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Nonlinear magneto-electro-mechanical vibration analysis of double-bonded sandwich Timoshenko microbeams based on MSGT using GDQM
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 Title & Authors
Nonlinear magneto-electro-mechanical vibration analysis of double-bonded sandwich Timoshenko microbeams based on MSGT using GDQM
Mohammadimehr, M.; Shahedi, S.;
In the present study, the nonlinear magneto-electro-mechanical free vibration behavior of rectangular double-bonded sandwich microbeams based on the modified strain gradient theory (MSGT) is investigated. It is noted that the top and bottom sandwich microbeams are considered with boron nitride nanotube reinforced composite face sheets (BNNTRC-SB) with electrical properties and carbon nanotube reinforced composite face sheets (CNTRC-SB) with magnetic fields, respectively, and also the homogenous core is used for both sandwich beams. The connections of every sandwich beam with its surrounding medium and also between them have been carried out by considering Pasternak foundations. To take size effect into account, the MSGT is introduced into the classical Timoshenko beam theory (CT) to develop a size-dependent beam model containing three additional material length scale parameters. For the CNTRC and BNNTRC face sheets of sandwich microbeams, uniform distribution (UD) and functionally graded (FG) distribution patterns of CNTs or BNNTs in four cases FG-X, FG-O, FG-A, and FG-V are employed. It is assumed that the material properties of face sheets for both sandwich beams are varied in the thickness direction and estimated through the extended rule of mixture. On the basis of the Hamilton`s principle, the size-dependent nonlinear governing differential equations of motion and associated boundary conditions are derived and then discretized by using generalized differential quadrature method (GDQM). A detailed parametric study is presented to indicate the influences of electric and magnetic fields, slenderness ratio, thickness ratio of both sandwich microbeams, thickness ratio of every sandwich microbeam, dimensionless three material length scale parameters, Winkler spring modulus and various distribution types of face sheets on the first two natural frequencies of double-bonded sandwich microbeams. Furthermore, a comparison between the various beam models on the basis of the CT, modified couple stress theory (MCST), and MSGT is performed. It is illustrated that the thickness ratio of sandwich microbeams plays an important role in the vibrational behavior of the double-bonded sandwich microstructures. Meanwhile, it is concluded that by increasing H/lm, the values of first two natural frequencies tend to decrease for all amounts of the Winkler spring modulus.
smart materials;nonlinear vibration analysis;double-bonded sandwich Timoshenko microbeams;size effect;MSGT;GDQM;
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Akgoz, B. and Civalek, O. (2011), "Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams", Int. J. Eng. Sci., 49(11), 1268-1280. crossref(new window)

Akgoz, B. and Civalek, O. (2012), "Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory", Arch. Appl. Mech., 82(3), 423-443. crossref(new window)

Akgoz, B. and Civalek, O. (2013a), "Buckling analysis of functionally graded microbeams based on the strain gradient theory", Acta. Mech., 224(9), 1-17. crossref(new window)

Akgoz, B. and Civalek, O. (2013b), "A size-dependent shear deformation beam model based on the strain gradient elasticity theory", Int. J. Eng. Sci., 70, 1-14. crossref(new window)

Alibeigloo, A. and Liew, K.M. (2014), "Free vibration analysis of sandwich cylindrical panel with functionally graded core using three-dimensional theory of elasticity", Compos. Struct., 113, 23-30. crossref(new window)

Allen, H.G. (1969), Analysis and Design of Structural Sandwich Panels, Pergamon Press, London, UK

Ansari, R., Gholami, R. and Sahmani, S. (2011), "Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory", Compos. Struct., 94(1), 221-228. crossref(new window)

Ansari, R., Gholami, R., Faghih Shojaei, M., Mohammadi, V. and Sahmani, S. (2013), "Size-dependent bending, buckling and free vibration of functionally graded Timoshenko microbeams based on the most general strain gradient theory", Compos. Struct., 100, 385-397. crossref(new window)

Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423. crossref(new window)

Bouremana, M., Houari, M.S.A., Tounsi, A., Kaci, A. and Bedia, E.A.A. (2013), "A new first shear deformation beam theory based on neutral surface position for functionally graded beams", Steel Compos. Struct., Int. J., 15(5), 467-479. crossref(new window)

Bui, T.Q., Khosravifard, A., Zhang, C., Hematiyan, M.R. and Golub, M.V. (2013), "Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method", Eng. Struct., 47, 90-104. crossref(new window)

Chehel Amirani, M., Khalili, S.M.R. and Nemati, N. (2009), "Free vibration analysis of sandwich beam with FG core using the element free Galerkin method", Compos. Struct., 90(3), 373-379. crossref(new window)

Damanpack, A.R. and Khalili, S.M.R. (2012), "High-order free vibration analysis of sandwich beams with a flexible core using dynamic stiffness method", Compos. Struct, 94(5), 1503-1514. crossref(new window)

Dariushi, S. and Sadighi, M. (2013), "A new nonlinear high order theory for sandwich beams: An analytical and experimental investigation", Compos. Struct., 108, 779-788.

Fleck, N.A. and Hutchinson, J.W. (1993), "A phenomenological theory for strain gradient effects in plasticity", J. Mech. Phys. Solids., 41(12), 1825-1857. crossref(new window)

Ghasemi, H., Brighenti, R., Zhuang, X., Muthu, J. and Rabczuk, T. (2014a), "Optimization of fiber distribution in fiber reinforced composite by using NURBS functions", Comput. Mater. Sci., 83(15), 463-473. crossref(new window)

Ghasemi, H., Rafiee, R., Zhuang, X., Muthu, J., Rabczuk, T. (2014b), "Uncertainties propagation in metamodel-based probabilistic optimization of CNT/polymer composite structure using stochastic multiscale modeling", Comput. Mater. Science, 85, 295-305. crossref(new window)

Ghasemi, H., Kerfriden, P., Bordas, S.P.A., Muthu, J., Zi, G. and Rabczuk, T. (2014c), "Interfacial shear stress optimization in sandwich beams with polymeric core using non-uniform distribution of reinforcing ingredients", Compos. Struct., 120, 221-230.

Ghasemi, H., Brighenti, R., Zhuang, X., Muthu, J. and Rabczuk, T. (2015), "Optimal fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach", Struct. Multidisc. Optim., 51(1), 99-112. crossref(new window)

Ghorbanpour Arani, A. and Amir, S. (2013), "Electro-thermal vibration of visco-elastically coupled BNNT systems conveying fluid embedded on elastic foundation via strain gradient theory", Physica B, 419, 1-6. crossref(new window)

Ghorbanpour Arani, A., Haghparast, E., Heidari Rarani, M. and Khoddami Maraghi, Z. (2015), "Strain gradient shell model for nonlinear vibration analysis of visco-elastically coupled Boron Nitride nano-tube reinforced composite micro-tubes conveying viscous fluid", Comput. Mater. Sci., 96, 448-458. crossref(new window)

Griebel, M. and Hamaekers, J. (2004), "Molecular dynamics simulations of the elastic moduli of polymer-carbon nanotube composites", Comput. Meth. Appl. Mech. Eng., 193, 1773-1788. crossref(new window)

Grygorowicz, M., Magnucki, K. and Malinowski, M. (2015), "Elastic buckling of a sandwich beam with variable mechanical properties of the core", Thin-Walled Struct., 87, 127-132. crossref(new window)

Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Comput. Mater. Sci., 39(2), 315-323. crossref(new window)

Jedari Salami, S., Sadighi, M. and Shakeri, M. (2015), "Improved High order analysis of sandwich beams by considering a bilinear elasto-plastic behavior of core: An analytical and experimental investigation", Int. J. Mech. Sci., 93, 270-289. crossref(new window)

Kahrobaiyan, M.H., Rahaeifard, M., Tajalli, S.A. and Ahmadian, MT. (2012), "A strain gradient functionally graded Euler-Bernoulli beam formulation", Int. J. Eng. Sci., 52, 65-76. crossref(new window)

Kong, S., Zhou, S., Nie, Z. and Wang, K. (2009), "Static and dynamic analysis of microbeams based on strain gradient elasticity theory", Int. J. Eng. Sci., 47(4), 487-498. crossref(new window)

Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51(8), 1477-1508. crossref(new window)

Lanc, D., Vo, T.P., Turkalj, G. and Lee, J. (2015), "Buckling analysis of thin-walled functionally graded sandwich box beams", Thin-Wall. Struct., 86, 148-156. crossref(new window)

Lei, J., He, Y., Zhang, B., Gan, Z. and Zeng, P. (2013), "Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory", Int. J. Eng. Sci., 72, 36-52. crossref(new window)

Liang, X., Hu, S. and Shen, S. (2014), "A new Bernoulli-Euler beam model based on a simplified strain gradient elasticity theory and its applications", Compos. Struct., 111, 317-323. crossref(new window)

Liew, K.M., Lei, Z.X. and Zhang, L.W. (2015), "Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review", Compos. Struct., 120, 90-97. crossref(new window)

Mohammadimehr, M., Saidi, A.R., Ghorbanpour Arani, A., Arefmanesh, A. and Han, Q. (2010), "Torsional buckling of a DWCNT embedded on winkler and pasternak foundations using nonlocal theory", J. Mech. Sci. Technol., 24(6), 1289-1299. crossref(new window)

Mohammadimehr, M., Monajemi, A.A. and Moradi, M. (2015a), "Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-pasternak foundation using DQM", J. Mech. Sci. Technol., 29(6), 2297-2305. crossref(new window)

Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2015b), "Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method", Compos. Struct., 131, 654-671. crossref(new window)

Mohammadimehr, M., Rostami, R. and Arefi, M. (2016a), "Electro-elastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT", Steel Compos. Struct., Int. J., 20(3), 513-543. crossref(new window)

Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2016b), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT", Compos. Part B, 87, 132-148. crossref(new window)

Mohammadimehr, M., Salemi, M. and Rousta Navi, B. (2016c), "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", Compos. Struct., 138, 361-380. crossref(new window)

Nanthakumar, S., Valizadeh, N., Park, H.S. and Rabczuk, T. (2015), "Shape and topology optimization of nanostructures using a coupled XFEM/level set method", Comput. Mech., 56(1), 97-112. crossref(new window)

Plantema, F.J. (1966), Sandwich Construction: The Bending and Buckling of Sandwich Beams, Plates and Shells, John Wiley and Sons, New York, NY, USA.

Rahmani, O., Khalili, S.M.R., Malekzadeh, K. and Hadavinia, H. (2009), "Free vibration analysis of sandwich structures with a flexible functionally graded syntactic core", Compos. Struct., 91(2), 229-235. crossref(new window)

Reissner, E. (1948), "Finite deflections of sandwich plates", J. Aeronaut. Sci., 15(7), 435-440. crossref(new window)

Sahmani, S. Bahrami, M. and Ansari, R. (2014), "Nonlinear free vibration analysis of functionally graded third-order shear deformable microbeams based on the modified strain gradient elasticity theory", Compos. Struct., 110, 219-230. crossref(new window)

Salehi-Khojin, A. and Jalili, N. (2008), "Buckling of boron nitride nanotube reinforced piezoelectric polymeric composites subject to combined electro-thermo-mechanical loadings", Compos. Sci. Technol., 68(6), 1489-1501. crossref(new window)

Shu, C. (2000), Differential Quadrature and its Application in Engineering, Springer Publication, New York, NY, USA.

Shu, C. and Du, H. (1997), "Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates", J. Sound Vib., 34(7), 819-835.

Taibi, F.Z., Benyoucef, S., Tounsi, A., Bouiadjra, R.B., Bedia, A.A. and Mahmoud, S. (2015), "A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 17, 99-129. crossref(new window)

Tajalli, S.A., Rahaeifard, M., Kahrobaiyan, M.H., Movahhedy, M.R., Akbari, J. and Ahmadian, M.T. (2013), "Mechanical behavior analysis of size-dependent micro-scaled functionally graded Timoshenko beams by strain gradient elasticity theory", Compos. Struct., 102, 72-80. crossref(new window)

Vinson, J.R. (1999), The Behavior of Sandwich Structures of Isotropic and Composite Materials, Technomic Publishing Co. Inc., Lancaster, England.

Vo, T.P., Thai, H.T., Nguyen, T.K., Maheri, A. and Lee, J. (2014), "Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory", Eng. Struct., 64, 12-22. crossref(new window)

Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F. and Lee, J. (2015), "A quasi-3D theory for vibration and buckling of functionally graded sandwich beams", Compos. Struct., 119, 1-12. crossref(new window)

Wang, Z.X. and Shen, H.S. (2011), "Nonlinear analysis of sandwich plates with FGM face sheets resting on elastic foundations", Compos. Struct., 93(10), 2521-2532. crossref(new window)

Wang, Z.X. and Shen, H.S. (2012), "Nonlinear vibration and bending of sandwich plates with nanotubereinforced composite face sheets", Compos. Part B, 43(2), 411-421. crossref(new window)

Wang, Y. and Wang, X. (2014), "Static analysis of higher order sandwich beams by weak form quadrature element method", Compos. Struct., 116, 841-848. crossref(new window)

Wang, B., Zhao, J. and Zhou, S. (2010), "A microscale Timoshenko beam model based on strain gradient elasticity theory", Eur. J. Mech. A-Solid, 29(4), 591-599. crossref(new window)

Yang, F., Chong, A.C.M. and Lam, D.C.C. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solid. Struct., 39(10), 2731-2743. crossref(new window)

Yang, Y., Lam, C.C., Kou, K.P. and Iu, V.P. (2014), "Free vibration analysis of the functionally graded sandwich beams by a meshfree boundary-domain integral equation method", Compos. Struct., 117, 32-39. crossref(new window)

Yas, M.H. and Samadi, N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", Int. J. Pressure Vessels Pip., 98, 119-128. crossref(new window)

Zenkert, D. (1995), An Introduction to Sandwich Construction, Chameleon Press Ltd., London, UK.

Zhang, C.L. and Shen, H.S. (2006), "Temperature-dependent elastic properties of single-walled carbon nanotubes: prediction from molecular dynamics simulation", Appl. Phys. Lett., 89(8), 081904. crossref(new window)

Zhang, B., He, Y., Liu, D., Gan, Z. and Shen, L. (2014), "Non-classical Timoshenko beam element based on the strain gradient elasticity theory", Finite Elem. Anal. Des., 79, 22-39. crossref(new window)