Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation

References

• Z. W. Pan, Z. R. Dai, and Z. L. Wang, Nanobelts of Semiconducting Oxides, Science, vol. 291, pp. 1947–1949, 2001.
   PubMed Web of Science ®Google Scholar
• K. M. Liew, J. Yang, and S. Kitipornchai, Postbuckling of Piezoelectric FGM Plates Subject to Thermo-electro-mechanical Loading, Int. J. Solids Struct., vol. 40, pp. 3869–3892, 2003.
   Web of Science ®Google Scholar
• X. L. Chen, Z. Y. Zhao, and K. M. Liew, Stability of Piezoelectric FGM Rectangular Plates Subjected to Non-uniformly Distributed Load, Heat and Voltage, Adv. Eng. Softw., vol. 39, pp. 121–31, 2008.
   Web of Science ®Google Scholar
• A. Alibeigloo and W. Q. Chen, Elasticity Solution for an FGM Cylindrical Panel Integrated with Piezoelectric Layers, Eur. J. Mech. A Solid., vol. 29, pp. 714–723, 2010.
   Web of Science ®Google Scholar
• M. Foda, A. Almajed, and M. ElMadany, Vibration Suppression of Composite Laminated Beams Using Distributed Piezoelectric Patches, Smart. Mater. Struct., vol. 19, pp. 115018, 2010.
   Web of Science ®Google Scholar
• N. D. Duc, T. Q. Quan, and V. D. Luat, Nonlinear Dynamic Analysis and Vibration of Shear Deformable Piezoelectric FGM Double Curved Shallow Shells Under Damping-thermo-electro-mechanical Loads, Compos. Struct., vol. 125, pp. 29–40, 2015.
   Web of Science ®Google Scholar
• J. Sun, X. Xu, C. W. Lim, Z. Zhou, and S. Xiao, Accurate Thermo-electro-mechanical Buckling of Shear Deformable Piezoelectric Fiber-reinforced Composite Cylindrical Shells, Compos. Struct., vol. 141, pp. 221–231, 2016.
   Web of Science ®Google Scholar
• A. M. Zenkour, Piezoelectric Behavior of an Inhomogeneous Hollow Cylinder with Thermal Gradient, Int. J. Thermophys., vol. 33, pp. 1288–1301, 2012.
   Web of Science ®Google Scholar
• M. N. M. Allam, A. M. Zenkour, and R. Tantawy, Analysis of Functionally Graded Piezoelectric Cylinders in a Hygrothermal Environment, Adv. Appl. Math. Mech., vol. 6, pp. 233–246, 2014.
   Web of Science ®Google Scholar
• A. M. Zenkour, Hygrothermoelastic Responses of Inhomogeneous Piezoelectric and Exponentially Graded Cylinders, Int. J. Press. Vess. Pip., vol. 119, pp. 8–18, 2014.
   Web of Science ®Google Scholar
• A. M. Zenkour, Exact Solution of Thermal Stress Problem of an Inhomogeneous Hygrothermal Piezoelectric Hollow Cylinder, Appl. Math. Model., vol. 38, pp. 6133–6143, 2014.
   Web of Science ®Google Scholar
• M. Cinefra, A. Lamberti, A. M. Zenkour, and E. Carrera, Axiomatic/Asymptotic Technique Applied to Refined Theories for Piezoelectric Plates, Mech. Adv. Mater. Struct., vol. 22, pp. 107–124, 2015.
   Web of Science ®Google Scholar
• F. Yang, A. C. M. Chong, D. C. C. Lam, and P. Tong, Couple Stress based Strain Gradient Theory for Elasticity, Int. J. Solids Struct., vol. 39, pp. 2731–2743, 2002.
   Web of Science ®Google Scholar
• E. C. Aifantis, Strain Gradient Interpretation of Size Effects, Int. J. Fract., vol. 95, pp. 1–4, 1999.
   Web of Science ®Google Scholar
• H. Sadeghi, M. Baghani, and R. Naghdabadi, Strain Gradient Elasticity Solution for Functionally Graded Micro-cylinders, Int. J. Eng. Sci., vol. 50, pp. 22–30, 2012.
   Web of Science ®Google Scholar
• A. C. Eringen, Theory of Micropolar Plates, Z. Angew. Math. Phys., vol. 18, pp. 12–30, 1967.
   Web of Science ®Google Scholar
• A. C. Eringen, Nonlocal Polar Elastic Continua, Int. J. Eng. Sci., vol. 10, pp. 1–16, 1972.
   Web of Science ®Google Scholar
• M. E. Gurtin, J. Weissmuller, and F. Larche, A General Theory of Curved Deformable Interfaces in Solids at Equilibrium, Philos. Mag. A, vol. 78, pp. 1093–1109, 1998.
   Google Scholar
• A. C. Eringen, On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves, J. Appl. Phys., vol. 54, pp. 4703–4710, 1983.
   Web of Science ®Google Scholar
• A. C. Eringen, Nonlocal Continuum Field Theories, Springer Verlag, New York, 2002.
   Google Scholar
• Z. G. Zhou, L. Z. Wu, and S. Y. Du, Non-local Theory Solution for a Mode I Crack in Piezoelectric Materials, Eur. J. Mech. A Solid., vol. 25, pp. 793–807, 2006.
   Web of Science ®Google Scholar
• L.-L. Ke and Y.-S. Wang, Thermoelectric-mechanical Vibration of Piezoelectric Nanobeams based on the Nonlocal Theory, Smart Mater. Struct., vol. 21, pp. 025018, 2012.
   Web of Science ®Google Scholar
• L.-L. Ke, Y.-S. Wang, and Z. D. Wang, Nonlinear Vibration of the Piezoelectric Nanobeams based on the Nonlocal Theory, Compos. Struct., vol. 94, pp. 2038–2047, 2012.
   Web of Science ®Google Scholar
• C. Liu, L.-L. Ke, Y.-S. Wang, J. Yang, and S. Kitipornchai, Thermo-electro-mechanical Vibration of Piezoelectric Nanoplates Based on the Nonlocal Theory, Compos. Struct., vol. 106, pp. 167–174, 2013.
   Web of Science ®Google Scholar
• L.-L. Ke, Y.-S. Wang, and J. N. Reddy, Thermo-electro-mechanical Vibration of Size-dependent Piezoelectric Cylindrical Nanoshells under Various Boundary Conditions, Compos. Struct., vol. 116, pp. 626–636, 2014.
   Web of Science ®Google Scholar
• L.-L. Ke, C. Liu, and Y.-S. Wang, Free Vibration of Nonlocal Piezoelectric Nanoplates under Various Boundary Conditions, Phys. E, vol. 66, pp. 93–106, 2015.
   Web of Science ®Google Scholar
• W. Wang, P. Li, F. Jin, and J. Wang, Vibration Analysis of Piezoelectric Ceramic Circular Nanoplates Considering Surface and Nonlocal Effects, Compos. Struct., vol. 140, pp. 758–775, 2016.
   Web of Science ®Google Scholar
• A. Ghorbanpour Arani, M. Abdollahian, and R. Kolahchi, Nonlinear Vibration of a Nanobeam Elastically Bonded with a Piezoelectric Nanobeam via Strain Gradient Theory, Int. J. Mech. Sci., vol. 100, pp. 32–40, 2015.
   Web of Science ®Google Scholar
• C. Liu, L.-L. Ke, Y.-S. Wang, and J. Yang, Nonlinear Vibration of Nonlocal Piezoelectric Nanoplates, Int. J. Struct. Stab. Dynam., vol. 15, pp. 1540013, 2015.
   Web of Science ®Google Scholar
• S. R. Asemi, A. Farajpour, and M. Mohammadi, Nonlinear Vibration Analysis of Piezoelectric Nano-electromechanical Resonators based on Nonlocal Elasticity Theory, Compos. Struct., vol. 116, pp. 703–712, 2014.
   Web of Science ®Google Scholar
• A. M. Zenkour, M. N. M. Allam, and M. Sobhy, Bending Analysis of FG Viscoelastic Sandwich Beams with Elastic Cores Resting on Pasternak’s Elastic Foundations, Acta Mech., vol. 212, pp. 233–252, 2010.
   Web of Science ®Google Scholar
• A. M. Zenkour, Bending of Orthotropic Plates Resting on Pasternak’s Foundations by Mixed Shear Deformation Theory, Acta Mech. Sinica, vol. 27, pp. 956–962, 2011.
   Web of Science ®Google Scholar
• B. Bouderba, M. S. A. Houari, and A. Tounsi, Thermomechanical Bending Response of FGM Thick Plates Resting on Winkler–Pasternak Elastic Foundations, Steel Compos. Struct., vol. 14, pp. 85–104, 2013.
   Web of Science ®Google Scholar
• A. M. Zenkour and M. Sobhy, Nonlocal Elasticity Theory for Thermal Buckling of Nanoplates Lying on Winkler–Pasternak Elastic Substrate Medium, Phys. E, vol. 53, pp. 251–259, 2013.
   Web of Science ®Google Scholar
• F. Bounouara, K. H. Benrahou, I. Belkorissat, and A. Tounsi, A Nonlocal Zeroth-order Shear Deformation Theory for Free Vibration of Functionally Graded Nanoscale Plates Resting on Elastic Foundation, Steel Compos. Struct., vol. 20, pp. 227–249, 2016.
   Web of Science ®Google Scholar
• A. M. Zenkour, Nonlocal Transient Thermal Analysis of a Single-layered Graphene Sheet Embedded in Viscoelastic Medium, Phys. E, vol. 79, pp. 87–97, 2016.
   Web of Science ®Google Scholar
• A. M. Zenkour, Vibration Analysis of a Single-layered Graphene Sheet Embedded in Visco-Pasternak’s Medium Using Nonlocal Elasticity Theory, J. Vibroeng., vol. 18, pp. 2319–2330, 2016.
   Web of Science ®Google Scholar
• A. C. Eringen and D. G. B. Edelen, On Nonlocal Elasticity, Int. J. Eng. Sci., vol. 10, pp. 233–248, 1972.
   Web of Science ®Google Scholar
• A. M. Zenkour, Generalized Shear Deformation Theory for Bending Analysis of Functionally Graded Plates, Appl. Math. Model., vol. 30, pp. 67–84, 2006.
   Web of Science ®Google Scholar
• A. M. Zenkour, Hygrothermal Effects on the Bending of Angle-ply Composite Plates Using a Sinusoidal Theory, Compos. Struct., vol. 94, pp. 3685–3696, 2012.
   Web of Science ®Google Scholar
• A. M. Zenkour, Exact Relationships between the Classical and Sinusoidal Plate Theories for FGM Plates, Mech. Adv. Mater. Struct., vol. 19, pp. 551–567, 2012.
   Web of Science ®Google Scholar
• A. M. Zenkour, Bending Analysis of Functionally Graded Sandwich Plates Using a Simple Four-unknown Shear and Normal Deformations Theory, J. Sand. Struct. Mater., vol. 15, pp. 629–656, 2013.
   Web of Science ®Google Scholar
• A. M. Zenkour, Bending of FGM Plates by a Simplified Four-unknown Shear and Normal Deformations Theory, Int. J. Appl. Mech., vol. 5, pp. 1350020 (15 pages), 2013.
   Web of Science ®Google Scholar
• A. Tounsi, M. S. A. Houari, S. Benyoucef, and E. A. Adda, Bedia, A Refined Trigonometric Shear Deformation Theory for Thermoelastic Bending of Functionally Graded Sandwich plates, Aerosp. Sci. Technol., vol. 24, pp. 209–220, 2013.
   Web of Science ®Google Scholar
• M. Zidi, A. Tounsi, M. S. A. Houari, and O. A. Bg, Bending Analysis of FGM Plates under Hygro-thermo-mechanical Loading Using a Four Variable Refined Plate Theory, Aerosp. Sci. Technol., vol. 34, pp. 24–34, 2014.
   Web of Science ®Google Scholar
• Z. Belabed, M. S. A. Houari, A. Tounsi, S. R. Mahmoud, and O. A. Bg, An Efficient and Simple Higher Order Shear and Normal Deformation Theory for Functionally Graded Material (FGM) Plates, Compos. B, vol. 60, pp. 274–283, 2014.
   Web of Science ®Google Scholar
• H. Hebali, A. Tounsi, M. S. A. Houari, A. Bessaim, and E. A. Adda, Bedia, A New Quasi-3D Hyperbolic Shear Deformation Theory for the Static and Free Vibration Analysis of Functionally Graded Plates, ASCE J. Eng. Mech., vol. 140, pp. 374–383, 2014.
   Web of Science ®Google Scholar
• A. Hamidi, M. S. A. Houari, S. R. Mahmoud, and A. Tounsi, A Sinusoidal Plate Theory with 5-Unknowns and Stretching Effect for Thermomechanical Bending of Functionally Graded Sandwich Plates, Steel Compos. Struct., vol. 18, pp. 235–253, 2015.
   Web of Science ®Google Scholar
• A. M. Zenkour, A Simplified Four-unknown Shear and Normal Deformations Theory for Bidirectional Laminated Plates, Sdhan, vol. 40, pp. 215–234, 2015.
   Web of Science ®Google Scholar
• M. Bourada, A. Kaci, M. S. A. Houari, and A. Tounsi, A New Simple Shear and Normal Deformations Theory for Functionally Graded Beams, Steel Compos. Struct., vol. 18, pp. 409–423, 2015.
   Web of Science ®Google Scholar
• B. Bouderba, M. S. A. Houari, A. Tounsi, and S. R. Mahmoud, Thermal Stability of Functionally Graded Sandwich Plates Using a Simple Shear Deformation Theory, Struct. Eng. Mech., vol. 58, pp. 397–422, 2016.
   Web of Science ®Google Scholar
• M. Bennoun, M. S. A. Houari, and A. Tounsi, A Novel Five Variable Refined Plate Theory for Vibration Analysis of Functionally Graded Sandwich Plates, Mech. Adv. Mater. Struct., vol. 23, pp. 423–431, 2016.
   Web of Science ®Google Scholar
• J. Rouzegar and F. Abad, Free Vibration Analysis of FG Plate with Piezoelectric Layers Using Four-variable Refined Plate Theory, Thin-Walled Struct., vol. 89, pp. 76–83, 2015.
   Web of Science ®Google Scholar
• M. Arefi and M. N. M. Allam, Nonlinear Responses of an Arbitrary FGP Circular Plate Resting on the Winkler–Pasternak Foundation, Smart Struct. Syst., vol. 16, pp. 81–100, 2015.
   Web of Science ®Google Scholar
• M. Arefi, Surface Effect and Non-local Elasticity in Wave Propagation of Functionally Graded Piezoelectric Nano-rod Excited to Applied Voltage, Appl. Math. Mech., vol. 37, 289–302, 2016.
   Web of Science ®Google Scholar
• M. Arefi, Nonlinear Electromechanical Analysis of a Functionally Graded Square Plate Integrated with Smart Layers Resting on Winkler–Pasternak Foundation, Smart Struct. Syst., vol. 16, pp. 195–211, 2015.
   Web of Science ®Google Scholar
• M. Arefi, Nonlinear Thermoelastic Analysis of Thick-walled Functionally Graded Piezoelectric Cylinder, Acta Mech., vol. 224, pp. 2771–2783, 2013.
   Web of Science ®Google Scholar
• M. Arefi, G. H. Rahimi, and M. J. Khoshgoftar, Exact Solution of a Thick Walled Functionally Graded Piezoelectric Cylinder under Mechanical, Thermal and Electrical loads in the Magnetic Field, Smart Struct. Syst., vol. 9, pp. 427–439, 2012.
   Web of Science ®Google Scholar
• M. Arefi and I. Nsahas, Nonlinear Electro Thermoelastic Analysis of a Thick Spherical Functionally Graded Piezoelectric Shell, Compos. Struct., vol. 118, pp. 510–518, 2014.
   Web of Science ®Google Scholar