This paper presents the multi-directional vibration behaviors of buckled viscoelastic nanoribbons based on the nonlocal theory containing scale effect, where the Lagrange’s motion equation is introduced to construct the nonlocal viscoelastic governing equation. The first-order transverse vibration mode and the first-order longitudinal vibration mode are considered to study the influences of the scale characteristics on the natural frequency of two different vibration modes. The Kelvin–Voigt model is used to characterize the material viscoelastic property, and an analytical method is presented to solve the nonlocal viscoelastic vibration behaviors of the buckled nanoribbon containing scale effect. Results show that the scale effect could decrease the natural frequency of buckled nanoribbon with viscoelastic behavior, as well as the half bandwidth during forced vibration. The presented results may be taken as a useful reference for the fabrications and applications of buckled nanostructures-based sensors & actuators, electronics, energy harvesters, etc.
KeYMeyerTShihWM, et al.Regulation at a distance of biomolecular interactions using a DNA origami nanoactuator. Nat Commun2016; 7: 10935–10935.
2.
HuangCJChenYSChangY. Counterion-activated nanoactuator: reversibly switchable killing/releasing bacteria on polycation brushes. ACS Appl Mater Interface2015; 7: 2415–23.
3.
WangCXuZChengH, et al.A hydrothermal route to water-stable luminescent carbon dots as nanosensors for pH and temperature. Carbon2015; 82: 87–95.
4.
WangCWuJJiangK, et al.Stable Ag nanoclusters-based nano-sensors: Rapid sonochemical synthesis and detecting Pb2+ in living cells. Sensors Actuator B: Chemical2017; 238: 1136–1143.
5.
LupanOPosticaVWolffN, et al.Localized synthesis of iron oxide nanowires and fabrication of high performance nanosensors based on a single Fe2O3 nanowire. Small2017; 13: 1602868–1602868.
6.
JinYLiXYangJ. Single layer of MX 3 (M = Ti, Zr; X = S, Se, Te): a new platform for nano-electronics and optics. Phys Chem Chem Phys2015; 17: 18665–18669.
7.
CollaertNAlianAArimuraH, et al.Ultimate nano-electronics: New materials and device concepts for scaling nano-electronics beyond the Si roadmap. Microelectronic Eng2015; 132: 218–225.
8.
WangXSummersCJWangZL. Large-scale hexagonal-patterned growth of aligned ZnO nanorods for nano-optoelectronics and nanosensor arrays. Nano Lett2004; 4: 423–426.
9.
JarrahiM. Advanced photoconductive terahertz optoelectronics based on nano-antennas and nano-plasmonic light concentrators. IEEE Transact Terahertz Sci Technol2015; 5: 391–397.
10.
HeMKravchykKWalterM, et al.Monodisperse antimony nanocrystals for high-rate Li-ion and Na-ion battery anodes: nano versus bulk. Nano Lett2014; 14: 1255–1262.
11.
WuSGeRLuM, et al.Graphene-based nano-materials for lithium–sulfur battery and sodium-ion battery. Nano Energy2015; 15: 379–405.
12.
WuHChanGChoiJW, et al.Stable cycling of double-walled silicon nanotube battery anodes through solid–electrolyte interphase control. Nat Nanotechnol2012; 7: 310–310.
13.
LingZHarveyAMcAteerD, et al.Quantifying the role of nanotubes in nano: nano composite supercapacitor electrodes. Adv Energy Mater2018; 8: 1702364–1702364.
14.
PedoneDMoglianettiMDe LucaE, et al.Platinum nanoparticles in nanobiomedicine. Chem Soc Rev2017; 46: 4951–4975.
15.
GaoZZhiCBandoY, et al.Noncovalent functionalization of boron nitride nanotubes in aqueous media opens application roads in nanobiomedicine. Nanobiomedicine2014; 1: 7–7.
16.
Marambio-JonesCHoekEM. A review of the antibacterial effects of silver nanomaterials and potential implications for human health and the environment. J Nanoparticle Res2010; 12: 1531–1551.
17.
DobrovolskaiaMAMcNeilSE. Immunological properties of engineered nanomaterials. Nature Nanotechnol2007; 2: 469–469.
18.
NovoselovKSGeimAKMorozovSV, et al.Electric field effect in atomically thin carbon films. Science2004; 306: 666–669.
19.
NovoselovKSFalVIColomboL, et al.A roadmap for graphene. Nature2012; 490: 192–192.
20.
TranTTBrayKFordMJ, et al.Quantum emission from hexagonal boron nitride monolayers. Nature Nanotechnol2016; 11: 37–37.
21.
LeeCYanHBrusLE, et al.Anomalous lattice vibrations of single-and few-layer MoS2. ACS Nano2010; 4: 2695–2700.
22.
WangGZhangJYangS, et al.Vertically aligned MoS2 nanosheets patterned on electrochemically exfoliated graphene for high‐performance lithium and sodium storage. Adv Energy Mater2018; 8: 1702254–1702254.
23.
YalonEMcClellanCJSmitheKK, et al.Energy dissipation in monolayer MoS2 electronics. Nano Lett2017; 17: 3429–3433.
24.
LeeGHYuYJLeeC, et al.Electron tunneling through atomically flat and ultrathin hexagonal boron nitride. Appl Phys Lett2011; 99: 243114–243114.
25.
YanKAFuLEPengH, et al.Designed CVD growth of graphene via process engineering. Accounts Chem Res2013; 46: 2263–2274.
26.
MengLSuYGengD, et al.Hierarchy of graphene wrinkles induced by thermal strain engineering. Appl Phys Lett2013; 103: 251610–251610.
27.
Rodriguez-HernandezJ. Wrinkled interfaces: taking advantage of surface instabilities to pattern polymer surfaces. Progr Polym Sci2015; 42: 1–41.
28.
VisaveliyaNRLeishmanCWNgK, et al.Surface wrinkling and porosity of polymer particles toward biological and biomedical applications. Adv Mater Interface2017; 4: 1700929–1700929.
29.
JiaFLiBCaoYP, et al.Wrinkling pattern evolution of cylindrical biological tissues with differential growth. Phys Rev E2015; 91: 012403–012403.
30.
YuCO’BrienKZhangYH, et al.Tunable optical gratings based on buckled nanoscale thin films on transparent elastomeric substrates. Appl Phys Lett2010; 96: 041111–041111.
31.
StaffordCMHarrisonCBeersKL, et al.A buckling-based metrology for measuring the elastic moduli of polymeric thin films. Nat Mater2004; 3: 545–545.
32.
CaoYPZhengXPLiB, et al.Determination of the elastic modulus of micro-and nanowires/tubes using a buckling-based metrology. Scripta Mater2009; 61: 1044–1047.
33.
KhangDYRogersJALeeHH. Mechanical buckling: mechanics, metrology, and stretchable electronics. Adv Function Mater2009; 19: 1526–1536.
34.
ChaeSHYuWJBaeJJ, et al.Transferred wrinkled Al 2 O 3 for highly stretchable and transparent graphene–carbon nanotube transistors. Nat Mater2013; 12: 403–403.
35.
ZhangYXuSFuH, et al.Buckling in serpentine microstructures and applications in elastomer-supported ultra-stretchable electronics with high areal coverage. Soft Matter2013; 9: 8062–8070.
36.
ZhuWLowTPerebeinosV, et al.Structure and electronic transport in graphene wrinkles. Nano Lett2012; 12: 3431–3436.
37.
XuPKangJChoiJB, et al.Laminated ultrathin chemical vapor deposition graphene films based stretchable and transparent high-rate supercapacitor. ACS Nano2014; 8: 9437–9445.
38.
KimSJKimDWLimJ, et al.Large-area buckled MoS2 films on the graphene substrate. ACS Appl Mater Interface2016; 8: 13512–13519.
39.
GuoYGuoW. Electronic and field emission properties of wrinkled graphene. J Phys Chem C2012; 117: 692–696.
40.
ChenWGuiXZhengY, et al.Synergistic effects of wrinkled graphene and plasmonics in stretchable hybrid platform for surface‐enhanced Raman spectroscopy. Adv Optical Mater2017; 5: 1600715–1600715.
41.
WangHNingXLiH, et al.Vibration of mechanically-assembled 3D microstructures formed by compressive buckling. J Mech Phys Solid2018; 112: 187–208.
42.
ThaiHT. A nonlocal beam theory for bending, buckling, and vibration of nanobeams. Int J Eng Sci2012; 52: 56–64.
43.
LiHWangXZhuF, et al.Viscoelastic characteristics of mechanically assembled three-dimensional structures formed by compressive buckling. J Appl Mech2018; 85: 121002–1.
44.
HuangRSuoZ. Wrinkling of a compressed elastic film on a viscous layer. J Appl Phys2002; 91: 1135–1142.
45.
HuangZYHongWSuoZ. Nonlinear analyses of wrinkles in a film bonded to a compliant substrate. J Mech Phys Solids2005; 53: 2101–2118.
46.
AraniAGAmirSShajariAR, et al.Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory. Compos Part B: Eng2012; 43: 195–203.
47.
BarzokiAMAraniAGKolahchiR, et al.Nonlinear buckling response of embedded piezoelectric cylindrical shell reinforced with BNNT under electro–thermo-mechanical loadings using HDQM. Compos Part B: Eng2013; 44: 722–727.
48.
ChaiHBabcockCDKnaussWG. One dimensional modelling of failure in laminated plates by delamination buckling. Int J Solids Struct1981; 17: 1069–1083.
49.
NilssonKFAspLEAlpmanJE, et al.Delamination buckling and growth for delaminations at different depths in a slender composite panel. Int J Solid Struct2001; 38: 3039–3071.
50.
BrunoDGrecoF. An asymptotic analysis of delamination buckling and growth in layered plates. Int J Solids Struct2000; 37: 6239–6276.
51.
TsengWYDugundjiJ. Nonlinear vibrations of a buckled beam under harmonic excitation. J Appl Mech1971; 38: 467–476.
52.
LestariWHanagudS. Nonlinear vibration of buckled beams: some exact solutions. Int J Solids Struct2001; 38: 4741–4757.
53.
CottoneFGammaitoniLVoccaH, et al.Piezoelectric buckled beams for random vibration energy harvesting. Smart Mater Struct2012; 21: 035021–035021.
54.
EmamSANayfehAH. On the nonlinear dynamics of a buckled beam subjected to a primary-resonance excitation. Nonlinear Dynam2004; 35: 1–7.
55.
MarynowskiK. Non-linear dynamic analysis of an axialy moving viscoelastic beam. J Theoretical Appl Mech2002; 40: 465–482.
56.
ArefiMZenkourAM. Nonlocal electro-thermo-mechanical analysis of a sandwich nanoplate containing a Kelvin–Voigt viscoelastic nanoplate and two piezoelectric layers. Acta Mech2017; 228: 475–493.
57.
RossikhinYAShitikovaMV. The analysis of the impact response of a thin plate via fractional derivative standard linear solid model. J Sound Vibrat2011; 330: 1985–2003.
58.
GhayeshMH. Nonlinear dynamic response of a simply-supported Kelvin–Voigt viscoelastic beam, additionally supported by a nonlinear spring. Nonlinear Analysis: Real World Appl2012; 13: 1319–1333.
59.
MahmoodiSNJaliliNKhademSE. An experimental investigation of nonlinear vibration and frequency response analysis of cantilever viscoelastic beams. J Sound Vibrat2008; 311: 1409–1419.
60.
SuYWuJFanZ, et al.Postbuckling analysis and its application to stretchable electronics. J Mech Phys Solid2012; 60: 487–508.
61.
HajmohammadMHFarrokhianAKolahchiR. Smart control and vibration of viscoelastic actuator-multiphase nanocomposite conical shells-sensor considering hygrothermal load based on layerwise theory. Aerosp Sci Technol2018; 78: 260–270.
62.
KolahchiR. A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods. Aerosp Sci Technol2017; 66: 235–248.
63.
LiC. Torsional vibration of carbon nanotubes: comparison of two nonlocal models and a semi-continuum model. Int J Mech Sci2014; 82: 25–31.
64.
Ghorbanpour-AraniAHRastgooASharafiMM, et al.Nonlocal viscoelasticity based vibration of double viscoelastic piezoelectric nanobeam systems. Meccanica2016; 51: 25–40.
65.
AttiaMAMahmoudFFAttiaMA, et al.Analysis of viscoelastic Bernoulli–Euler nanobeams incorporating nonlocal and microstructure effects. Int J Mech Mater Des2017; 13: 385–406.
66.
AnsariROskouieMFGholamiR. Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory. Phys E: Low-Dimension Syst Nanostruct2016; 75: 266–271.
67.
TsengWYDugundjiJ. Nonlinear vibrations of a buckled beam under harmonic excitation. J Appl Mech Transact ASME1971; 38: 467–476.
68.
TangDMDowellEH. On the threshold force for chaotic motions for a forced buckled beam. J Appl Mech-Transact ASME1988; 55: 190–196.
69.
EringenACEdelenDGB. On nonlocal elasticity. Int J Eng Sci1972; 10: 233–248.
70.
FarajpourAMohammadiMShahidiAR, et al.Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model. Physica E2011; 43: 1820–1825.
71.
ChenCRosenblattSBolotinKI, et al.Performance of monolayer graphene nanomechanical resonators with electrical readout. Nat Nanotechnol2009; 4: 861–861.
