Vibrational Study on Multilayer Sandwich Plates: Porous FGM Core, Nanocomposite and Piezoelectric Face Sheets

Subject Areas : Mechanics of Solids

M Pakize ¹ , M Irani Rahaghi ² , Z Khoddami Maraghi ³ , Sh Niknejad ⁴ , A Ghorbanpour Arani ⁵

1 - Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
2 - Department of Solid Mechanics, Faculty of Mechanical Engineeirng, University of Kashan, Kashan, Iran
3 - Faculty of Engineering, Mahallat Institute of Higher Education, Mahallat, Iran
4 - Faculty of Mechanical Engineering, Department of Solid Mechanics, University of Kashan, Kashan, Iran
5 - Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

Received: 2020-09-13 Accepted : 2021-04-28 Published : 2024-10-12

Keywords: Vibration, Porous, Sandwich plate, Carbon Nanotube, Quasi-3D plate theory,

Abstract :

A quasi-3D sinusoidal shear deformation theory and an analytical solution are presented for free vibration analysis of a 5-layer sandwich plate. The core of the sandwich plate is composed of a functionally graded porous (FGP) material that is distributed in two different types of nonlinear functions. The porous core is surrounded by two randomly oriented straight single walled CNT reinforced layers and two piezoelectric face sheets. Eight various couples of distribution of CNTs are considered for interior layers of sandwich plate. Symmetric distributions include uniform distribution and FG-XX, FG-OO, and FG-VA and asymmetric distributions are FG-XO, FG-UO, FG-UX, and FG-AV. Effective elastic moduli of the nanocomposite layers are calculated by Mori-Tanaka approach; the set of the governing equations are derived using Hamilton’s principle and are solved for the simply supported boundary conditions using Navier’s method. Accuracy of the presented solution is confirmed and effects of different parameters on the natural frequencies of the plate are studied including aspect ratio, porosity parameter, porosity distribution pattern, volume fraction and distribution pattern of CNTs and Winkler and shear coefficients of the foundation.

References:

[1] Chen, D., Yang, J. and Kitipornchai, S., 2015. Elastic buckling and static bending of shear deformable functionally graded porous beam. Composite Structures, 133, pp.54-61.
[2] Chen, D., Yang, J. and Kitipornchai, S., 2016. Free and forced vibrations of shear deformable functionally graded porous beams. International journal of mechanical sciences, 108, pp.14-22.
[3] Chen, D., Kitipornchai, S. and Yang, J., 2016. Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. Thin-Walled Structures, 107, pp.39-48..
[4] Shafiei, N., Mousavi, A. and Ghadiri, M., 2016. On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams. International Journal of Engineering Science, 106, pp.42-56.
[5] Ebrahimi, F. and Jafari, A., 2016. Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory. Struct. Eng. Mech, 59(2), pp.343-371.
[6] Barati, M.R. and Zenkour, A.M., 2018. Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions. Journal of Vibration and Control, 24(10), pp.1910-1926.
[7] Ebrahimi, F. and Barati, M.R., 2017. Porosity-dependent vibration analysis of piezo-magnetically actuated heterogeneous nanobeams. Mechanical Systems and Signal Processing, 93, pp.445-459.
[8] Safarpour, H., Mohammadi, K., Ghadiri, M. and Barooti, M.M., 2018. Effect of porosity on flexural vibration of CNT-reinforced cylindrical shells in thermal environment using GDQM. International Journal of Structural Stability and Dynamics, 18(10), p.1850123.
[9] Shahsavari, D., Shahsavari, M., Li, L. and Karami, B., 2018. A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation. Aerospace Science and Technology, 72, pp.134-149.
[10] Daikh, A.A. and Zenkour, A.M., 2019. Effect of porosity on the bending analysis of various functionally graded sandwich plates. Materials Research Express, 6(6), p.065703.
[11] Amir, S., Arshid, E., Rasti-Alhosseini, S.A. and Loghman, A., 2020. Quasi-3D tangential shear deformation theory for size-dependent free vibration analysis of three-layered FG porous micro rectangular plate integrated by nano-composite faces in hygrothermal environment. Journal of Thermal Stresses, 43(2), pp.133-156
[12] Akbari, H., Azadi, M. and Fahham, H., 2020. Free vibration analysis of thick sandwich cylindrical panels with saturated FG-porous core. Mechanics Based Design of Structures and Machines, pp.1-19.
[13] Iijima, S., 1991. Helical microtubules of graphitic carbon. nature, 354(6348), pp.56-58.
[14] Ghorbanpour Arani, A., Maghamikia, S., Mohammadimehr, M. and Arefmanesh, A., 2011. Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods. Journal of mechanical science and technology, 25(3), pp.809-820.
[15] Wang, Z.X. and Shen, H.S., 2012. Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets. Composites Part B: Engineering, 43(2), pp.411-421.
[16] Zhu, P., Lei, Z.X. and Liew, K.M., 2012. Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory. Composite Structures, 94(4), pp.1450-1460.
[17] Lei, Z.X., Liew, K.M. and Yu, J.L., 2013. Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method. Composite Structures, 98, pp.160-168.
[18] Lei, Z.X., Liew, K.M. and Yu, J.L., 2013. Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment. Composite Structures, 106, pp.128-138.
[19] Bhardwaj, G., Upadhyay, A.K., Pandey, R. and Shukla, K.K., 2013. Non-linear flexural and dynamic response of CNT reinforced laminated composite plates. Composites Part B: Engineering, 45(1), pp.89-100.
[20] Alibeigloo, A., 2013. Static analysis of functionally graded carbon nanotube-reinforced composite plate embedded in piezoelectric layers by using theory of elasticity. Composite Structures, 95, pp.612-622.
[21] Jeyaraj, P. and Rajkumar, I., 2013. Static behavior of FG-CNT polymer nano composite plate under elevated non-uniform temperature fields. Procedia Engineering, 64, pp.825-834.
[22] Natarajan, S., Haboussi, M. and Manickam, G., 2014. Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets. Composite Structures, 113, pp.197-207.
[23] Wattanasakulpong, N. and Chaikittiratana, A., 2015. Exact solutions for static and dynamic analyses of carbon nanotube-reinforced composite plates with Pasternak elastic foundation. Applied Mathematical Modelling, 39(18), pp.5459-5472.
[24] Mohammadimehr, M., Monajemi, A.A. and Afshari, H., 2017. Free and forced vibration analysis of viscoelastic damped FG-CNT reinforced micro composite beams. Microsystem Technologies, pp.1-15..
[25] Mohammadimehr, M., Akhavan Alavi, S.M., Okhravi, S.V. and Edjtahed, S.H., 2018. Free vibration analysis of micro-magneto-electro-elastic cylindrical sandwich panel considering functionally graded carbon nanotube–reinforced nanocomposite face sheets, various circuit boundary conditions, and temperature-dependent material properties using high-order sandwich panel theory and modified strain gradient theory. Journal of Intelligent Material Systems and Structures, 29(5), pp.863-882.
[26] Ghorbanpour Arani, A., Kiani, F. and Afshari, H., 2019. Aeroelastic analysis of laminated FG-CNTRC cylindrical panels under yawed supersonic flow. International Journal of Applied Mechanics, 11(06), p.1950052.
[27] Ghorbanpour Arani, A., Kiani, F. and Afshari, H., 2019. Free and forced vibration analysis of laminated functionally graded CNT-reinforced composite cylindrical panels. Journal of Sandwich Structures & Materials, p.1099636219830787.
[28] Arefi, M., Kiani, M. and Zenkour, A.M., 2020. Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak’s foundation via MCST. Journal of Sandwich Structures & Materials, 22(1), pp.55-86.
[29] Zenkour, A.M., 2005. On vibration of functionally graded plates according to a refined trigonometric plate theory. International Journal of Structural Stability and Dynamics, 5(02), pp.279-297.
[30] Zenkour, A.M., 2007. Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate. Archive of Applied Mechanics, 77(4), pp.197-214.
[31] Levy, M., 1877. Mémoire sur la théorie des plaques élastiques planes. Journal de mathématiques pures et appliquées, pp.219-306.
[32] Stein, M., 1986. Nonlinear theory for plates and shells including the effects of transverse shearing. AIAA journal, 24(9), pp.1537-1544.
[33] Zenkour, A.M., Allam, M.N.M., Radwan, A.F. and El-Mekawy, H.F., 2015. Thermo-mechanical bending response of exponentially graded thick plates resting on elastic foundations. International Journal of Applied Mechanics, 7(04), p.1550062.
[34] Zenkour, A.M., 2013. Bending analysis of functionally graded sandwich plates using a simple four-unknown shear and normal deformations theory. Journal of Sandwich Structures & Materials, 15(6), pp.629-656.
[35] Sadd, M.H., 2009. Elasticity: theory, applications, and numerics. Academic Press.
[36] Reddy, J.N., 2003. Mechanics of laminated composite plates and shells: theory and analysis. CRC press.
[37] Ghorbanpour Arani, A. and Zamani, M.H., 2019. Investigation of electric field effect on size-dependent bending analysis of functionally graded porous shear and normal deformable sandwich nanoplate on silica Aerogel foundation. Journal of Sandwich Structures & Materials, 21(8), pp.2700-2734.
[38] Moradi-Dastjerdi, R. and Behdinan, K., 2020. Stability analysis of multifunctional smart sandwich plates with graphene nanocomposite and porous layers. International Journal of Mechanical Sciences, 167, p.105283.
[39] Eshelby, J.D., 1957. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the royal society of London. Series A. Mathematical and physical sciences, 241(1226), pp.376-396.
[40] Mori, T. and Tanaka, K., 1973. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta metallurgica, 21(5), pp.571-574.
[41] Hill, R., 1965. A self-consistent mechanics of composite materials. Journal of the Mechanics and Physics of Solids, 13(4), pp.213-222.
[42] Ghorbanpour Arani, A., Khani Arani, H. and Khoddami Maraghi, Z., 2016. Vibration analysis of sandwich composite micro-plate under electro-magneto-mechanical loadings. Applied Mathematical Modelling, 40(23-24), pp.10596-10615.
[43] J.N. Reddy, Energy principles and variational methods in applied mechanics, John Wiley & Sons2017.
[44] Srinivas, S., Rao, C.J. and Rao, A.K., 1970. An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates. Journal of sound and vibration, 12(2), pp.187-199.
[45] Reddy, J.N. and Phan, N.D., 1985. Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory. Journal of sound and vibration, 98(2), pp.157-170.
[46] Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Bedia, E.A.A., 2014. New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. Journal of Engineering Mechanics, 140(2), pp.374-383.
[47] Leissa, A.W., 1973. The free vibration of rectangular plates. Journal of sound and vibration, 31(3), pp.257-293.
[48] Bardell, N.S., 1989. The application of symbolic computing to the hierarchical finite element method. International Journal for Numerical Methods in Engineering, 28(5), pp.1181-1204.
[49] X. Wang, Y.L. Wang, R.B. Chen, Static and free vibrational analysis of rectangular plates by the differential quadrature element method, Communications in Numerical Methods in Engineering 14(12) (1998) 1133-1141.
[50] Akhavan, H., Hashemi, S.H., Taher, H.R.D., Alibeigloo, A. and Vahabi, S., 2009. Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part II: Frequency analysis. Computational Materials Science, 44(3), pp.951-961.
[51] Atmane, H.A., Tounsi, A. and Mechab, I., 2010. Free vibration analysis of functionally graded plates resting on Winkler–Pasternak elastic foundations using a new shear deformation theory. International Journal of Mechanics and Materials in Design, 6(2), pp.113-121.
[52] Moradi-Dastjerdi, R., Payganeh, G. and Malek-Mohammadi, H., 2015. Free vibration analyses of functionally graded CNT reinforced nanocomposite sandwich plates resting on elastic foundation. Journal of Solid Mechanics, 7(2), pp.158-172.
[53] Arefi, M., Zamani, M.H. and Kiani, M., 2018. Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak’s foundation. Journal of Intelligent Material Systems and Structures, 29(5), pp.774-786.
[54] Ghorbanpour Arani, A., BabaAkbar Zarei, H. and Haghparast, E., 2018. Vibration response of viscoelastic sandwich plate with magnetorheological fluid core and functionally graded-piezoelectric nanocomposite face sheets. Journal of Vibration and Control, 24(21), pp.5169-5185.