Nonlinear Dynamic Buckling of Viscous-Fluid-Conveying PNC Cylindrical Shells with Core Resting on Visco-Pasternak Medium

Document Type : Research Paper


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

2 Faculty of Mechanical Engineering, University of Kashan


The use of intelligent nanocomposites in sensing and actuation applications has become quite common over the past decade. In this article, electro-thermo-mechanical nonlinear dynamic buckling of an orthotropic piezoelectric nanocomposite (PNC) cylindrical shell conveying viscous fluid is investigated. The composite cylindrical shell is made from Polyvinylidene Fluoride (PVDF) and reinforced by zigzag boron nitride nanotubes (BNNTs) where characteristics of the equivalent PNC being determined using micro-mechanical model. The poly ethylene (PE) foam-core is modeled based on Pasternak foundation. Employing the charge equation, Donnell's theory and Hamilton's principle, the four coupled nonlinear differential equations containing displacement and electric potential terms are derived. Harmonic differential quadrature method (HDQM) is applied to obtain the critical dynamic buckling load. A detailed parametric study is conducted to elucidate the influences of the geometrical aspect ratio, in-fill ratio of core, viscoelastic medium coefficients, material types of the shell and temperature gradient on the dynamic buckling load of the PNC cylindrical shell. Results indicate that the dimensionless critical dynamic buckling load increases when piezoelectric effect is considered.


[1] Kim S.E., Kim Ch.S., 2002, Buckling strength of the cylindrical shell and tank subjected to axially compressive loads, Thin-Walled Structures 40:329-353.
[2] Ghorbanpour Arani A., Golabi S., Loghman A., Daneshi H., 2007, Investigating elastic stability of cylindrical shell with an elastic core under axial compression by energy method, Journal of Mechanical Science and Technology 21:693-698.
[3] Ghorbanpour Arani A., Loghman A., Mosallaie Barzoki A.A., Kolahchi R., 2011, Elastic buckling analysis of ring and stringer-stiffened cylindrical shells under general pressure and axial compression via the Ritz method, Journal of Solid Mechanics 1:332-347.
[4] Das P.K., Thavalingam A., Bai Y., 2003, Buckling and ultimate strength criteria of stiffened shells under combined loading for reliability analysis, Thin-Walled Structures 41:69-88.
[5] Hubner A., Albiez M., Kohler D., Saal H., 2007, Buckling of long steel cylindrical shells subjected to external pressure, Thin-Walled Structures 45:1-7.
[6] Patel S.N., Datta P.K., Sheikh A.H. 2006, Buckling and dynamic instability analysis of stiffened shell panels, Thin-Walled Structures 44:321-333.
[7] Huang H., Han Q., 2010, Nonlinear dynamic buckling of functionally graded cylindrical shells subjected to time-dependent axial load, Composite Structures 92:593-598.
[8] Bisagni C.H., 2005, Dynamic buckling of fiber composite shells under impulsive axial compression, Thin-Walled Structures 43:499-514.
[9] Shariyat M., 2010, Non-linear dynamic thermo-mechanical buckling analysis of the imperfect sandwich plates based on a generalized three-dimensional high-order global–local plate theory, Composite Structures 92:72-85.
[10] Wan H., Delale F., Shen L., 2005, Effect of CNT length and CNT-matrix interphase in carbon nanotube (CNT) reinforced composites, Mechanics Research Communication 32:481-489.
[11] Li K., Saigal S., 2007, Micromechanical modeling of stress transfer in carbon nanotube reinforced polymer composites, Materials Science Engineering A 457:44-57.
[12] Han S.C.H., Tabiei A., Park W.T., 2008, Geometrically nonlinear analysis of laminated composite thin shells using a modified first-order shear deformable element-based Lagrangian shell element, Composite Structures 82:465-474.
[13] Wang X., 2007, Nonlinear stability analysis of thin doubly curved orthotropic shallow shells by the differential quadrature method, Computer Methods in Applied Mechanics and Engineering 196:2242-2251.
[14] Haftchenari H., Darvizeh M., Darvizeh A., Ansari R., Sharma C.B., 2007, Dynamic analysis of composite cylindrical shells using differential quadrature method (DQM), Composite Structures 78:292-298.
[15] Alibeigloo A., 2009, Static and vibration analysis of axi-symmetric angle-ply laminated cylindrical shell using state space differential quadrature method, International Journal of Pressure and Vessel and Piping 86:738-747.
[16] Mosallaie Barzoki A.A., Ghorbanpour Arani A., Kolahchi R., Mozdianfard M.R., 2012, Electro-thermo-mechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core, Applied Mathematical Modelling 36:2983-2995.
[17] Mosallaie Barzoki A.A., Ghorbanpour Arani A., Kolahchi R., Mozdianfard M.R., Loghman A., 2013, Nonlinear buckling response of embedded piezoelectric cylindrical shell reinforced with BNNT under electro–thermo-mechanical loadings using HDQM, Composite Part B: Engineering 44:722-727.
[18] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., 2011, Effect of material inhomogeneity on electro-thermo-mechanical behaviors of functionally graded piezoelectric rotating cylinder, Applied Mathematical Modelling 35:2771-2789.
[19] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., Loghman A., 2012, Electro-thermo-mechanical behaviors of FGPM spheres using analytical method and ANSYS software, Applied Mathematical Modelling 36:139-157.
[20] Ghorbanpour Arani A., Mosallaie Barzoki A.A, Kolahchi R., Mozdianfard M.R., Loghman A., 2011, Semi-analytical solution of time-dependent electro-thermo-mechanical creep for radially polarized piezoelectric cylinder, Computers and Structures 89: 1494-1502.
[21] Amabili M. 2008, Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, New York.
[22] Liew K.M., Han J.B., Xiao Z.M., 1996, Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility, International Journal of Solids and Structures 33:2647-2658.
[23] Civalek Ö., 2004, Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns, Engineering Structures 26:171-186.
[24] Abdollahian M., Ghorbanpour Arani A., Mosallaie 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.