Vibration Analysis of Magneto-Electro-Elastic Timoshenko Micro Beam Using Surface Stress Effect and Modified Strain Gradient Theory under Moving Nano-Particle
Subject Areas : EngineeringM Mohammadimehr 1 , H Mohammadi Hooyeh 2
1 - Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
2 - Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Keywords:
Abstract :
[1] Sun K.H., Kim Y.Y., 2010, Layout design optimization for magneto-electro-elastic laminate composites for maximized energy conversion under mechanical loading, Smart Materials and Structures 19: 055008.
[2] Wang B.L., Niraula O.P., 2007, Transient thermal fracture analysis of transversely isotropic magneto-electro-elastic materials, Journal of Thermal Stresses 30: 297-317.
[3] Priya S., Islam R., Dong S., Viehland D., 2007, Recent advancements in magneto-electric particulate and laminate composites, Journal of Electroceramics 19: 149-166.
[4] Zhai J., Xing Z., Dong S., Li J., Viehland D., 2008, Magnetoelectric laminate composites: an overview, Journal of the American Ceramic Society 91: 351-358.
[5] Nan C.W., Bichurin M., Dong S., Viehland D., Srinivasan G., 2008, Multiferroic magnetoelectric composites: historical perspective, status, and future directions, Journal of Applied Physics 103: 031101.
[6] Bhangale R.K., Ganesan N., 2006, Free vibration of functionally graded non-homogeneous magneto-electro-elastic cylindrical shell, International Journal for Computational Methods in Engineering Science and Mechanics 7: 191-200.
[7] 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.
[8] Razavi S., Shooshtari A., 2015, Nonlinear free vibration of magneto-electro-elastic rectangular plates, Composite Structures 119: 377-384.
[9] Ke L.L., Wang Y.S., Yang J., Kitipornchai S., 2014, Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory, Acta Mechanica Sinica 30: 516-525.
[10] Li Y.S., Cai Z.Y., Shi S.Y., 2014, Buckling and free vibration of magneto-electro-elastic nanoplate based on nonlocal theory, Composite Structures 111: 522-529.
[11] Shooshtari A., Razavi S., 2015, Linear and nonlinear free vibration of a multilayered magneto-electro-elastic doubly-curved shell on elastic foundation, Composite Part B 78: 95-108.
[12] Shooshtari A., Razavi S., 2015, Large amplitude free vibration of symmetrically laminated magneto-electro-elastic rectangular plates on Pasternak type foundation, Mechanics Research Communications 69: 103-113.
[13] Mohammadimehr M., Rostami R., Arefi M., 2016, Electro-elastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT, Steel and Composite Structures 20: 513-543.
[14] Ansari R., Gholami R., Rouhi H., 2015, Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko Nano beams based upon the nonlocal elasticity theory, Composite Structures 126: 216-226.
[15] Xin L., Hu Z., 2015, Free vibration of layered magneto-electro-elastic beams by SS-DSC approach, Composite Structures 125: 96-103.
[16] Xin L., Hu Z., 2015, Free vibration of simply supported and multilayered magneto-electro-elastic plates, Composite Structures 121: 344-350.
[17] Mohammadimehr M., Monajemi A.A., Moradi M., 2015, Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-Pasternak foundation using DQM, Journal of Mechanical Science and Technology 29 (6): 2297-2305.
[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: Condensed Matter 440: 88-98.
[19] Ke L.L., Wang Y.S., 2014, Free vibration of size-dependent magneto-electro-elastic Nano beams based on the nonlocal theory, Phisyca E 63: 52-61.
[20] Wang Y., Xu R., Ding H., 2011, Axisymmetric bending of functionally graded circular magneto-electro-elastic plates, European Journal of Mechanics-A/Solid 30: 999-1011.
[21] Rao M.N., Schmidt R., Schröder K.U., 2015, Geometrically nonlinear static FE-simulation of multilayered magneto-electro-elastic, Composite Structures 127: 120-131.
[22] 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 Structures 131: 654-671.
[23] Mohammadimehr M., Rousta Navi B., Ghorbanpour Arani A., 2016, Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT, Composite Part B: Engineering 87: 132-148.
[24] Kattimani S.C., Ray M.C., 2015, Control of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic plates, International Journal of Mechanical Sciences 99: 154-167.
[25] Liu Y., Han Q., Li C., Liu X., Wu B., 2015, Guided wave propagation and mode differentiation in the layered magneto-electro-elastic hollow cylinder, Composite Structures 132: 558-566.
[26] Sedighi H. M., Farjam N., 2016, A modified model for dynamic instability of CNT based actuators by considering rippling deformation, tip-charge concentration and Casimir attraction, Microsystem Technologies 23: 2175-2191.
[27] Zare J., 2015, Pull-in behavior analysis of vibrating functionally graded micro-cantilevers under suddenly DC voltage, Journal of Applied and Computational Mechanics 1(1): 17-25.
[28] Sedighi H. M., 2014, The influence of small scale on the pull-in behavior of nonlocal nano bridges considering surface effect, Casimir and van der Waals attractions, International Journal of Applied Mechanics 6(3): 1450030.
[29] Fleck N. A., Hutchinson J. W., 1993, Phenomenological theory for strain gradient effects in plasticity, Journal of the Mechanics and Physics of Solids 41(12): 1825-1857.
[30] Fleck N. A., Hutchinson J. W., 1997, Strain gradient plasticity, Advances in Applied Mechanics 33: 296-358.
[31] Fleck N. A., Hutchinson J. W., 2001, A reformulation of strain gradient plasticity, Journal of the Mechanics and Physics of Solids 49(10): 2245- 2271.
[32] Lam D.D.C., Yang F., Chong A.C.M., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics Solids 51: 1477-1508.
[33] 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.
[34] Mohammadimehr M., Salemi M., Rousta Navi B., 2016, Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature- dependent material properties under hydro-thermo-mechanical loadings using DQM, Composite Structures 138: 361-380.
[35] Gurtin M., Ian Murdoch A., 1975, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis 57: 291-323.
[36] Gurtin M., Ian Murdoch A., 1987, Surface stress in solids, International Journal of Solids and Structures 14: 431-440.
[37] Mohammadimehr M., Rousta Navi B., Ghorbanpour Arani A., 2015, Surface stress effect on the nonlocal biaxial buckling and bending analysis of polymeric piezoelectric Nano plate reinforced by CNT using Eshelby-Mori-Tanaka approach, Journal of Solid Mechanics 7( 2): 173-190.
[38] Karimi M., Shokrani M. H., Shahidi A. R., 2015, Size-dependent free vibration analysis of rectangular nanoplates with the consideration of surface effects using finite difference method, Journal of Applied and Computational Mechanics 1(3): 122-133.
[39] Ghorbanpour Arani A., Kolahchi R., Mosayebi M., Jamali M., 2016, Pulsating fluid induced dynamic instability of visco-double-walled carbon nano-tubes based on sinusoidal strain gradient theory using DQM and Bolotin method, International Journal of Mechanics and Materials in Design 12(1): 17-38.
[40] Ansari R., Gholami R., Sahmani S., 2011, Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory, Composite Structures 94 : 221-228.
[41] Şimşek M., Kocatürk T., Akbaş Ş.D., 2013, Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory, Composite Structures 95: 740-747.
[42] Li Y.S., Feng W.J., Cai Z.Y., 2014, Bending and free vibration of functionally graded piezoelectric beam based on modified strain gradient theory, Composite Structures 115: 41-50.
[43] Ghorbanpour Arani A., Abdollahian M., Kolahchi R., 2015, Nonlinear vibration of a Nano beam elastically bonded with a piezoelectric Nano beam via strain gradient theory, International Journal of Mechanical Sciences 100: 32-40.
[44] Ansari R., Mohammadi V., Faghih Shojaei M., Gholami R., Rouhi H., 2013, Nonlinear vibration analysis of Timoshenko Nano beams based on surface stress elasticity theory, European Journal of Mechanics-A/Solid 45 :143-152.
[45] Ke L.L., Wang Y.S., Wang Z.D., 2012, Nonlinear vibration of the piezoelectric Nano beams based on the nonlocal theory, Composite Structures 94: 2038-2047.
[46] Şimşek M., 2011, Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle, Computational Materials Science 50: 2112-2123.
[47] Ghorbanpour Arani A., Mortazavi S.A., Kolahchi R., Ghorbanpour Arani A.H., 2015, Vibration response of an elastically connected double-Smart Nano beam-system based nano-electro-mechanical sensor, Journal of Solid Mechanics 7: 121-130.
[48] Ghorbanpour Arani A., Atabakhshian V., Loghman A., Shajari A.R., Amir S., 2012, Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method, Phisyca B 407: 2549-2555.
[49] Murmu T., Pradhan S.C., 2009, Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Phisyca E 41: 1232-1239.
[50] Civalek O., 2006, Harmonic differential quadrature-finite differences coupled approaches for geometrically nonlinear static and dynamic analysis of rectangular plates on elastic foundation, Journal of Sound and Vibrations 294: 966-980.
[51] Akgoz B., Civalek O., 2011, Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams, International Journal of Engineering Science 49: 1268-1280.
[52] Zhang B., He Y., Liu D., Gan Z., Shen L., 2014, Non - classical Timoshenko beam element based on the strain gradient elasticity theory, Finite Element in Analysis and Design 79: 22-39.
[53] Ansari R., Gholami R., Darabi M.A., 2012, A non-linear Timoshenko beam formulation based on strain gradient theory, Journal of Mechanics of Materials and Structures 7: 195-211.
[54] Ghorbanpour Arani A., Kolahchi R., Zarei M.Sh., 2015, Visco-surface-nonlocal piezo-elasticity effects on nonlinear dynamic stability of graphene sheets integrated with ZnO sensors and actuators using refined zigzag theory, Composite Structures 132: 506-526.