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.

References

References
1.
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
.
2.
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
.
3.
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
.
4.
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
.
5.
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
.
6.
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
.
7.
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
.
8.
Boechler
,
N. S.
,
2011
, “
Granular Crystals: Controlling Mechanical Energy With Nonlinearity and Discreteness
,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
9.
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
.
10.
Bonanomi
,
L.
,
Theocharis
,
G.
, and
Daraio
,
C.
,
2015
, “
Wave Propagation in Granular Chains With Local Resonances
,”
Phys. Rev. E
,
91
(
3
), p.
033208
.
11.
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
.
12.
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
.
13.
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
.
14.
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.
15.
Schwan
,
L.
, and
Boutin
,
C.
,
2013
, “
Unconventional Wave Reflection Due to ‘Resonant Surface’
,”
Wave Motion
,
50
(
4
), pp.
852
868
.
16.
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
.
17.
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
.
18.
Lazan
,
B. J.
,
Damping of Materials and Members in Structural Mechanics
,
Pergamon Press
,
Oxford, NY
.
19.
Hartog
,
J. P. D.
,
1930
, “
LXXIII. Forced Vibrations With Combined Viscous and Coulomb Damping
,”
Philos. Mag. Ser. 7
,
9
(
59
), pp.
801
817
.
20.
Cattaneo
,
C.
,
1938
, “
Sul Contatto di Due Corpo Elastici
,”
Atti Accad. Naz. Lincei, Cl. Sci. Fis., Mat. Nat.
,
27
, pp.
342
348
.
21.
Mindlin
,
R.
,
1949
, “
Compliance of Elastic Bodies in Contact
,”
ASME J. Appl. Mech.
,
16
, pp.
259
268
.
22.
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
.
23.
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
.
24.
Gaul
,
L.
, and
Nitsche
,
R.
,
2000
, “
Friction Control for Vibration Suppression
,”
Mech. Syst. Signal Process.
,
14
(
2
), pp.
139
150
.
25.
Beards
,
C. F.
,
1983
, “
The Damping of Structural Vibration by Controlled Interfacial Slip in Joints
,”
ASME J. Vib. Acoust.
,
105
(
3
), pp.
369
373
.
26.
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
.
27.
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
.
28.
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
.
29.
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
.
30.
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
.
31.
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
.
32.
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
.
33.
Patil
,
D. B.
, and
Eriten
,
M.
,
2015
, “
Effect of Roughness on Frictional Energy Dissipation in Presliding Contacts
,”
ASME J. Tribol.
,
138
(
1
), p.
011401
.
34.
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
.
35.
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
.
You do not currently have access to this content.