={0.1,0.3,0.5,0.7,0.9}

Grahic Jump Location
Fig. 6

The normalized energy dissipation ζps on Ω-η plane for misalignment angle of α=π/4 and Λ=0.5

Grahic Jump Location
Fig. 3

Curved 2D contact geometry (a) and generic loading cycle used in energy dissipation calculations for microslip regime

Grahic Jump Location
Fig. 7

Rectangular surface pattern design




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