Monotonous, symmetric, and nonsymmetric patterns of porous core in vibration study of nano-composite sandwich plate bonded by piezoelectric sheets
Document Type : Research Paper
Authors
1 Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran.
2 Faculty of Engineering, Mahallat Institute of Higher Education, Mahallat, Iran.
3 Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan, Iran.
Abstract
This paper deals with the free vibrations of a 5-layer sandwich plate consisting of a sutured porous material core. Two randomly oriented straight single-walled carbon nanotube (CNT) reinforced composites and face sheets manufactured of piezoelectric material that is subjected to an external electric voltage, are placed on a Visco-Pasternak foundation. The relationship between strain and stress in the core is expressed by considering the pore fluid pressure based on the Biot theory, and for pore distribution along the core thickness, three uniform, symmetric and nonsymmetric patterns are considered. A quasi-3D sinusoidal shear deformation theory which that couples the effects of shear strain and normal deformation without the need for any shear correction factor which uses Hamilton’s principle and Navier’s method is used to derive the governing equations of the sandwich structure for the simply supported case. Effects of different parameters on the natural frequencies of the plate are studied including layer thickness ratio, porosity parameter, porosity distribution pattern, pores compressibility, the volume fraction of CNTs and external voltage. The maximum frequency in different modes could be an important design factor that is calculated based on the type of the porosity distribution. Controlling the material properties based on specific needs is the most important advantage of the 5-layer sandwich structure. This paper introduces sandwich panels with porous cores, nanocomposite layers and piezoelectric overlays for the first time which is analyzed to determine system vibration frequencies under external voltage and by changing various parameters with emphasis on different porosity distributions. The frequency of monotonous distribution was 4% higher than symmetric and asymmetric distributions for a constant porosity.
Keywords
[1] M. Babaei, F. Kiarasi, K. Asemi, M. Hosseini, Functionally graded saturated porous structures: A review, Journal of Computational Applied Mechanics, Vol. 53, No. 2, pp. 297-308, 2022.
[2] M. Goodarzi, M. Mohammadi, M. Khooran, F. Saadi, Thermo-Mechanical Vibration Analysis of FG Circular and Annular Nanoplate Based on the Visco-Pasternak Foundation, Journal of Solid Mechanics, Vol. 8, No. 4, pp. 788-805, 2016.
[3] M. Mohammadi, M. Hosseini, M. Shishesaz, A. Hadi, A. Rastgoo, Primary and secondary resonance analysis of porous functionally graded nanobeam resting on a nonlinear foundation subjected to mechanical and electrical loads, European Journal of Mechanics - A/Solids, Vol. 77, pp. 103793, 2019/09/01/, 2019.
[4] M. Mohammadi, A. Rastgoo, Nonlinear vibration analysis of the viscoelastic composite nanoplate with three directionally imperfect porous FG core, Structural Engineering and Mechanics, An Int'l Journal, Vol. 69, No. 2, pp. 131-143, 2019.
[5] M. Mohammadi, A. Rastgoo, Primary and secondary resonance analysis of FG/lipid nanoplate with considering porosity distribution based on a nonlinear elastic medium, Mechanics of Advanced Materials and Structures, Vol. 27, No. 20, pp. 1709-1730, 2020/10/15, 2020.
[6] Y. S. Al Rjoub, A. G. Hamad, Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method, KSCE Journal of Civil Engineering, Vol. 21, No. 3, pp. 792-806, 2017.
[7] D. Chen, J. Yang, S. Kitipornchai, Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams, Composites Science and Technology, Vol. 142, pp. 235-245, 2017.
[8] A. M. Zenkour, A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities, Composite Structures, Vol. 201, pp. 38-48, 2018.
[9] E. Arshid, A. R. Khorshidvand, Free vibration analysis of saturated porous FG circular plates integrated with piezoelectric actuators via differential quadrature method, Thin-Walled Structures, Vol. 125, pp. 220-233, 2018.
[10] B. Safaei, R. Moradi-Dastjerdi, K. Behdinan, Z. Qin, F. Chu, Thermoelastic behavior of sandwich plates with porous polymeric core and CNT clusters/polymer nanocomposite layers, Composite Structures, Vol. 226, pp. 111209, 2019.
[11] E. Arshid, S. Amir, A. Loghman, Static and dynamic analyses of FG-GNPs reinforced porous nanocomposite annular micro-plates based on MSGT, International Journal of Mechanical Sciences, Vol. 180, pp. 105656, 2020.
[12] W. Gao, Z. Qin, F. Chu, Wave propagation in functionally graded porous plates reinforced with graphene platelets, Aerospace Science and Technology, Vol. 102, pp. 105860, 2020.
[13] M. Askari, A. Saidi, A. Rezaei, An investigation over the effect of piezoelectricity and porosity distribution on natural frequencies of porous smart plates, Journal of Sandwich Structures & Materials, Vol. 22, No. 7, pp. 2091-2124, 2020.
[14] M. Balak, S. J. Mehrabadi, H. M. Monfared, H. Feizabadi, Free vibration analysis of a composite elliptical plate made of a porous core and two piezoelectric layers, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, Vol. 235, No. 4, pp. 796-812, 2021.
[15] M. Safari, M. Mohammadimehr, H. Ashrafi, Free vibration of electro-magneto-thermo sandwich Timoshenko beam made of porous core and GPLRC, Advances in nano research, Vol. 10, No. 2, pp. 115-128, 2021.
[16] M. R. Ebrahimian, Z. Azimzadeh, A. Fatahi-Vajari, M. Shariati, Nonlinear coupled torsional-radial vibration of single-walled carbon nanotubes using numerical methods, Journal of Computational Applied Mechanics, Vol. 52, No. 4, pp. 642-663, 2021.
[17] M. Shariati, M. Shishesaz, R. Mosalmani, S. A. Seyed Roknizadeh, M. Hosseini, Nonlocal effect on the axisymmetric nonlinear vibrational response of nano-disks using variational iteration method, Journal of Computational Applied Mechanics, Vol. 52, No. 3, pp. 507-534, 2021.
[18] M. Shariati, M. Shishesaz, H. Sahbafar, M. Pourabdy, M. Hosseini, A review on stress-driven nonlocal elasticity theory, Journal of Computational Applied Mechanics, Vol. 52, No. 3, pp. 535-552, 2021.
[19] S. R. Asemi, M. Mohammadi, A. Farajpour, A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory, Latin American Journal of Solids and Structures, Vol. 11, pp. 1541-1546, 2014.
[20] M. Baghani, M. Mohammadi, A. Farajpour, Dynamic and stability analysis of the rotating nanobeam in a nonuniform magnetic field considering the surface energy, International Journal of Applied Mechanics, Vol. 8, No. 04, pp. 1650048, 2016.
[21] M. Danesh, A. Farajpour, M. Mohammadi, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, Vol. 39, No. 1, pp. 23-27, 2012.
[22] A. Farajpour, M. Danesh, M. Mohammadi, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, No. 3, pp. 719-727, 2011.
[23] A. Farajpour, M. Mohammadi, A. Shahidi, M. Mahzoon, Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E: Low-dimensional Systems and Nanostructures, Vol. 43, No. 10, pp. 1820-1825, 2011.
[24] A. Farajpour, A. Shahidi, M. Mohammadi, M. Mahzoon, Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics, Composite Structures, Vol. 94, No. 5, pp. 1605-1615, 2012.
[25] M. Mohammadi, A. Farajpour, A. Moradi, M. Hosseini, Vibration analysis of the rotating multilayer piezoelectric Timoshenko nanobeam, Engineering Analysis with Boundary Elements, Vol. 145, pp. 117-131, 2022/12/01/, 2022.
[26] H.-S. Shen, Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments, Composite Structures, Vol. 91, No. 1, pp. 9-19, 2009.
[27] L.-L. Ke, J. Yang, S. Kitipornchai, Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Composite Structures, Vol. 92, No. 3, pp. 676-683, 2010.
[28] H.-S. Shen, Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells, Composite Structures, Vol. 93, No. 8, pp. 2096-2108, 2011.
[29] J. Jam, A. Pourasghar, S. Kamarian, Effect of the aspect ratio and waviness of carbon nanotubes on the vibrational behavior of functionally graded nanocomposite cylindrical panels, Polymer Composites, Vol. 33, No. 11, pp. 2036-2044, 2012.
[30] A. Pourasghar, M. Yas, S. Kamarian, Local aggregation effect of CNT on the vibrational behavior of four‐parameter continuous grading nanotube‐reinforced cylindrical panels, Polymer Composites, Vol. 34, No. 5, pp. 707-721, 2013.
[31] L. Zhang, B. Selim, Vibration analysis of CNT-reinforced thick laminated composite plates based on Reddy’s higher-order shear deformation theory, Composite Structures, Vol. 160, pp. 689-705, 2017.
[32] L. Zhang, Z. Lei, K. Liew, Vibration characteristic of moderately thick functionally graded carbon nanotube reinforced composite skew plates, Composite Structures, Vol. 122, pp. 172-183, 2015.
[33] P. T. Thang, T.-T. Nguyen, J. Lee, A new approach for nonlinear buckling analysis of imperfect functionally graded carbon nanotube-reinforced composite plates, Composites Part B: Engineering, Vol. 127, pp. 166-174, 2017.
[34] R. Moradi-Dastjerdi, F. Aghadavoudi, Static analysis of functionally graded nanocomposite sandwich plates reinforced by defected CNT, Composite Structures, Vol. 200, pp. 839-848, 2018.
[35] H. Daghigh, V. Daghigh, A. Milani, D. Tannant, T. E. Lacy Jr, J. Reddy, Nonlocal bending and buckling of agglomerated CNT-reinforced composite nanoplates, Composites Part B: Engineering, Vol. 183, pp. 107716, 2020.
[36] H. Asemi, S. Asemi, A. Farajpour, M. Mohammadi, Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermo-electro-mechanical loads, Physica E: Low-dimensional Systems and Nanostructures, Vol. 68, pp. 112-122, 2015.
[37] S. Asemi, A. Farajpour, H. Asemi, M. Mohammadi, Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM, Physica E: Low-dimensional Systems and Nanostructures, Vol. 63, pp. 169-179, 2014.
[38] S. Asemi, A. Farajpour, M. Mohammadi, Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory, Composite Structures, Vol. 116, pp. 703-712, 2014.
[39] A. M. Zenkour, Hygrothermal analysis of heterogeneous piezoelectric elastic cylinders, Mathematical Models in Engineering, Vol. 2, No. 1, pp. 1-17, 2016.
[40] M. Arefi, R. Karroubi, M. Irani-Rahaghi, Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer, Applied Mathematics and Mechanics, Vol. 37, No. 7, pp. 821-834, 2016.
[41] M. Ghasemi Shiri, A. Jaamialahmadi, Buckling Analysis of intelligent Nanoplate under Inplane Loading Based on Nonlocal Elasticity and Shear and normal Deformation Theories, Modares Mechanical Engineering, Vol. 17, No. 2, pp. 427-438, 2017.
[42] M. Arefi, A. M. Zenkour, Vibration and bending analysis of a sandwich microbeam with two integrated piezo-magnetic face-sheets, Composite Structures, Vol. 159, pp. 479-490, 2017.
[43] F. Ebrahimi, S. H. S. Hosseini, Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite resting on viscoelastic foundation, The Journal of Strain Analysis for Engineering Design, Vol. 55, No. 1-2, pp. 53-68, 2020.
[44] A. G. Arani, A. Farazin, M. Mohammadimehr, S. Lenjannejadian, Energy harvesting of sandwich beam with laminated composite core and piezoelectric face sheets under external fluid flow, Smart Structures and Systems, Vol. 27, No. 4, pp. 641-650, 2021.
[45] A. M. Zenkour, On vibration of functionally graded plates according to a refined trigonometric plate theory, International Journal of Structural Stability and Dynamics, Vol. 5, No. 02, pp. 279-297, 2005.
[46] A. Zenkour, Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate, Archive of Applied Mechanics, Vol. 77, No. 4, pp. 197-214, 2007.
[47] M. Levy, Mémoire sur la théorie des plaques élastiques planes, Journal de mathématiques pures et appliquées, pp. 219-306, 1877.
[48] M. Stein, Nonlinear theory for plates and shells including the effects of transverse shearing, AIAA journal, Vol. 24, No. 9, pp. 1537-1544, 1986.
[49] A. Zenkour, M. Allam, A. Radwan, H. El-Mekawy, Thermo-mechanical bending response of exponentially graded thick plates resting on elastic foundations, International Journal of Applied Mechanics, Vol. 7, No. 04, pp. 1550062, 2015.
[50] A. M. Zenkour, Bending analysis of functionally graded sandwich plates using a simple four-unknown shear and normal deformations theory, Journal of Sandwich Structures & Materials, Vol. 15, No. 6, pp. 629-656, 2013.
[51] M. H. Sadd, 2009, Elasticity: theory, applications, and numerics, Academic Press,
[52] D. Chen, S. Kitipornchai, J. Yang, Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core, Thin-Walled Structures, Vol. 107, pp. 39-48, 2016.
[53] M. Biot, Theory of buckling of a porous slab and its thermoelastic analogy, 1964.
[54] J. D. Eshelby, 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, Vol. 241, No. 1226, pp. 376-396, 1957.
[55] T. Mori, K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta metallurgica, Vol. 21, No. 5, pp. 571-574, 1973.
[56] R. Hill, A self-consistent mechanics of composite materials, Journal of the Mechanics and Physics of Solids, Vol. 13, No. 4, pp. 213-222, 1965.
[57] A. G. Arani, H. K. Arani, Z. K. Maraghi, Vibration analysis of sandwich composite micro-plate under electro-magneto-mechanical loadings, Applied Mathematical Modelling, Vol. 40, No. 23-24, pp. 10596-10615, 2016.
[58] A. Ghorbanpour Arani, M. Zamani, 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, Vol. 21, No. 8, pp. 2700-2734, 2019.
[59] J. N. Reddy, 2017, Energy principles and variational methods in applied mechanics, John Wiley & Sons,
[60] M. Arefi, A. H. Soltan Arani, Higher order shear deformation bending results of a magnetoelectrothermoelastic functionally graded nanobeam in thermal, mechanical, electrical, and magnetic environments, Mechanics Based Design of Structures and Machines, Vol. 46, No. 6, pp. 669-692, 2018.
[61] J. Reddy, Nonlocal theories for bending, buckling and vibration of beams, International journal of engineering science, Vol. 45, No. 2-8, pp. 288-307, 2007.
[62] S. Srinivas, C. J. Rao, A. Rao, An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates, Journal of sound and vibration, Vol. 12, No. 2, pp. 187-199, 1970.
[63] J. Reddy, N. Phan, Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory, Journal of sound and vibration, Vol. 98, No. 2, pp. 157-170, 1985.
[64] H. Hebali, A. Tounsi, M. S. A. Houari, A. Bessaim, E. A. A. Bedia, New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates, Journal of Engineering Mechanics, Vol. 140, No. 2, pp. 374-383, 2014.
[65] Z.-X. Wang, H.-S. Shen, Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets, Composites Part B: Engineering, Vol. 43, No. 2, pp. 411-421, 2012.
[66] A. W. Leissa, The free vibration of rectangular plates, Journal of sound and vibration, Vol. 31, No. 3, pp. 257-293, 1973.
[67] N. Bardell, The application of symbolic computing to the hierarchical finite element method, International Journal for Numerical Methods in Engineering, Vol. 28, No. 5, pp. 1181-1204, 1989.
[68] 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, Vol. 14, No. 12, pp. 1133-1141, 1998.
[69] H. Akhavan, S. H. Hashemi, H. R. D. Taher, A. Alibeigloo, S. Vahabi, Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part II: Frequency analysis, Computational Materials Science, Vol. 44, No. 3, pp. 951-961, 2009.
[70] H. A. Atmane, A. Tounsi, I. Mechab, 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, Vol. 6, No. 2, pp. 113-121, 2010.
[71] R. Moradi-Dastjerdi, G. Payganeh, H. Malek-Mohammadi, Free vibration analyses of functionally graded CNT reinforced nanocomposite sandwich plates resting on elastic foundation, Journal of Solid Mechanics, Vol. 7, No. 2, pp. 158-172, 2015.
[72] Q. Li, V. Iu, K. Kou, Three-dimensional vibration analysis of functionally graded material sandwich plates, Journal of Sound and Vibration, Vol. 311, No. 1-2, pp. 498-515, 2008.
[73] M. Arefi, M. Zamani, M. Kiani, 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, Vol. 29, No. 5, pp. 774-786, 2018.
[74] A. G. Arani, S. Maghamikia, M. Mohammadimehr, A. Arefmanesh, Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods, Journal of mechanical science and technology, Vol. 25, No. 3, pp. 809-820, 2011.
[75] S. Amir, E. Arshid, S. A. Rasti-Alhosseini, A. Loghman, 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, Vol. 43, No. 2, pp. 133-156, 2020.
[76] A. Ghorbanpour Arani, H. BabaAkbar Zarei, E. Haghparast, Vibration response of viscoelastic sandwich plate with magnetorheological fluid core and functionally graded-piezoelectric nanocomposite face sheets, Journal of Vibration and Control, Vol. 24, No. 21, pp. 5169-5185, 2018.
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Volume 53, Issue 3
September 2022Pages 444-477
- Receive Date: 16 July 2022
- Revise Date: 21 September 2022
- Accept Date: 22 September 2022