Vibration Analysis of Size-Dependent Piezoelectric Nanobeam Under Magneto-Electrical Field
محورهای موضوعی : Mechanical Engineering
M Ghadiri
1
(Department of Mechanics, Imam Khomeini International University, Qazvin, Iran)
M Karimi Asl
2
(Department of Mechanics, Imam Khomeini International University, Qazvin, Iran)
M Noroozi
3
(Department of Mechanics, Imam Khomeini International University, Qazvin, Iran)
کلید واژه: Nonlocal strain gradient, Piezoelectric nanobeam, Vibration analysis, Magneto-electro-viscoelastic, Viscoelastic damping,
چکیده مقاله :
The damping vibration characteristics of magneto-electro-viscoelastic (MEV) nanobeam resting on viscoelastic foundation based on nonlocal strain gradient elasticity theory (NSGT) is studied in this article. For this purpose, by considering the effects of Winkler-Pasternak, the viscoelastic medium consists of linear and viscous layers. with respect to the displacement field in accordance with the refined shear deformable beam theory (RSDT) and the Kelvin-Voigt viscoelastic damping model, the governing equations of motion are obtained using Hamilton’s principle based on nonlocal strain gradient theory (NSGT). Using Fourier Series Expansion, The Galerkin’s method adopted to solving differential equations of nanobeam with both of simply supported and clamped boundary conditions. Numerical results are obtained to show the influences of nonlocal parameter, the length scale parameter, slenderness ratio and magneto-electro-mechanical loadings on the vibration behavior of nanobeam for both types of boundary conditions. It is found that by increasing the magnetic potential, the dimensionless frequency can be increased for any value of the damping coefficient and vice versa. Moreover, negative/positive magnetic potential decreases/increases the vibration frequencies of thinner nanobeam. Also, the vibrating frequency decreases and increases with increasing nonlocal parameter and length scale parameter respectively.
[1] Eringen A., 1968, Mechanics of micromorphic continua, Mechanics of Generalized Continua 104: 18-35.
[2] Leissa A.W., 1969, Vibration of Plates, Ohio State University Columbus.
[3] Eringen A., 1972, Nonlocal polar elastic continua, International Journal of Engineering Science 10:1-16.
[4] Van den Boomgard J., Terrell D.R., Born R.A.J., 1974, An in situ grown eutectic magnetoelectric composite material, Journal of Materials Science 9: 1705-1709.
[5] Eringen A., 1976, Nonlocal Micropolar Field Theory, In Continuum Physics, Academic Press, New York.
[6] Eringen A., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54(9): 4703-4710.
[7] Eringen A., 2002, Nonlocal Continuum Field Theories, Springer, New York.
[8] Lam D.C.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 of Solids 51(8): 1477-1508.
[9] Peddieson J., Buchanan G.R., McNitt R.P., 2003, Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science 41(3-5): 305-312.
[10] Zheng H.,Wang J., Lofland S.E., 2004, Multiferroic BaTiO3-CoFe2O4 nanostructures, Science 303: 661-663.
[11] Wang Q., 2005, Wave propagation in carbon nanotubes via nonlocal continuum mechanics, Journal of Applied Physics 98: 124301.
[12] Eringen A., 2006, Nonlocal continuum mechanics based on distributions, International Journal of Engineering Science 44(3): 141-147.
[13] Martin L.W., Crane S.P., Chu Y.H., 2008, Multiferroics and magnetoelectrics: Thin films and nanostructures, Journal of Physics: Condensed Matter 20: 434220.
[14] Wang C.M., Kitipornchai S., Lim C.W., Eisenberger M., 2008, Beam bending solutions based on nonlocal Timoshenko beam theory, Journal of Engineering Mechanics 134: 475-481.
[15] 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, Physica E: Low-Dimensional Systems and Nanostructures 41(7): 1232-1239.
[16] Yang J., Ke L.L., Kitipornchai S., 2010, Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory, Physica E: Low-Dimensional Systems and Nanostructures 42(5): 1727-1735.
[17] Wang Y., Hu J.M., Lin Y.H., 2010, Multiferroic magnetoelectric composite nanostructures, NPG Asia Materials 2: 61-68.
[18] Civalek O., Demir C., 2011, Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory, Applied Mathematical Modelling 35: 2053-2067.
[19] Roque C.M.C., Ferreira A.J.M., Reddy J.N., 2011, Analysis of Timoshenko nanobeams with a nonlocal formulation and meshless method, International Journal of Engineering Science 49(9): 976-984.
[20] Prashanthi K., Shaibani P.M., Sohrabi A., 2012, Nanoscale magnetoelectric coupling in multiferroic BiFeO3 nanowires, Physica Status Solidi 6: 244-246.
[21] Zenkour A.M., Sobhy M., 2013, Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium, Physica E: Low-Dimensional Systems and Nanostructures, 53: 251-259.
[22] Şimşek M., Yurtcu H.H., 2013, Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory, Composite Structures 97: 378-386.
[23] 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(4): 516-525.
[24] Ke L.L., Wang Y.S., 2014, Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory, Physica E: Low-Dimensional Systems and Nanostructures 63: 52-61.
[25] Mantari J.L., Bonilla E.M., Soares C.G., 2014, A new tangential-exponential higher order shear deformation theory for advanced composite plates, Composites Part B: Engineering 60: 319-328.
[26] Li L., Hu Y., Ling L., 2015, Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory, Composite Structures 133: 1079-1092.
[27] Ebrahimi F., Salari E., 2015a, Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent FG nanobeams, Mechanics of Advanced Materials and Structures 23: 1379-1397.
[28] Arefi M., Zenkour A.M., 2016, A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment, Journal of Sandwich Structures & Materials 18(5): 624-651.
[29] Ebrahimi F., Barati M.R., 2016, Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment, Journal of Vibration and Control 24: 549-564.
[30] Ebrahimi F., Barati M.R., 2016, Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium, Journal of the Brazilian Society of Mechanical Sciences and Engineering 39: 937-952.
[31] Ebrahimi F., Barati M.R., 2016, Dynamic modeling of a thermo–piezo-electrically actuated nanosize beam subjected to a magnetic field, Applied Physics A 122(4): 1-18.
[32] Ebrahimi F., Barati M.R., 2016, Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment, International Journal of Smart and Nano Materials 7(2): 1-22.
[33] Ebrahimi F., Barati M.R., 2016, An exact solution for buckling analysis of embedded piezoelectro-magnetically actuated nanoscale beams, Advances in Nano Research 4(2): 65-84.
