Abstract
In this research, an analytical solution is developed for the analysis of free vibration of functionally graded composite plates reinforced by carbon-nanotube submerged in a fluid medium. Here, the distribution of carbon-nanotube along the direction of the plate thickness may be functionally graded or uniform. Hypotheses are made for the fluid such as incompressible, ideal, irrotational, and inviscid. Thus, the impacts of free-surface waves and hydrostatic pressure are not considered. Based on the four-variable shear deformation refined plate theory (HSDT4), the set of governing equations for the fluid-plates system is obtained by implementing Hamilton’s principle. The potential of fluid velocity is first derived from the plates-fluid system’s boundary conditions and then employed to calibrate added mass. The Navier’s solution for the plates with simply supported boundary conditions at all four edges is derived. Several numerical examples validate the accuracy of the presented solution. Some new parametric studies regarding the effects of different material properties, boundary conditions, and geometrical parameters on the plates’ free vibration responses are examined and discussed in detail.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Amabili, M.: Vibrations of circular plates resting on a sloshing liquid: solution of the fully coupled problem. J. Sound Vib. 245(2), 261–283 (2001)
Canales, F., Mantari, J.: Discrepancy on the free vibration of laminated composite plates coupled to a compressible and incompressible fluid domain. Ocean Eng. 167, 267–281 (2018)
Chang, T.-P., Liu, M.-F.: Vibration analysis of rectangular composite plates in contact with fluid (2001)
Cho, D.S., Kim, B.H., Kim, J.-H., Vladimir, N., Choi, T.M.: Frequency response of rectangular plate structures in contact with fluid subjected to harmonic point excitation force. Thin-Walled Struct. 95, 276–286 (2015)
Duc, N.D., Lee, J., Nguyen-Thoi, T., Thang, P.T.: Static response and free vibration of functionally graded carbon nanotube-reinforced composite rectangular plates resting on Winkler-Pasternak elastic foundations. Aerosp. Sci. Technol. 68, 391–402 (2017)
Esawi, A.M., Farag, M.M.: Carbon nanotube reinforced composites: potential and current challenges. Mater. Des. 28(9), 2394–2401 (2007)
Fidelus, J., Wiesel, E., Gojny, F., Schulte, K., Wagner, H.: Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites. Compos. A Appl. Sci. Manuf. 36(11), 1555–1561 (2005)
Fu, Y., Price, W.: Interactions between a partially or totally immersed vibrating cantilever plate and the surrounding fluid. J. Sound Vib. 118(3), 495–513 (1987)
Han, Y., Elliott, J.: Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Comput. Mater. Sci. 39(2), 315–323 (2007)
Hashemi, S.H., Karimi, M., Taher, H.R.D.: Vibration analysis of rectangular Mindlin plates on elastic foundations and vertically in contact with stationary fluid by the Ritz method. Ocean Eng. 37(2–3), 174–185 (2010)
Hosseini-Hashemi, S., Karimi, M., Rokni, H.: Natural frequencies of rectangular Mindlin plates coupled with stationary fluid. Appl. Math. Model. 36(2), 764–778 (2012)
Huang, B., et al.: Bending and free vibration analyses of antisymmetrically laminated carbon nanotube-reinforced functionally graded plates. J. Compos. Mater. 51(22), 3111–3125 (2017)
Huu, Q.T., Minh, T., Van Tham, V.: Free vibration analysis of smart laminated functionally graded CNT reinforced composite plates via new four-variable refined plate theory. Materials 12(22), 3675 (2019)
Kerboua, Y., Lakis, A., Thomas, M., Marcouiller, L.: Vibration analysis of rectangular plates coupled with fluid. Appl. Math. Model. 32(12), 2570–2586 (2008)
Khorshid, K., Farhadi, S.: Free vibration analysis of a laminated composite rectangular plate in contact with a bounded fluid. Compos. Struct. 104, 176–186 (2013)
Khorshidi, K., Bakhsheshy, A.: Free vibration analysis of a functionally graded rectangular plate in contact with a bounded fluid. Acta Mech. 226(10), 3401–3423 (2015). https://doi.org/10.1007/s00707-015-1368-5
Khorshidi, K., Akbari, F., Ghadirian, H.: Experimental and analytical modal studies of vibrating rectangular plates in contact with a bounded fluid. Ocean Eng. 140, 146–154 (2017)
Khourshidi, K.: Effect of hydrostatic pressure on vibrating rectangular plates coupled with fluid (2010)
Kwak, M.: Hydroelastic vibration of circular plates. J. Sound Vib. 201(3), 293–303 (1997)
Kwak, M.K.: Hydroelastic vibration of rectangular plates (1996)
Lamb, H.: On the vibrations of an elastic plate in contact with water. In: Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 98, no. 690, pp. 205–216 (1920)
Lei, Z., Zhang, L., Liew, K.: Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method. Compos. Struct. 127, 245–259 (2015)
Lei, Z., Zhang, L., Liew, K.: Analysis of laminated CNT reinforced functionally graded plates using the element-free kp-Ritz method. Compos. B Eng. 84, 211–221 (2016)
Liao, C.-Y., Ma, C.-C.: Vibration characteristics of rectangular plate in compressible inviscid fluid. J. Sound Vib. 362, 228–251 (2016)
Mehar, K., Panda, S.K.: Numerical investigation of nonlinear thermomechanical deflection of functionally graded CNT reinforced doubly curved composite shell panel under different mechanical loads. Compos. Struct. 161, 287–298 (2017)
Rahmanei, H., Jafari, A.A.: Vibration analysis of a rectangular composite plate in contact with fluid. Iran. J. Mech. Eng. Trans. ISME 17(2), 67–83 (2016)
Shafiee, A.A., Daneshmand, F., Askari, E., Mahzoon, M.: Dynamic behavior of a functionally graded plate resting on Winkler elastic foundation and in contact with fluid. Struct. Eng. Mech 50(1), 53–71 (2014)
Shahbaztabar, A., Ranji, A.R.: Effects of in-plane loads on free vibration of symmetrically cross-ply laminated plates resting on Pasternak foundation and coupled with fluid. Ocean Eng. 115, 196–209 (2016)
Shahbaztabar, A., Ranji, A.R.: Free vibration analysis of functionally graded plates on two-parameter elastic supports and in contact with stationary fluid. J. Offshore Mech. Arctic Eng. 140(2) (2018)
Shen, H.-S.: Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Compos. Struct. 91(1), 9–19 (2009)
Shen, H.-S., Zhu, Z.H.: Buckling and postbuckling behavior of functionally graded nanotube-reinforced composite plates in thermal environments. Comput. Mater. Continua (CMC) 18(2), 155 (2010)
Shen, H.-S., Zhang, C.-L.: Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates. Mater. Des. 31(7), 3403–3411 (2010)
Thinh, T.I., Tu, T.M., Van Long, N.: Free vibration of a horizontal functionally graded rectangular plate submerged in fluid medium. Ocean Eng. 216, 107593 (2020)
Wang, Z.-X., Shen, H.-S.: Nonlinear vibration of nanotube-reinforced composite plates in thermal environments. Comput. Mater. Sci. 50(8), 2319–2330 (2011)
Wattanasakulpong, N., Chaikittiratana, A.: Exact solutions for static and dynamic analyses of carbon nanotube-reinforced composite plates with Pasternak elastic foundation. Appl. Math. Model. 39(18), 5459–5472 (2015)
Zhang, L., Cui, W., Liew, K.: Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges. Int. J. Mech. Sci. 103, 9–21 (2015)
Zhou, D., Cheung, Y.: Vibration of vertical rectangular plate in contact with water on one side. Earthq. Eng. Struct. Dyn. 29(5), 693–710 (2000)
Zhu, P., Lei, Z., Liew, K.M.: Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory. Compos. Struct. 94(4), 1450–1460 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Huan, D.T., Quoc, T.H., Van Tham, V., Binh, C.T. (2022). Vibration Characteristics of Functionally Graded Carbon Nanotube-Reinforced Composite Plates Submerged in Fluid Medium. In: Tien Khiem, N., Van Lien, T., Xuan Hung, N. (eds) Modern Mechanics and Applications. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-3239-6_21
Download citation
DOI: https://doi.org/10.1007/978-981-16-3239-6_21
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-3238-9
Online ISBN: 978-981-16-3239-6
eBook Packages: EngineeringEngineering (R0)