Nonlocal Piezomagnetoelasticity Theory for Buckling Analysis of Piezoelectric/Magnetostrictive Nanobeams Including Surface Effects

Document Type: Research Paper

Authors

1 Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran --- Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan, Iran

2 Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

Abstract

This paper presents the surface piezomagnetoelasticity theory for size-dependent buckling analysis of an embedded piezoelectric/magnetostrictive nanobeam (PMNB). It is assumed that the subjected forces from the surrounding medium contain both normal and shear components. Therefore, the surrounded elastic foundation is modeled by Pasternak foundation. The nonlocal piezomagnetoelasticity theory is applied so as to consider the small scale effects. Based on Timoshenko beam (TB) theory and using energy method and Hamilton’s principle the motion equations are obtained. By employing an analytical method, the critical magnetic, electrical and mechanical buckling loads of the nanobeam are yielded. Results are presented graphically to show the influences of small scale parameter, surrounding elastic medium, surface layers, and external electric and magnetic potentials on the buckling behaviors of PMNBs. Results delineate the significance of surface layers and external electric and magnetic potentials on the critical buckling loads of PMNBs. It is revealed that the critical magnetic, electrical and mechanical buckling loads decrease with increasing the small scale parameter. The results of this work is hoped to be of use in micro/nano electro mechanical systems (MEMS/NEMS) especially in designing and manufacturing electromagnetoelastic sensors and actuators.

Keywords

[1] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 4703-4710.
[2] Aydogdu M., 2009, A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration, Physica E 41: 1651-1655.
[3] Thai H.T., 2012, A nonlocal beam theory for bending, buckling, and vibration of nanobeams, International Journal of Engineering Science 52: 56-64.
[4] Nazemnezhad R., Hosseini-Hashemi S., 2014, Nonlocal nonlinear free vibration of functionally graded nanobeams, Composite Structure 110: 192-199.
[5] Rahmani O., Pedram O., 2014, Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory, International Journal of Engineering Science 77: 55-70.
[6] Marotti de Sciarra F., Barretta R., 2014, A gradient model for Timoshenko nanobeams, Physica E 62: 1-9.
[7] Akgöz B., Civalek Ö., 2013, A size-dependent shear deformation beam model based on the strain gradient elasticity theory, International Journal of Engineering Science 70: 1-14.
[8] Mohammad Abadi M., Daneshmehr A.R., 2014, Size dependent buckling analysis of microbeams based on modified couple stress theory with high order theories and general boundary conditions, International Journal of Engineering Science 74: 1-14.
[9] Muralt P., 2001, Piezoelectric thin films for MEMS, Encyclopedia of Materials: Science and Technology 6999-7008.
[10] Nabar B.P., Çelik-Butler Z., Butler D.P., 2014, Piezoelectric ZnO nanorod carpet as a NEMS vibrational energy harvester, Nano Energy 10: 71-82.
[11] Falconi C., Mantini G., D’Amico A., Wang Z.L., 2009, Studying piezoelectric nanowires and nanowalls for energy harvesting, Sensors and Actuators B 139: 511-519.
[12] Sun C., Shi J., Wang X., 2010, Fundamental study of mechanical energy harvesting using piezoelectric nanostructures, Journal of Applied Physics 108: 034309.
[13] Ghorbanpour Arani A., Abdollahian M., Kolahchi R., Rahmati A.H., 2013, Electro-thermo-torsional buckling of an embedded armchair DWBNNT using nonlocal shear deformable shell model, Composites Part B 51: 291-299.
[14] Chen C., Li S., Dai L., Qian C.Z., 2014, Buckling and stability analysis of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces, Communications in Nonlinear Science and Numerical Simulation 19: 1626-1637.
[15] Asemi S.R., Farajpour A., Mohammadi M., 2014, Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory, Composite Structures 116: 703-712.
[16] Pradhan S.C., Reddy G.K., 2011, Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasticity theory and DTM, Computational Materials Science 50: 1052-1056.
[17] Han Q., Lu G., 2003, Torsional buckling of a double-walled carbon nanotube embedded in an elastic medium, European Journal of Mechanics-A/Solids 22: 875-883.
[18] Rahmati A.H., Mohammadimehr M., 2014, Vibration analysis of non-uniform and non-homogeneous boron nitride nanorods embedded in an elastic medium under combined loadings using DQM, Physica B 440: 88-98.
[19] Abdollahian A., Ghorbanpour Arani A., Mosallaei Barzoki A.A., Kolahchi, R., Loghman A., 2013, Non-local wave propagation in embedded armchair TWBNNTs conveying viscous fluid using DQM, Physica B 418: 1-15.
[20] Zenkour A.M., Sobhy M., 2013, Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium, Physica E 53: 251-259.
[21] Moshtaghin A.F., Naghdabadi R., Asghari M., 2012, Effects of surface residual stress and surface elasticity on the overall yield surfaces of nanoporous materials with cylindrical nanovoids, Mechanics of Materials 51: 74-87.
[22] Zhang C.h., Chen W., Zhang C.h., 2012, On propagation of anti-plane shear waves in piezoelectric plates with surface effect, Physics Letters A 376: 3281-3286.
[23] Zhang L.L., Liu J.X., Fang X.Q., Nie G.Q., 2014, Effects of surface piezoelectricity and nonlocal scale on wave propagation in piezoelectric nanoplates, European Journal of Mechanics-A/Solids 46: 22-29.
[24] Hosseini-Hashemi S., Nazemnezhad R., Bedroud M., 2014, Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity, Applied Mathematical Modelling 38: 3538-3553.
[25] Ansari R., Sahmani S., 2011, Bending behavior and buckling of nanobeams including surface stress effects corresponding to different beam theories, International Journal of Engineering Science 49: 1244-1255.
[26] Reddy K.S.M., Estrine E.C., Lim D.H., Smyrl W.H., Stadler B.J.H., 2012, Controlled electrochemical deposition of magnetostrictive Fe1-xGax alloys, Electrochemistry Communications 18: 127-130.
[27] Guo J., Moritaa S., Yamagataa Y., Higuchi T., 2013, Magnetostrictive vibrator utilizing iron–cobalt alloy, Sensors and Actuators A 200: 101-106.
[28] Wang H., Zhang Z.D., Wu R.Q., Sun L.Z., 2013, Large-scale first-principles determination of anisotropic mechanical properties of magnetostrictive Fe–Ga alloys, Acta Materialia 61: 2919-2925.
[29] Espinosa-Almeyda Y., Rodríguez-Ramos R., Guinovart-Díaz R., Bravo-Castillero J., López-Realpozo J.C., Camacho-Montes H., Sabina F.J., Lebon F., 2014, Antiplane magneto-electro-elastic effective properties of three-phase fiber composites, International Journal of Solids and Structures 51: 3508-3521.
[30] Elloumi R., Kallel-Kamoun I., El-Borgi S., Guler M.A., 2014, On the frictional sliding contact problem between a rigid circular conducting punch and a magneto-electro-elastic half-plane, International Journal of Mechanical Sciences 87: 1-17.
[31] Ma J., Ke L.L., Wang Y.S., 2014, Frictionless contact of a functionally graded magneto-electro-elastic layered half-plane under a conducting punch, International Journal of Solids and Structures 51: 2791-2806.
[32] Wei J., Su X., 2008, Transient-state response of wave propagation in magneto-electro-elastic square column, Acta Mechanica Solida Sinica 21: 491-499.
[33] Lang Z., Xuewu L., 2013, Buckling and vibration analysis of functionally graded magneto-electro-thermo-elastic circular cylindrical shells, Applied Mathematical Modelling 37: 2279-2292.
[34] Li Y.S., 2014, Buckling analysis of magnetoelectroelastic plate resting on Pasternak elastic foundation, Mechanics Research Communications 56: 104-114.
[35] Razavi S., Shooshtari A., 2015, Nonlinear free vibration of magneto-electro-elastic rectangular plates, Composite Structures 119: 377-384.
[36] Li Y.S., Cai Z.Y., Shi S.Y., 2014, Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory, Composite Structures 111: 522-529.
[37] Ke L.L., Wang Y.S., 2014, Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory, Physica E 63: 52-61.
[38] Ghorbanpour Arani A., Abdollahian M., Kolahchi R., 2014, Nonlinear vibration of embedded smart composite microtube conveying fluid based on modified couple stress theory, Polymer Composites 36: 1314-1324.
[39] Gurtin M.E., Murdoch A.I., 1957, A continuum theory of elastic material surface, Archived for Rational Mechanics Analysis 57: 291-323.
[40] Ansari R., Mohammadi V., Faghih Shojaei M., Gholami R., Sahmani S., 2013, Postbuckling characteristics of nanobeams based on the surface elasticity theory, Composites part B 55: 240-246.
[41] Lu P., He L.H., Lee H.P., Lu C., 2006, Thin plate theory including surface effects, International Journal of Solids and Structures 43: 4631-4647.