Effect of surface on nano-beam mechanical behaviors: a parametric analysis

Microsystem Technologies - Tập 27 - Trang 665-672 - 2020
Ehsan Maani Miandoab1
1School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran

Tóm tắt

In this paper, effect of surface, including its elasticity, residual stress and density is investigated on the nano-beam stiffness and mass analytically. To this aim, the governing equation of the nano-beam dynamic behavior is extracted utilizing Gurtin–Murdoch’s theory and Euler–Bernoulli hypothesis which incorporates the surface effects. Effect of surface parameters on nano-beam lumped mass and stiffness is investigated parametrically and necessary conditions for hardening and softening behavior are presented based on the surface stress and elasticity for both clamped–clamped and clamped-free nano-beams. The performed analysis revealed that surface may have different effects on similar nano-beams with only different boundary conditions. The obtained results in this paper can be utilized in analysis and design of nano-systems.

Tài liệu tham khảo

Aifantis EC (2009) Exploring the applicability of gradient elasticity to certain micro/nano reliability problems. Microsyst Technol 15(1):109–115 Ansari R et al (2014) A geometrically non-linear plate model including surface stress effect for the pull-in instability analysis of rectangular nanoplates under hydrostatic and electrostatic actuations. Int J Nonlinear Mech 67:16–26 Azizi S, Chorsi MT, Bakhtiari-Nejad F (2016) On the secondary resonance of a MEMS resonator: a conceptual study based on shooting and perturbation methods. Int J Nonlinear Mech 82:59–68 Chasiotis I, Knauss WG (2003) The mechanical strength of polysilicon films: Part 2. Size effects associated with elliptical and circular perforations. J Mech Phys Solids 51(8):1551–1572 Chen C et al (2006) Size dependence of Young’s modulus in ZnO nanowires. Phys Rev Lett 96(7):075505 Cuenot S, Demoustier-Champagne S, Nysten B (2000) Elastic modulus of polypyrrole nanotubes. Phys Rev Lett 85(8):1690 Cuenot S et al (2004) Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Phys Rev B 69(16):165410 Fu Y, Zhang J (2010) Modeling and analysis of microtubules based on a modified couple stress theory. Physica E 42(5):1741–1745 Fu Y, Zhang J, Jiang Y (2010) Influences of the surface energies on the nonlinear static and dynamic behaviors of nanobeams. Physica E 42(9):2268–2273 Georgakaki D, Ziogos O, Polatoglou H (2014) Vibrational and mechanical properties of Si/Ge nanowires as resonators: a molecular dynamics study. Phys Status Solidi (a) 211(2):267–276 Gholami R, Ansari R, Rouhi H (2015) Studying the effects of small scale and Casimir force on the non-linear pull-in instability and vibrations of FGM microswitches under electrostatic actuation. Int J Nonlinear Mech 77:193–207 Jia N et al (2017) Size effect in the bending of a Timoshenko nanobeam. Acta Mech 228(6):2363–2375 Kong S et al (2008) The size-dependent natural frequency of Bernoulli-Euler micro-beams. Int J Eng Sci 46(5):427–437 Kong S et al (2009) Static and dynamic analysis of micro beams based on strain gradient elasticity theory. Int J Eng Sci 47(4):487–498 Kopycinska-Müller M et al (2005) Elastic-property measurements of ultrathin films using atomic force acoustic microscopy. Nanotechnology 16(6):703 Lam DC, Chong A (1999) Indentation model and strain gradient plasticity law for glassy polymers. J Mater Res 14(09):3784–3788 Lam D et al (2003) Experiments and theory in strain gradient elasticity. J Mech Phys Solids 51(8):1477–1508 Larkin K et al (2020) Nonlinear size dependent analysis and effectiveness of nanocrystalline micro/nanogyroscopes. Phys E Low Dimens Syst Nanostruct 117:113808 Lim CW (2010) Is a nanorod (or nanotube) with a lower Young’s modulus stiffer? Is not Young’s modulus a stiffness indicator? Sci China Phys Mech Astron 53(4):712–724 Liu C, Rajapakse R, Phani AS (2011) Finite element modeling of beams with surface energy effects. J Appl Mech 78(3):031014 Mahmoud M, Alrahmani MA, Alawadi HA (2019) Resonance patterns in cantilevered plates with micro electromechanical systems (MEMS) applications. Microsyst Technol 25(3):997–1016 McFarland AW, Colton JS (2005) Role of material microstructure in plate stiffness with relevance to microcantilever sensors. J Micromech Microeng 15(5):1060 Miandoab EM, Yousefi-Koma A, Pishkenari HN (2015) Nonlocal and strain gradient based model for electrostatically actuated silicon nano-beams. Microsyst Technol 21(2):457–464 Miandoab EM et al (2017) A general closed-form solution for the static pull-in voltages of electrostatically actuated MEMS/NEMS. Phys E Low Dimens Syst Nanostruct 90:7–12 Mojahedi M, Zand MM, Ahmadian M (2010) Static pull-in analysis of electrostatically actuated microbeams using homotopy perturbation method. Appl Math Model 34(4):1032–1041 Nilsson SG, Borrise X, Montelius L (2004) Size effect on Young’s modulus of thin chromium cantilevers. Appl Phys Lett 85:3555 Pishkenari HN, Afsharmanesh B, Akbari E (2015) Surface elasticity and size effect on the vibrational behavior of silicon nanoresonators. Curr Appl Phys 15(11):1389–1396 Rana S et al (2020) Nanoelectromechanical relay without pull-in instability for high-temperature non-volatile memory. Nat Commun 11(1):1–10 Rocha LA, Cretu E, Wolffenbuttel RF (2004) Analysis and analytical modeling of static pull-in with application to MEMS-based voltage reference and process monitoring. J Microelectromech Syst 13(2):342–354 Rokni H, Lu W (2013) Surface and thermal effects on the pull-in behavior of doubly-clamped graphene nanoribbons under electrostatic and Casimir loads. J Appl Mech 80(6):061014 Sharma AK, Godara R, Joglekar M (2019) Static and DC dynamic pull-in analysis of curled microcantilevers with a compliant support. Microsyst Technol 25(3):965–975 Skrzypacz P et al (2019) Analysis of dynamic pull-in voltage of a graphene MEMS model. Nonlinear Anal Real World Appl 45:581–589 Tajaddodianfar F et al (2015a) On the dynamics of bistable micro/nano resonators: analytical solution and nonlinear behavior. Commun Nonlinear Sci Numer Simul 20(3):1078–1089 Tajaddodianfar F et al (2015b) Classification of the nonlinear dynamics in an initially curved bistable micro/nano-electro-mechanical system resonator. Micro Nano Lett 10(10):583–588 Tajaddodianfar F et al (2015c) Size-dependent bistability of an electrostatically actuated arch NEMS based on strain gradient theory. J Phys D Appl Phys 48(24):245503 Tang C, Alici G (2011) Evaluation of length-scale effects for mechanical behaviour of micro-and nanocantilevers: II. Experimental verification of deflection models using atomic force microscopy. J Phys D Appl Phys 44(33):335502 Yang X, Xiao S, Hu W (2013) Atomistic simulation for the size effect on the mechanical properties of Ni/Ni 3 Al nanowire. J Appl Phys 114(9):094303 Yao Y, Chen S (2016) Surface effect in the bending of nanowires. Mech Mater 100:12–21 Younis M, Nayfeh A (2003) A study of the nonlinear response of a resonant microbeam to an electric actuation. Nonlinear Dyn 31(1):91–117 Zhen Y-X, Wen S-L, Tang Y (2019) Free vibration analysis of viscoelastic nanotubes under longitudinal magnetic field based on nonlocal strain gradient Timoshenko beam model. Phys E 105:116–124 Zurlo G (2013) Non-local elastic effects in electroactive polymers. Int J Nonlinear Mech 56:115–122