Journal of Applied and Computational Mechanics
Dynamic Response of Functionally Graded Carbon Nanotube-Reinforced Hybrid Composite Plates
Document Type : Research Paper
Authors
1 Department of Mechanical Engineering, Lunghwa University of Science and Technology, Guishan Shiang 33306, Taiwan
2 Department of Mechanical Engineering, Oriental Institute of Technology, Pan-Chiao 22061, Taiwan
3 Department of Mechanical Engineering, Ming Chi University of Technology, Tai-Shan 24301, Taiwan
4 Department of Mechanical Engineering, Chinese Culture University, Taipei 11114, Taiwan
Abstract
Dynamic instability behavior of functionally graded carbon nanotube reinforced hybrid composite plates subjected to periodic loadings is studied. The governing equations of motion of Mathieu-type are established by using the Galerkin method with reduced eigenfunctions transforms. With the Mathieu equations, the dynamic instability regions of hybrid nanocomposite plates are determined by using the Bolotin’s method. Results reveal that the dynamic instability is significantly affected by the carbon nanotube volume fraction, layer thickness ratio, bending stress, static and dynamic load parameters. The effects of important parameters on the instability region and dynamic instability index of hybrid nanocomposite plates are discussed.
Keywords
Main Subjects
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[1] Fantuzzi, N., Tornabene, F., Viola, E., A strong formulation finite element method (SFEM) based on RBF and GDQ techniques for the static and dynamic analyses of laminated plates of arbitrary shape, Meccanica, 49, 2014, 2503-2542.
[2] Tornabene. F., Fantuzzi. N., Bacciocchi M., Dynamic analysis of thick and thin elliptic shell structures made of laminated composite materials, Composite Structures, 133, 2015, 278-299.
[3] Sofiyev, A.H., Kuruoglu, N., Dynamic instability of three-layered cylindrical shells containing an FGM interlayer, Thin Walled Structures, 93, 2015, 10-21.
[4] Sofiyev, A.H., Influences of shear stresses on the dynamic instability of exponentially graded sandwich cylindrical shells, Composites Part B-Engineering, 77, 2015, 349-362.
[5] Sofiyev, A.H., Kuruoglu, N., Parametric instability of shear deformable sandwich cylindrical shells containing an FGM core under static and time dependent periodic axial loads, International Journal of Mechanical Sciences, 101-102, 2015,114-123.
[6] Sofiyev, A.H., Kuruoglu, N., Domains of dynamic instability of FGM conical shells under time dependent periodic loads, Composite Structures, 136, 2016,139-148.
[7] Sofiyev, A.H., Pancar, E.B., The effect of heterogeneity on the parametric instability of axially excited orthotropic conical shells, Thin–Walled Structures 115, 2017, 240–246.
[8] Sofiyev, A.H., Zerin, Z., Allahverdiev, B.P., Hui, D., Turan, F., Erdem, H., The dynamic instability of FG orthotropic conical shells within the SDT, Steel and Composite Structures, 25, 2017, 581-591.
[9] Enrique, G.M., Luis, R.T., Andrés, S., Bending and free vibration analysis of functionally graded graphene vs. carbon nanotube reinforced composite plates, Composite Structures, 186, 2018, 123-138.
[10] Zhao, J., ,Choe, K., Shuai, C., Wang, A., Wang, Q., Free vibration analysis of functionally graded carbon nanotube reinforced composite truncated conical panels with general boundary conditions, Composite Part B: Engineering, 160, 2019, 225-240.
[11] Avey, M., Yusufoglu, E., On the solution of large-amplitude vibration of carbon nanotube-based double-curved shallow shells, Mathematical Methods in the Applied Sciences, 2020, 1–13.
[12] Yusufoglu, E., Avey, M., Nonlinear dynamic behavior of hyperbolic paraboloidal shells reinforced by carbon nanotubes with various distributions, Journal of Applied and Computational Mechanics, 7, 2021, 913-921.
[13] Sofiyev, A.H., Avey, M., Kuruoglu, N., An approach to the solution of nonlinear forced vibration problem of structural systems reinforced with advanced materials in the presence of viscous damping, Mechanical Systems and Signal Processing, 161, 2021, 107991.
[14] Ansari, R., Gholami, R., Sahmani, S., On the dynamic stability of embedded single-walled carbon nanotubes including thermal environment effects, Scientia Iranica, 19, 2012, 919-925.
[15] Yas, M.H., Heshmati, M., Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load, Applied Mathematical Modelling, 36, 2012, 1371-1394.
[16] Bhardwaj, G., Upadhyay, A.K., Pandey R., Non-linear flexural and dynamic response of CNT reinforced laminated composite plates, Composite Part B: Engineering, 45, 2013, 89-100.
[17] Rasool, M.D., Foroutan, M., Pourasghar A., Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method, Materials & Design, 44, 2013, 256-266.
[18] Ke, L.L., Yang J., Dynamic stability of functionally graded carbon nanotube-reinforced composite beams, Mechanics of Advanced Materials and Structures, 20, 2013, 28-37.
[19] Rafiee, M., He, X.Q., Liew, K.M., Non-linear dynamic stability of piezoelectric functionally graded carbon nanotube-reinforced composite plates with initial geometric imperfection, International Journal of Non-Linear Mechanics, 59, 2014, 37-51.
[20] Lei, Z.X., Zhang, L.W. and Liew, K.M., Dynamic stability analysis of carbon nanotube-reinforced functionally graded cylindrical panels using the element-free kp-Ritz method, Composite Structures, 113, 2014, 328-338.
[21] Lei, Z.X., Zhang. L.W., Liew, K.M., Elastodynamic analysis of carbon nanotube-reinforced functionally graded plates, International Journal of Mechanic Science, 99, 2015, 208-217.
[22] Belkorissat, I., Houari, M.S.A., Tounsi, A., On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model, Steel and Composite Structures, 18, 2015, 1063-1081.
[23] Wang, Z.X, Shen, H.S., Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments, Nonlinear Dynamics, 70, 2012, 735-754.
[24] Sayer, M., Bektas, N.B., Sayman, B., An experimental investigation on the impact behavior of hybrid composite plates, Composite Structures, 92, 2010, 1256-1262.
[25] Fu Y., Zhong J., Shao X., Tao C., Analysis of nonlinear dynamic stability for carbon nanotube-reinforced composite plates resting on elastic foundations, Mechanics of Advances Materials Structures, 23, 2016, 1284-1289.
[26] Wu H., Yang J., Kitipornchai S., Parametric instability of thermo-mechanically loaded functionally graded graphene reinforced nanocomposite plates, International Journal of Mechanic Science, 135, 2018, 431-440.
[27] Singh V., Kumar R., Patel S.N., Parametric instability analysis of functionally graded CNT-reinforced composite (FG-CNTRC) plate subjected to different types of non-uniform in-plane loading, In: Singh S.B., Sivasubramanian M.V.R., Chawla H. (eds) Emerging Trends of Advanced Composite Materials in Structural Applications. Composites Science and Technology. Springer, Singapore, 2021.
[28] Kapuria, S., Yasin, M.Y., Active vibration suppression of multilayered plates integrated with piezoelectric fiber reinforced composites using an efficient finite element model, Journal of Sound and Vibration, 329, 2010, 3247-3265.
[29] Khalili, S.M.R., Dehkordi, M.B., Carrera, E., Non-linear dynamic analysis of a sandwich beam with pseudoelastic SMA hybrid composite faces based on higher order finite element theory, Composite Structures, 96, 2013, 243-255.
[30] Frikh, A., Zghal, S., Dammak, F., Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element, Aerospace Science and Technology, 78, 2018, 438-451.
[31] Harras, B., Benamar, R., Whit, R.G., Experimental and theoretical investigation of the linear and non-linear dynamic behaviour of a glare 3 hybrid composite panel, Journal of Sound and Vibration, 252, 2002, 281-315.
[32] Kao, J.Y., Chen, C.S., Chen, W.R., Parametric vibration response of foam-filled sandwich plates under pulsating loads, Mechanics of Composite Materials, 48, 2012, 525-538.
[33] Chen, C.S., Liu, F.H., Chen, W.R., Dynamic characteristics of functionally graded material sandwich plate in thermal environments, Mechanics of Advanced Materials and Structures, 24, 2017, 157-167.
[34] Chen, C.S., Fung, C.P., Yang, J.G., Assessment of plate theories for initially stressed hybrid laminated plates, Composite Structures, 88, 2009, 195-201.
[35] Chen, L.W., Yang, J.Y., Dynamic stability of laminated composite plates by the finite element method, Computer and Structures, 36, 1990, 845-851.
[36] Chattopadhyay, A., Radu, A.G., Dragomir-Daescu D., A higher order plate theory for dynamic stability analysis of delaminated composite plates, Computational Mechanics, 26, 2000, 302-308.
[37] Shen, H.S., Nonlinear bending of functionally graded carbon nanotube reinforced composite plates in thermal environments, Composite Structures, 91, 2009, 9-19.
[38] Zhang, C.L., Shen, H.S., Temperature dependent elastic properties of single-walled carbon nanotubes: prediction from molecular dynamics simulation, Applied Physics Letters, 89, 2006, 81904-81907.
[39] Shen, H.S., Zhang, C.L. Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates, Materials & Design, 31, 2010, 3403-3411.
[40] Wang, Z.X., Shen, H.S., Nonlinear vibration of nanotube-reinforced composite plates in thermal environments, Computational Materials Science, 50, 2011, 2319-2330.
[41] Alibeigloo, A., Emtehani, A., Static and free vibration analyses of carbon nanotube-reinforced composite plate using differential quadrature method, Meccanica, 50, 2015, 61-76.
[42] Lei, Z.X., Liew, K.M., Yu, J.L., Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method, Composite Structures, 98, 2013, 160-168.
[43] Malekzadeh, P., Shojaee, M., Buckling analysis of quadrilateral laminated plates with carbon nanotubes reinforced composite layers, Thin-Walled Structures, 71, 2013, 108–118.
[2] Tornabene. F., Fantuzzi. N., Bacciocchi M., Dynamic analysis of thick and thin elliptic shell structures made of laminated composite materials, Composite Structures, 133, 2015, 278-299.
[3] Sofiyev, A.H., Kuruoglu, N., Dynamic instability of three-layered cylindrical shells containing an FGM interlayer, Thin Walled Structures, 93, 2015, 10-21.
[4] Sofiyev, A.H., Influences of shear stresses on the dynamic instability of exponentially graded sandwich cylindrical shells, Composites Part B-Engineering, 77, 2015, 349-362.
[5] Sofiyev, A.H., Kuruoglu, N., Parametric instability of shear deformable sandwich cylindrical shells containing an FGM core under static and time dependent periodic axial loads, International Journal of Mechanical Sciences, 101-102, 2015,114-123.
[6] Sofiyev, A.H., Kuruoglu, N., Domains of dynamic instability of FGM conical shells under time dependent periodic loads, Composite Structures, 136, 2016,139-148.
[7] Sofiyev, A.H., Pancar, E.B., The effect of heterogeneity on the parametric instability of axially excited orthotropic conical shells, Thin–Walled Structures 115, 2017, 240–246.
[8] Sofiyev, A.H., Zerin, Z., Allahverdiev, B.P., Hui, D., Turan, F., Erdem, H., The dynamic instability of FG orthotropic conical shells within the SDT, Steel and Composite Structures, 25, 2017, 581-591.
[9] Enrique, G.M., Luis, R.T., Andrés, S., Bending and free vibration analysis of functionally graded graphene vs. carbon nanotube reinforced composite plates, Composite Structures, 186, 2018, 123-138.
[10] Zhao, J., ,Choe, K., Shuai, C., Wang, A., Wang, Q., Free vibration analysis of functionally graded carbon nanotube reinforced composite truncated conical panels with general boundary conditions, Composite Part B: Engineering, 160, 2019, 225-240.
[11] Avey, M., Yusufoglu, E., On the solution of large-amplitude vibration of carbon nanotube-based double-curved shallow shells, Mathematical Methods in the Applied Sciences, 2020, 1–13.
[12] Yusufoglu, E., Avey, M., Nonlinear dynamic behavior of hyperbolic paraboloidal shells reinforced by carbon nanotubes with various distributions, Journal of Applied and Computational Mechanics, 7, 2021, 913-921.
[13] Sofiyev, A.H., Avey, M., Kuruoglu, N., An approach to the solution of nonlinear forced vibration problem of structural systems reinforced with advanced materials in the presence of viscous damping, Mechanical Systems and Signal Processing, 161, 2021, 107991.
[14] Ansari, R., Gholami, R., Sahmani, S., On the dynamic stability of embedded single-walled carbon nanotubes including thermal environment effects, Scientia Iranica, 19, 2012, 919-925.
[15] Yas, M.H., Heshmati, M., Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load, Applied Mathematical Modelling, 36, 2012, 1371-1394.
[16] Bhardwaj, G., Upadhyay, A.K., Pandey R., Non-linear flexural and dynamic response of CNT reinforced laminated composite plates, Composite Part B: Engineering, 45, 2013, 89-100.
[17] Rasool, M.D., Foroutan, M., Pourasghar A., Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method, Materials & Design, 44, 2013, 256-266.
[18] Ke, L.L., Yang J., Dynamic stability of functionally graded carbon nanotube-reinforced composite beams, Mechanics of Advanced Materials and Structures, 20, 2013, 28-37.
[19] Rafiee, M., He, X.Q., Liew, K.M., Non-linear dynamic stability of piezoelectric functionally graded carbon nanotube-reinforced composite plates with initial geometric imperfection, International Journal of Non-Linear Mechanics, 59, 2014, 37-51.
[20] Lei, Z.X., Zhang, L.W. and Liew, K.M., Dynamic stability analysis of carbon nanotube-reinforced functionally graded cylindrical panels using the element-free kp-Ritz method, Composite Structures, 113, 2014, 328-338.
[21] Lei, Z.X., Zhang. L.W., Liew, K.M., Elastodynamic analysis of carbon nanotube-reinforced functionally graded plates, International Journal of Mechanic Science, 99, 2015, 208-217.
[22] Belkorissat, I., Houari, M.S.A., Tounsi, A., On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model, Steel and Composite Structures, 18, 2015, 1063-1081.
[23] Wang, Z.X, Shen, H.S., Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments, Nonlinear Dynamics, 70, 2012, 735-754.
[24] Sayer, M., Bektas, N.B., Sayman, B., An experimental investigation on the impact behavior of hybrid composite plates, Composite Structures, 92, 2010, 1256-1262.
[25] Fu Y., Zhong J., Shao X., Tao C., Analysis of nonlinear dynamic stability for carbon nanotube-reinforced composite plates resting on elastic foundations, Mechanics of Advances Materials Structures, 23, 2016, 1284-1289.
[26] Wu H., Yang J., Kitipornchai S., Parametric instability of thermo-mechanically loaded functionally graded graphene reinforced nanocomposite plates, International Journal of Mechanic Science, 135, 2018, 431-440.
[27] Singh V., Kumar R., Patel S.N., Parametric instability analysis of functionally graded CNT-reinforced composite (FG-CNTRC) plate subjected to different types of non-uniform in-plane loading, In: Singh S.B., Sivasubramanian M.V.R., Chawla H. (eds) Emerging Trends of Advanced Composite Materials in Structural Applications. Composites Science and Technology. Springer, Singapore, 2021.
[28] Kapuria, S., Yasin, M.Y., Active vibration suppression of multilayered plates integrated with piezoelectric fiber reinforced composites using an efficient finite element model, Journal of Sound and Vibration, 329, 2010, 3247-3265.
[29] Khalili, S.M.R., Dehkordi, M.B., Carrera, E., Non-linear dynamic analysis of a sandwich beam with pseudoelastic SMA hybrid composite faces based on higher order finite element theory, Composite Structures, 96, 2013, 243-255.
[30] Frikh, A., Zghal, S., Dammak, F., Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element, Aerospace Science and Technology, 78, 2018, 438-451.
[31] Harras, B., Benamar, R., Whit, R.G., Experimental and theoretical investigation of the linear and non-linear dynamic behaviour of a glare 3 hybrid composite panel, Journal of Sound and Vibration, 252, 2002, 281-315.
[32] Kao, J.Y., Chen, C.S., Chen, W.R., Parametric vibration response of foam-filled sandwich plates under pulsating loads, Mechanics of Composite Materials, 48, 2012, 525-538.
[33] Chen, C.S., Liu, F.H., Chen, W.R., Dynamic characteristics of functionally graded material sandwich plate in thermal environments, Mechanics of Advanced Materials and Structures, 24, 2017, 157-167.
[34] Chen, C.S., Fung, C.P., Yang, J.G., Assessment of plate theories for initially stressed hybrid laminated plates, Composite Structures, 88, 2009, 195-201.
[35] Chen, L.W., Yang, J.Y., Dynamic stability of laminated composite plates by the finite element method, Computer and Structures, 36, 1990, 845-851.
[36] Chattopadhyay, A., Radu, A.G., Dragomir-Daescu D., A higher order plate theory for dynamic stability analysis of delaminated composite plates, Computational Mechanics, 26, 2000, 302-308.
[37] Shen, H.S., Nonlinear bending of functionally graded carbon nanotube reinforced composite plates in thermal environments, Composite Structures, 91, 2009, 9-19.
[38] Zhang, C.L., Shen, H.S., Temperature dependent elastic properties of single-walled carbon nanotubes: prediction from molecular dynamics simulation, Applied Physics Letters, 89, 2006, 81904-81907.
[39] Shen, H.S., Zhang, C.L. Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates, Materials & Design, 31, 2010, 3403-3411.
[40] Wang, Z.X., Shen, H.S., Nonlinear vibration of nanotube-reinforced composite plates in thermal environments, Computational Materials Science, 50, 2011, 2319-2330.
[41] Alibeigloo, A., Emtehani, A., Static and free vibration analyses of carbon nanotube-reinforced composite plate using differential quadrature method, Meccanica, 50, 2015, 61-76.
[42] Lei, Z.X., Liew, K.M., Yu, J.L., Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method, Composite Structures, 98, 2013, 160-168.
[43] Malekzadeh, P., Shojaee, M., Buckling analysis of quadrilateral laminated plates with carbon nanotubes reinforced composite layers, Thin-Walled Structures, 71, 2013, 108–118.
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