This paper investigated the nonlinear vibration and dynamic response of the carbon nanotube polymer composite elliptical cylindrical shells on elastic foundations in thermal environment. The material properties of the nanocomposite elliptical cylindrical shells are assumed to depend on temperature and graded in the thickness direction according to various linear functions. The shell is subjected to the combination of the uniformly distributed transverse load in harmonic form and the uniform temperature rise. The motion and geometrical compatibility equations are derived based on the Reddy’s higher order shear deformation shell theory. The natural frequencies and the deflection amplitude–time curves of the shell are determined by using the Galerkin method and fourth-order Runge–Kutta method. The numerical results show not only the positive influences of carbon nanotube volume fraction and elastic foundations but also the negative influences of initial imperfection and temperature increment on the nonlinear vibration and dynamic response of the carbon nanotube polymer composite elliptical cylindrical shells. The reliability of the present results is verified by comparing with other publications.
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Ahmed, M.K.: Buckling behavior of a radially loaded corrugated orthotropic thin-elliptic cylindrical shell on an elastic foundation. Thin Walled Struct. 107, 90–100 (2016)
Alibeigloo, A.: Free vibration analysis of functionally graded carbon nanotube-reinforced composite cylindrical panel embedded in piezoelectric layers by using theory of elasticity. Eur. J. Mech. A Solids 44, 104–115 (2014)
Arani, A.G., Haghparast, E., Khoddami Maraghi, Z., Amir, S.: CNTRC cylinder under non-axisymmetric thermo-mechanical loads and uniform electromagnetic fields. Arab. J. Sci. Eng. 39, 9057–9069 (2014)
Asadi, H., Wang, Q.: Dynamic stability analysis of a pressurized FG-CNTRC cylindrical shell interacting with supersonic airflow. Compos. B Eng. 118, 15–25 (2017)
Baloch, W.L., Khushnood, R.A., Khaliq, W.: Influence of multi-walled carbon nanotubes on the residual performance of concrete exposed to high temperatures. Constr. Build. Mater. 185, 44–56 (2018)
Brush, D.D., Almroth, B.O.: Buckling of bars, plates and shells. McGraw-Hill, New York (1975)
Chen, Y., Jin, G., Zhang, C., Ye, T., Xue, Y.: Thermal vibration of FGM beams with general boundary conditions using a higher-order shear deformation theory. Compos. B Eng. 153, 376–386 (2018)
Dastjerdi, S., Abbasi, M., Yazdanparast, L.: A new modified higher-order shear deformation theory for nonlinear analysis of macro- and nano-annular sector plates using the extended Kantorovich method in conjunction with SAPM. Acta Mech. 228, 3381–3401 (2017)
Duc, N.D., Quan, T.Q., Luat, V.D.: Nonlinear dynamic analysis and vibration of shear deformable piezoelectric FGM double curved shallow shells under damping-thermo-electro-mechanical loads. Compos. Struct. 125, 29–40 (2015)
Duc, N.D., Tuan, N.D., Tran, P., Cong, P.H., Nguyen, P.D.: Nonlinear stability of eccentrically stiffened S-FGM elliptical cylindrical shells in thermal environment. Thin Walled Struct. 108, 280–290 (2016)
Duc, N.D., Quan, T.Q., Khoa, N.D.: New approach to investigate nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube reinforced composite double curved shallow shells subjected to blast load and temperature. Aerosp. Sci. Technol. 71, 360–372 (2017)
Ganapathi, M., Patel, B.P., Patel, H.G.: Free flexural vibration behavior of laminated angle-ply elliptical cylindrical shells. Comput. Struct. 82, 509–518 (2004)
Jadhav, P., Bajoria, K.: Stability analysis of thick piezoelectric metal based FGM plate using first order and higher order shear deformation theory. Int. J. Mech. Mater. Des. 11, 387–403 (2015)
Kazemi, E., Darvizeh, M., Darvizeh, A., Ansari, R.: An investigation of the buckling behavior of composite elliptical cylindrical shells with piezoelectric layers. Acta Mech. 223, 2225–2242 (2012)
Keleshteri, M.M., Asadi, H., Wang, Q.: Postbuckling analysis of smart FG-CNTRC annular sector plates with surface-bonded piezoelectric layers using generalized differential quadrature method. Comput. Methods Appl. Mech. Eng. 325, 689–710 (2017)
Khalifa, M.: Effects of non-uniform Winkler foundation and non-homogeneity on the free vibration of an orthotropic elliptical cylindrical shell. Eur. J. Mech. A Solids 49, 570–581 (2015)
Kumar, R.S., Kundalwal, S.I., Ray, M.C.: Control of large amplitude vibrations of doubly curved sandwich shells composed of fuzzy fiber reinforced composite facings. Aerosp. Sci. Technol. 70, 10–28 (2017)
Kundalwal, S.I., Meguid, S.A.: Effect of carbon nanotube waviness on active damping of laminated hybrid composite shells. Acta Mech. 226, 2035–2052 (2015)
Kundalwal, S.I., Ray, M.C.: Smart damping of fuzzy fiber reinforced composite plates using 1–3 piezoelectric composites. J. Vib. Control 22, 1526–1546 (2016)
Lam, K.Y., Loy, C.T.: Effects of boundary conditions on frequencies of a multilayered cylindrical shell. J. Sound Vib. 188, 363–384 (1995)
Lei, Z.X., Zhang, L.W., Liew, K.M.: Buckling analysis of CNT reinforced functionally graded laminated composite plates. Compos. Struct. 152, 62–73 (2016)
Li, T.Y., Xiong, L., Zhu, X., Xiong, Y.P., Zhang, G.J.: The prediction of the elastic critical load of submerged elliptical cylindrical shell based on the vibro-acoustic model. Thin Walled Struct. 84, 255–262 (2014)
Mantari, J.L., Oktem, A.S., Guedes Soares, C.: Bending and free vibration analysis of isotropic and multilayered plates and shells by using a new accurate higher-order shear deformation theory. Compos. B Eng. 43, 3348–3360 (2012)
Mirzaei, M., Kiani, Y.: Thermal buckling of temperature dependent FG-CNT reinforced composite plates. Meccanica 51, 2185–2201 (2016)
Phung-Van, P., De Lorenzis, L., Thai, C.H., Abdel-Wahab, M., Nguyen-Xuan, H.: Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements. Comput. Mater. Sci. 96, 495–505 (2015)
Pradyumna, S., Bandyopadhyay, J.N.: Dynamic instability behavior of laminated hypar and conoid shells using a higher-order shear deformation theory. Thin Walled Struct. 49, 77–84 (2011)
Reddy, J.N.: Mechanics of laminated composite plates and shells: theory and analysis. CRC Press, Boca Raton (2004)
Shen, H.S.: Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Compos. Struct. 91, 9–19 (2009)
Shen, H.S.: Nonlinear vibration of shear deformable FGM cylindrical shells surrounded by an elastic medium. Compos. Struct. 94, 1144–1154 (2012)
Shen, H.-S., Xiang, Y.: Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments. Comput. Methods Appl. Mech. Eng. 213–216, 196–205 (2012)
Tu, T.M., Thach, L.N., Quoc, T.H.: Finite element modeling for bending and vibration analysis of laminated and sandwich composite plates based on higher-order theory. Comput. Mater. Sci. 49, S390–S394 (2010)
Xie, F., Qu, Y., Zhang, W., Peng, Z., Meng, G.: Nonlinear aerothermoelastic analysis of composite laminated panels using a general higher-order shear deformation zig-zag theory. Int. J. Mech. Sci. 150, 226–237 (2019)
Xu, Z., Gardner, L., Sadowski, A.J.: Nonlinear stability of elastic elliptical cylindrical shells under uniform bending. Int. J. Mech. Sci. 128–129, 593–606 (2017)
Xuebin, L.: Study on free vibration analysis of circular cylindrical shells using wave propagation. J. Sound Vib. 311, 667–682 (2008)
Zarei, H., Fallah, M., Bisadi, H., Daneshmehr, A.R., Minak, G.: Multiple impact response of temperature-dependent carbon nanotube-reinforced composite (CNTRC) plates with general boundary conditions. Compos. B Eng. 113, 206–217 (2017)
Zhang, G.J., Li, T.Y., Zhu, X., Yang, J., Miao, Y.Y.: Free and forced vibration characteristics of submerged finite elliptic cylindrical shell. Ocean Eng. 129, 92–106 (2017)
This work has been supported/partly supported by Vietnam National University, Hanoi (VNU), under Project No. QG.18.37.
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Dat, N.D., Quan, T.Q. & Duc, N.D. Nonlinear thermal vibration of carbon nanotube polymer composite elliptical cylindrical shells. Int J Mech Mater Des 16, 331–350 (2020). https://doi.org/10.1007/s10999-019-09464-y
- Nonlinear thermal vibration
- The carbon nanotube polymer composite elliptical cylindrical shells
- The Reddy’s higher order shear deformation shell theory
- Elastic foundations