[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.12989/sem.2016.60.3.489

Dynamic buckling of FGM viscoelastic nano-plates resting on orthotropic elastic medium based on sinusoidal shear deformation theory

Arani, A. Ghorbanpour (Faculty of Mechanical Engineering, University of Kashan)
Cheraghbak, A. (Faculty of Mechanical Engineering, University of Kashan)
Kolahchi, R. (Faculty of Mechanical Engineering, University of Kashan)

Publication Information

Structural Engineering and Mechanics / v.60, no.3, 2016 , pp. 489-505 More about this Journal

Abstract

Sinusoidal shear deformation theory (SSDT) is developed here for dynamic buckling of functionally graded (FG) nano-plates. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. In order to present a realistic model, the structural damping of nano-structure is considered using Kelvin-Voigt model. The surrounding elastic medium is modeled with a novel foundation namely as orthotropic visco-Pasternak medium. Size effects are incorporated based on Eringen'n nonlocal theory. Equations of motion are derived from the Hamilton's principle. The differential quadrature method (DQM) in conjunction with Bolotin method is applied for obtaining the dynamic instability region (DIR). The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, orthotropic visco-Pasternak foundation, power index of FG plate, structural damping and boundary conditions on the dynamic instability of system. The results are compared with those of first order shear deformation theory and higher-order shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the dynamic buckling responses of system.

Keywords

dynamic buckling; FG nano-plate; SSDT; viscoelastic; orthotropic visco-Pasternak medium;

Citations & Related Records

Times Cited By KSCI : 2 (Citation Analysis)

Reference
Cited By KSCI

1	Nami, M.R. and Janghorban, M. (2014), "Static analysis of rectangular nanoplates using exponential shear deformation theory based on strain gradient elasticity theory", Iran. J. Mat. Form., 1, 1-13.
2	Narendar, S. (2011), "Buckling analysis of micro/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects", Compos. Struct., 93, 3093-3103. DOI
3	Wang, Y.Z. and Li, F.M. (2012), "Static bending behaviors of Nanoplate embedded in elastic matrix with small scale effects", Mech. Res.Commun., 41, 44-48. DOI
4	Zenkour, A.M. (2009), "The refined sinusoidal theory for FGM plates on elastic foundations", Int. J. Mech. Sci., 51, 869-880. DOI
5	Amabili, M. (2004), "Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments", Comput. Struct., 82, 2587-2605. DOI
6	Bolotin, V.V. (1964), "The dynamic stability of elastic systems. in: the dynamic stability of elastic systems", Holden-Day, San Francisco.
7	Chakraverty, S. and Behera L. (2015), "Small scale effect on the vibration of non-uniform nanoplates", Struct. Eng. Mech., 55, 495-510. DOI
8	Chien, R.D. and Chen, C.S. (2006), "Nonlinear vibration of laminated plates on an elastic foundation", Thin Wall. Struct., 44, 852-860. DOI
9	Ebraheem, O., Ashraf, A. and Zenkour, M. (2013), "Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium", Compos. Struct., 105, 163-172. DOI
10	Ebrahimi, F. and Salari, E. (2015), "Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment", Acta Astronaut., 113, 29-50. DOI
11	Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. DOI
12	Lei, Y., Adhikari, S. and Friswell, M.I. (2013b), "Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams", Int. J. Eng. Sci., 66, 1-13.
13	Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011b), "Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure", Compos. Struct., 93, 722-735. DOI
14	Karlicic, D., Adhikari, S., Murmu, T. and Cajic, M. (2014), "Exact closed-form solution for non-local vibration and biaxial buckling of bonded multi-nanoplate system", Compos. Part B: Eng., 66, 328-339. DOI
15	Kutlu, A. and Omurtag, M.H. (2012), "Large deflection bending analysis of elliptic plates on orthotropic elastic foundation with mixed finite element method", Int. J. Mech. Sci., 65, 64-74 DOI
16	Lanhe, W., Hongjun, W. and Daobin, W. (2007), "Dynamic stability analysis of FGM plates by the moving least squares differential quadrature method", Compos. Struct., 77, 383-394. DOI
17	Lei, J., He, Y., Zhang, B., Gan, Z. and Zeng, P.C. (2013a), "Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory", Int. J. Eng. Sci., 72, 36-52. DOI
18	Li, J.J. and Cheng, C.J. (2005), "Differential quadrature method for nonlinear vibration of orthotropic plates with finite deformation and transverse shear effect", J. Sound Vib., 281, 295-309. DOI
19	Lu, P., Zhang, P.Q., Lee, H.P., Wang, C.M. and Reddy, J.N. (2007), "Non-local elastic plate theories", Proc. R. Soc. A, 463, 3225-3240. DOI
20	Malekzadeh, P. (2008), "Nonlinear free vibration of tapered Mindlin plates with edges elastically restrained against rotation using DQM", Thin Wall. Struct., 46.11-26. DOI
21	Nami, M.R. and Janghorban, M. (2013), "Static analysis of rectangular nanoplates using trigonometric shear deformation theory based on nonlocal elasticity theory", Beilstein J. Nanotechnol., 4, 968-973. DOI
22	Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011a), "A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates", Int. J. Mech. Sci., 53, 11-22. DOI
23	Ghorbanpour Arani, A., Kolahchi, R., Mosallaie Barzoki, A.A., Mozdianfard, M.R. and Noudeh Farahani, S.M. (2012), "Elastic foundation effect on nonlinear thermo-vibration of embedded double-layered orthotropic grapheme sheets using differential quadrature method", Inst. Mech. Eng. Part C, J. Mech. Eng. Sci., 227, 862-879.
24	Ghorbanpour Arani, A., Mosallaie Barzoki, A.A., Kolahchi, R. and Loghman, A. (2011), "Pasternak foundation effect on the axial and torsional waves propagation in embedded DWCNTs using nonlocal elasticity cylindrical shell theory", J. Mech. Sci. Tech., 25, 2385-2391. DOI

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