Pull-In Instability of MSGT Piezoelectric Polymeric FG-SWCNTs Reinforced Nanocomposite Considering Surface Stress Effect
الموضوعات :A Ghorbanpour Arani 1 , B Rousta Navi 2 , M Mohammadimehr 3 , S Niknejad 4 , A.A Ghorbanpour Arani 5 , A Hosseinpour 6
1 - Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran----Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan, Iran
2 - Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
3 - Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
4 - Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
5 - School of Mechnical Engineering, College of Engineering, University of Tehran, Tehran, Iran
6 - Department of Mechanical Engineering and Engineering Science,University of North Carolina at Charlotte, USA
الکلمات المفتاحية: Surface stress effect, Pull-in instability, Piezoelectric polymeric nanocomposite plates, Modified strain gradient theory (MSGT),
ملخص المقالة :
In this paper, the pull-in instability of piezoelectric polymeric nanocomposite plates reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) based on modified strain gradient theory (MSGT) is investigated. Various types of SWCNTs are distributed in piezoelectric polymeric plate and also surface stress effect is considered in this research. The piezoelectric polymeric nanocomposite plate is subjected to electro-magneto-mechanical loadings. The nonlinear governing equations are derived from Hamilton's principle. Then, pull-in voltage and natural frequency of the piezoelectric polymeric nanocomposite plates are calculated by Newton-Raphson method. There is a good agreement between the obtained and other researcher results. The results show that the pull-in voltage and natural frequency increase with increasing of applied voltage, magnetic field, FG-SWCNTs orientation angle and small scale parameters and decrease with increasing of van der Waals and Casimir forces, residual surface stress constant. Furthermore, highest and lowest pull-in voltages are belonging to FG-X and FG-O distribution types of SWCNTs.
[1] Rocha L.A., Mol L., Wolffenbuttel R.F., Lage A., 2008, A time based micro- accelerometer, Proceeding of Eurossensors XXII, Dresden, Germany.
[2] Degani O., Nemirovsky Y., 2002, Design considerations of rectangular electrostatic torsion actuators based on new analytical pull-in expressions, Journal of Microelectromechanical Systems 11(1): 20-26.
[3] Degani O., Socher E., Lipson A., Leitner T., Setter D.J., Kaldor S., Nemirovsky Y., 1998, Pull-in study of an electrostatic torsion microactuator, Journal of Microelectromechanical Systems 7(4): 373-379.
[4] Zhang L.X., Zhao Y.P., 2003, Electromechanical model of RF MEMS switches, Microsystem Technologies 9: 420-426.
[5] Senturia S.D., 2001, Microsystem Design, Boston, MA: Kluwer Academic.
[6] Koumela A., Mercier D., Marcoux C., Purcell S.T., 2012, Performances of suspended silicon nanowire resonators for time reference applications, Proceedings of IEEE International Frequency Control Symposium, Baltimore, MD, USA.
[7] Hassani F.A., Cobianu C., Armini S., Petrescu V., Merken P., Tsamados D., Ionescu A.M., Tsuchiya Y., Mizuta H., 2011, Numerical analysis of zeptogram/Hz-level mass responsivity for in-plane resonant nano-electro-mechanical sensors, Microelectronic Engineering 88: 2879-2884.
[8] Colinet E., Durand C., Duraffourg L., Audebert P., Dumas G., Casset F., Ollier E., Ancey P., Carpentier J.F., Buchaillot L., Ionescu A.M., 2009, Ultra-sensitive capacitive detection based on SGMOSFET compatible with front-end CMOS process, IEEE Journal of Solid-State Circuits 44: 247-257.
[9] Fu Y., Zhang J., 2011, Size-dependent pull-in phenomena in electrically actuated nanobeams incorporating surface energies, Applied Mathematical Modelling 35: 941-951.
[10] Mohammadimehr M., Mohandes M., Moradi M., 2016, Size dependent effect on the buckling and vibration analysis of double-bonded nanocomposite piezoelectric plate reinforced by boron nitride nanotube based on modified couple stress theory, Journal of Vibration and Control 22(7): 1790-1807.
[11] Wang Y.G., Lin W.H., Feng Z.J., Li X.M., 2012, Characterization of extensional multi-layer microbeams in pull-in phenomenon and vibrations, International Journal of Mechanical Sciences 54: 225-233.
[12] Stephan D.A., Hannot Daniel J.R., 2013, A palette of methods for computing pull-in curves for numerical models of Microsystems, Finite Elements in Analysis and Design 67: 76-90.
[13] Rudolf H.R.J., Seethaler A.S., Hosseini-Hashemi M., Li X.F., 2013, Analytical closed-form solutions for size-dependent static pull-in behavior in electrostatic micro-actuators via Fredholm integral equation, Sensors and Actuators A: Physical 190: 32-43.
[14] Duan J.S., Rach R., Wazwaz A.M., 2013, Solution of the model of beam-type micro- and nano-scale electrostatic actuators by a new modified Adomian decomposition method for nonlinear boundary value problems, International Journal of Non-Linear Mechanics 49: 159-169.
[15] Mousavi T., Bornassi S., Haddadpour H., 2013, The effect of small scale on the pull-in instability of nano-switches using DQM, International Journal of Solids and Structures 50: 1193-1202.
[16] Sedighi H.M., Daneshmand F., Zare J., 2014, The influence of dispersion forces on the dynamic pull-in behavior of vibrating nano-cantilever based NEMS including fringing field effect, Archives of Civil and Mechanical Engineering 14: 766-775.
[17] Wang K.F., Wang B.L., 2014, Influence of surface energy on the non-linear pull-in instability of nano-switches, International Journal of Non-Linear Mechanics 59: 69-75.
[18] Fakhrabadi M.M.S., Rastgoo A., Ahmadian M.T., 2014, Non-linear behaviors of carbon nanotubes under electrostatic actuation based on strain gradient theory, International Journal of Non-Linear Mechanics 67: 236-244.
[19] Yazdanpanahi E., Noghrehabadi A., Ghalambaz M., 2014, Pull-in instability of electrostatic doubly clamped nanoactuators: Introduction of a balanced liquid layer (BLL), International Journal of Non-Linear Mechanics 58: 128-138.
[20] Askari A.R., Tahani M., 2015, Size-dependent dynamic pull-in analysis of beam-type MEMS under mechanical shock based on the modified couple stress theory, Applied Mathematical Modelling 39: 934-946.
[21] Mojahedi M., Ahmadian M.T., Firoozbakhsh K., 2014, The influence of the intermolecular surface forces on the static deflection and pull-in instability of the micro/nano cantilever gyroscopes, Composite Part B 56: 336-343.
[22] Jia X.L., Zhang S.M., Ke L.L., Yang J., Kitipornchai S., 2014, Thermal effect on the pull-in instability of functionally graded micro-beams subjected to electrical actuation, Composite Structure 116: 136-146.
[23] Juillard J., 2015, Analysis of resonant pull-in of micro- electromechanical oscillators, Journal of Sound and Vibration 350: 123-139.
[24] Huang Y.T., Chen H.L., Hsu W., 2014, An analytical model for calculating the pull-in voltage of micro cantilever beams subjected to tilted and curled effects, Microelectronic Engineering 125: 73-77.
[25] Wang K.F., Kitamura T., Wang B., 2015, Nonlinear pull-in instability and free vibration of micro/nanoscale plates with surface energy- a modified couple stress theory model, International Journal of Mechanical Sciences 99: 288-296.
[26] Rahaeifard M., Ahmadian M.T., 2015, On pull-in instabilities of microcantilevers, International Journal of Engineering Science 87: 23-31.
[27] Shaat M., Abdelkefi A., 2015, Pull-in instability of multi-phase nanocrystalline silicon beams under distributed electrostatic force, International Journal of Engineering Science 90: 58-75.
[28] Xiao Y., Wang B., Zhou S., 2015, Pull-in voltage analysis of electrostatically actuated MEMS with piezoelectric layers: A size-dependent model, Mechanics Research Communications 66: 7-14.
[29] Moghimi Zand M., 2012, The dynamic pull-in instability and snap-through behavior of initially curved microbeams, Mechanics of Advanced Materials and Structures 19: 485-491.
[30] Ghorbanpour Arani A., Jalilvand A., Ghaffari M., Talebi Mazraehshahi M., Kolahchi R., Roudbari M.A., Amir S., 2014, Nonlinear pull-in instability of boron nitride nano-switches considering electrostatic and Casimir forces, Scientia Iranica F 21(3): 1183-1196.
[31] Ghorbanpour Arani A., Ghaffari M., Jalilvan A., Kolahchi R., 2013, Nonlinear nonlocal pull-in instability of boron nitride nanoswitch, Acta Mechanica 224: 3005-3019.
[32] Lin S.M., Lee S.J., 2016, Coupled mechanism and pull-in instability of several probe-membrane assemblies subjected to electrostatic force, Mechanics of Advanced Materials and Structures 25: 267-278.
[33] Yang W.D., Wang X., Fang C.Q., Lu G., 2014, Electromechanical coupling characteristics of carbon nanotube reinforced cantilever nano-actuator, Sensors and Actuators A: Physical 220: 178-187.
[34] Tajalli S.A., Moghimi Zand M., Ahmadian M.T., 2009, Effect of geometric nonlinearity on dynamic pull-in behavior of coupled-domain microstructures based on classical and shear deformation plate theories, European Journal of Mechanics A/Solids 28: 916-925.
[35] Fakhrabadi M.M.S., Rastgoo A., Ahmadian M.T., 2014, On the pull-in instability of double-walled carbon nanotube-based nano electromechanical systems with cross-linked walls, Fullerenes, Nanotubes and Carbon Nanostructures 23: 300-314.
[36] Keivani M., Mokhtari J., Kanani A., Abadian N., Rach R., Abadyan M., 2016, A size-dependent model for instability analysis of paddle-type and double-sided NEMS measurement sensors in the presence of centrifugal force, Mechanics of Advanced Materials and Structures 24: 809-819.
[37] Talebian S., Rezazadeh G., Toosi F.B.M., 2010, Effect of temperature on pull-in voltage and natural frequency of an electrostatically actuated microplate, Mechatronics 20: 666-673.
[38] Zheng J.J., Dai J.G., 2014, Prediction of the nonlinear pull-out response of FRP ground anchors using an analytical transfer matrix method, Engineering Structures 81: 377-385.
[39] Mohammadimehr M., Salemi M., 2014, Bending and buckling analysis of functionally graded Mindlin nano-plate model based on strain gradient elasticity theory, Indian Journal of Scientific Research 2: 587-598.
[40] Ansari R., Gholami R., FaghihShojaei M., Mohammadi V., Sahmani S., 2014, Surface stress effect on the pull-in instability of circular nanoplates, Acta Astronautica 102: 140-150.
[41] Ansari R., Mohammadi V., Faghih M., Shojaei R., Gholami M.A., Darabi A., 2014, Geometrically non-linear plate model including surface stress effect for the pull-in instability analysis of rectangular nanoplates under hydrostatic and electrostatic actuations, International Journal of Non-Linear Mechanics 67: 16-26.
[42] Mohammadimehr M., Rousta Navi B., Ghorbanpour Arani A., 2015, Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method, Composite Structure 131: 654-671.
[43] Mao R., Lu G., Wang Z., Zhao L., 2016, Large deflection behavior of circular sandwich plates with metal foam-core, European Journal of Mechanics A/Solids 55: 57-66.
[44] Ghorbanpour Arani A., Rousta Navi B., Mohammadimehr M., 2015, Surface stress and agglomeration effects on nonlocal biaxial buckling polymeric nanocomposite plate reinforced by CNT using various approaches, Advanced Composite Matererial 220: 1-19.
[45] Ghorbanpour Arani A., Khoddami Maraghi Z., Khani Arani H., 2016, smart vibration control of magnetostrictive nano-plate using nonlocal continuum theory, Journal of Solid Mechanics 8(2): 300-314.
[46] Mohammadimehr M., Rousta Navi B., Ghorbanpour Arani A., 2015, Surface stress effect on the nonlocal biaxial buckling and bending analysis of polymeric piezoelectric nanoplate reinforced by cnt using eshelby-mori-tanaka approach, Journal of Solid Mechanics 7(2): 173-190.
[47] Shojaeian M., Zeighampour H., 2016, Size dependent pull-in behavior of functionally graded sandwich nanobridges using higher order shear deformation theory, Composite Structures 143: 117-129.
[48] Yang W.D., Wang X., Fang C.Q., 2015, Pull-in instability of carbon nanotube-reinforced nano-switches considering scale, surface and thermal effects, Composites Part B 82: 143-151.
[49] Mohammadimehr M., Rousta Navi B., Ghorbanpour Arani A., 2017, Dynamic stability of modified strain gradient theory sinusoidal viscoelastic piezoelectric polymeric functionally graded single-walled carbon nanotubes reinforced nanocomposite plate considering surface stress and agglomeration effects under hydro-thermo-electro-magneto-mechanical loadings, Mechanics of Advanced Materials and Structures 24: 1325-1342.
[50] Alibeigloo A., 2014, Free vibration analysis of functionally graded carbon nanotube-reinforced composite cylindrical panel embedded in piezoelectric layers by using theory of elasticity, European Journal of Mechanics A/Solids 44: 104-115.
[51] Sedighi H.M., Bozorgmehri A., 2016, Dynamic instability analysis of doubly clamped cylindrical nanowires in the presence of Casimir attraction and surface effects using modified couple stress theory, Acta Mechanica 227: 1575-1591.
[52] Hosseini S.A.H., Rahmani O., 2017, Exact solution for axial and transverse dynamic response of functionally graded nanobeam under moving constant load based on nonlocal elasticity theory, Meccanica 52(6): 1441-1457.
[53] Malikan M., 2017, Analytical predictions for the buckling of a nanoplate subjected to non-uniform compression based on the four-variable plate theory, Journal of Applied Computational Mechanics 3(3): 218-228.
[54] Ghorbanpour Arani A., Kolahchi R., Jamali M., Mosayyebi M., Alinaghian I., 2017, Dynamic instability of visco-SWCNTs conveying pulsating fluid based on sinusoidal surface couple stress theory, Journal of Solid Mechanics 9(2): 225-238.
[55] Amiri A., Rezazadeh G., Shabani R., Khanchehgardan A., 2016, On the stability of an electrostatically-actuated functionally graded magneto-electro-elastic micro- beams under magneto-electric conditions, Journal of Solid Mechanics 8(4): 756-772.
[56] Shaat M., Abdelkefi A., 2016, Size dependent and micromechanical modeling of strain gradient-based nanoparticle composite plates with surface elasticity, European Journal of Mechanics-A/Solids 58: 54-68.
[57] Shaat M., Mahmoud F., Alshorbagy A., Alieldin S., 2013, Bending analysis of ultra-thin functionally graded Mindlin plates incorporating surface energy effects, International Journal of Mechanical Sciences 75: 223-232.
[58] Shaat M., Mahmoud F., Gao X.L., Faheem A.F., 2014, Size-dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects, International Journal of Mechanical Sciences 79: 31-37.
[59] Ansari R., Ashrafi M., Pourashraf T., Sahmani S., 2015, Vibration and buckling characteristics of functionally graded nanoplates subjected to thermal loading based on surface elasticity theory, Acta Astronautica 109: 42-51.
[60] Ansari R., Gholami R., 2016, Size-dependent modeling of the free vibration characteristics of post-buckled third-order shear deformable rectangular nano plates based on the surface stress elasticity theory, Composites Part B: Engineering 95: 301-316.
[61] Batra R.C., Porfiri M., Spinello D., 2006, Capacitance estimate for electrostatically actuated narrow microbeams, Micro & Nano Letters 1(2): 71-73.
[62] Israelachvili J.N., 2011, Intermolecular and Surface Forces, Academic Press, London.
[63] Lamoreaux S.K., 2005, The casimir force background, experiments, and applications, Reports on Progress in Physics 68(1): 201-236.
