Skip to content
BY-NC-ND 4.0 license Open Access Published by De Gruyter Open Access May 24, 2018

Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels with general elastic supports

  • Fei Xie , Jinyuan Tang , Ailun Wang , Cijun Shuai and Qingshan Wang EMAIL logo

Abstract

In this paper, a unified solution for vibration analysis of the functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical panels with general elastic supports is carried out via using the Ritz method. The excellent accuracy and reliability of the present method are compared with the results of the classical boundary cases found in the literature. New results are given for vibration characteristics of FG-CNTRC cylindrical panels with various boundary conditions. The effects of the elastic restraint parameters, thickness, subtended angle and volume fraction of carbon nanotubes on the free vibration characteristic of the cylindrical panels are also reported.

References

[1] K. Liew, Z. Lei, L. Zhang, Mechanical analysis of functionally graded carbon nanotube reinforced composites: a review, Composite Structures, 120 (2015) 90-97.10.1016/j.compstruct.2014.09.041Search in Google Scholar

[2] F. Lin, Y. Xiang, Vibration of carbon nanotube reinforced composite beams based on the first and third order beam theories, Appl. Math. Model., 38 (2014) 3741-3754.10.1016/j.apm.2014.02.008Search in Google Scholar

[3] M. Rafiee, J. Yang, S. Kitipornchai, Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers, Composite Structures, 96 (2013) 716-725.10.1016/j.compstruct.2012.10.005Search in Google Scholar

[4] L.-L. Ke, J. Yang, S. Kitipornchai, Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Composite Structures, 92 (2010) 676-683.10.1016/j.compstruct.2009.09.024Search in Google Scholar

[5] L.-L. Ke, J. Yang, S. Kitipornchai, M.A. Bradford, Bending, buckling and vibration of size-dependent functionally graded annular microplates, Composite structures, 94 (2012) 3250-3257.10.1016/j.compstruct.2012.04.037Search in Google Scholar

[6] H.-S. Shen, Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments, Composite Structures, 91 (2009) 9-19.10.1016/j.compstruct.2009.04.026Search in Google Scholar

[7] P. Zhu, Z. Lei, K.M. Liew, 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 (2012) 1450-1460.10.1016/j.compstruct.2011.11.010Search in Google Scholar

[8] L. Zhang, Z. Lei, K. Liew, Vibration characteristic of moderately thick functionally graded carbon nanotube reinforced composite skew plates, Composite Structures, 122 (2015) 172-183.10.1016/j.compstruct.2014.11.070Search in Google Scholar

[9] L. Zhang, Z. Lei, K. Liew, Free vibration analysis of functionally graded carbon nanotube-reinforced composite triangular plates using the FSDT and element-free IMLS-Ritz method, Composite Structures, 120 (2015) 189-199.10.1016/j.compstruct.2014.10.009Search in Google Scholar

[10] L. Zhang, Z. Lei, K. Liew, J. Yu, Static and dynamic of carbon nanotube reinforced functionally graded cylindrical panels, Composite Structures, 111 (2014) 205-212.10.1016/j.compstruct.2013.12.035Search in Google Scholar

[11] P. Malekzadeh, A. Zarei, Free vibration of quadrilateral laminated plateswith carbon nanotube reinforced composite layers, Thin-Walled Structures, 82 (2014) 221-232.10.1016/j.tws.2014.04.016Search in Google Scholar

[12] P. Malekzadeh, Y. Heydarpour, Mixed Navier-layerwise differential quadrature three-dimensional static and free vibration analysis of functionally graded carbon nanotube reinforced composite laminated plates, Meccanica, 50 (2015) 143-167.10.1007/s11012-014-0061-4Search in Google Scholar

[13] S. Natarajan, M. Haboussi, G. Manickam, Application of higherorder structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets, Composite Structures, 113 (2014) 197-207.10.1016/j.compstruct.2014.03.007Search in Google Scholar

[14] Z.-X. Wang, H.-S. Shen, Nonlinear vibration of nanotubereinforced composite plates in thermal environments, Computational Materials Science, 50 (2011) 2319-2330.10.1016/j.commatsci.2011.03.005Search in Google Scholar

[15] Z.-X. Wang, H.-S. Shen, Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets, Composites Part B: Engineering, 43 (2012) 411-421.10.1016/j.compositesb.2011.04.040Search in Google Scholar

[16] Z.-X. Wang, H.-S. Shen, Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments, Nonlinear Dynamics, 70 (2012) 735-754.10.1007/s11071-012-0491-2Search in Google Scholar

[17] Z. Lei, L. Zhang, K. Liew, Elastodynamic analysis of carbon nanotube-reinforced functionally graded plates, International Journal of Mechanical Sciences, 99 (2015) 208-217.10.1016/j.ijmecsci.2015.05.014Search in Google Scholar

[18] L. Zhang, Z. Song, K. Liew, State-space Levy method for vibration analysis of FG-CNT composite plates subjected to in-plane loads based on higher-order shear deformation theory, Composite Structures, 134 (2015) 989-1003.10.1016/j.compstruct.2015.08.138Search in Google Scholar

[19] L. Zhang, W. Cui, K. Liew, Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges, International Journal of Mechanical Sciences, 103 (2015) 9-21.10.1016/j.ijmecsci.2015.08.021Search in Google Scholar

[20] Z. Lei, L. Zhang, K. Liew, Free vibration analysis of laminated FGCNT reinforced composite rectangular plates using the kp-Ritz method, Composite Structures, 127 (2015) 245-259.10.1016/j.compstruct.2015.03.019Search in Google Scholar

[21] L. Zhang, Z. Lei, K. Liew, Buckling analysis of FG-CNT reinforced composite thick skew plates using an element-free approach, Composites Part B: Engineering, 75 (2015) 36-46.10.1016/j.compositesb.2015.01.033Search in Google Scholar

[22] L. Zhang, K. Liew, J. Reddy, Postbuckling of carbon nanotube reinforced functionally graded plates with edges elastically restrained against translation and rotation under axial compression, Computer Methods in Applied Mechanics and Engineering, 298 (2016) 1-28.10.1016/j.cma.2015.09.016Search in Google Scholar

[23] Z. Lei, L. Zhang, K. Liew, Analysis of laminated CNT reinforced functionally graded plates using the element-free kp-Ritz method, Composites Part B: Engineering, 84 (2016) 211-221.10.1016/j.compositesb.2015.08.081Search in Google Scholar

[24] L. Zhang, K. Liew, Large deflection analysis of FG-CNT reinforced composite skew plates resting on Pasternak foundations using an element-free approach, Composite Structures, 132 (2015) 974-983.10.1016/j.compstruct.2015.07.017Search in Google Scholar

[25] L. Zhang, Z. Song, K. Liew, Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLS-Ritz method, Composite Structures, 128 (2015) 165-175.10.1016/j.compstruct.2015.03.011Search in Google Scholar

[26] L. Zhang, K. Liew, Geometrically nonlinear large deformation analysis of functionally graded carbon nanotube reinforced composite straight-sided quadrilateral plates, Computer Methods in Applied Mechanics and Engineering, 295 (2015) 219-239.10.1016/j.cma.2015.07.006Search in Google Scholar

[27] Z. Lei, L. Zhang, K. Liew, J. Yu, Dynamic stability analysis of carbon nanotube-reinforced functionally graded cylindrical panels using the element-free kp-Ritz method, Composite Structures, 113 (2014) 328-338. 10.1016/j.compstruct.2014.03.035Search in Google Scholar

[28] M. Mirzaei, Y. Kiani, Free Vibration of Functionally Graded Carbon Nanotube Reinforced Composite Cylindrical Panels, Composite Structures, (2016).10.1016/j.compstruct.2015.12.071Search in Google Scholar

[29] F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola, J.N. Reddy, A numerical investigation on the natural frequencies of FGM sandwich shells with variable thickness by the local generalized differential quadrature method, Applied Sciences, 7 (2017) 131.10.3390/app7020131Search in Google Scholar

[30] F. Tornabene, N. Francesco, E. Viola, Inter-laminar stress recovery procedure for doubly-curved, singly-curved, revolution shells with variable radii of curvature and plates using generalized higher-order theories and the local GDQ method, Mechanics of Advanced Materials and Structures, 23 (2016) 1019-1045.10.1080/15376494.2015.1121521Search in Google Scholar

[31] F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola, Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells, Compos Part B-Eng, 89 (2016) 187-218.10.1016/j.compositesb.2015.11.016Search in Google Scholar

[32] F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola, J. Reddy, A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method, Applied Sciences, 7 (2017) 131.10.3390/app7020131Search in Google Scholar

[33] F. Tornabene, N. Fantuzzi, M. Bacciocchi, J. Reddy, An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells, Applied Sciences, 7 (2017) 17.10.3390/app7010017Search in Google Scholar

[34] F. Tornabene, N. Fantuzzi, M. Bacciocchi, A new doubly-curved shell element for the free vibrations of arbitrarily shaped laminated structures based on Weak Formulation IsoGeometric Analysis, Composite Structures, 171 (2017) 429-461.10.1016/j.compstruct.2017.03.055Search in Google Scholar

[35] S. Brischetto, F. Tornabene, N. Fantuzzi, M. Bacciocchi, Interpretation of boundary conditions in the analytical and numerical shell solutions for mode analysis of multilayered structures, International Journal of Mechanical Sciences, 122 (2017) 18-28.10.1016/j.ijmecsci.2016.12.017Search in Google Scholar

[36] D. Banić, M. Bacciocchi, F. Tornabene, A. Ferreira, Influence of Winkler-Pasternak Foundation on the Vibrational Behavior of Plates and Shells Reinforced by Agglomerated Carbon Nanotubes, Applied Sciences, 7 (2017) 1228.10.3390/app7121228Search in Google Scholar

[37] F. Tornabene, S. Brischetto, N. Fantuzzi, M. Bacciocchi, Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded Structures, Shock Vibrat., 2016 (2016) 17.10.1155/2016/2373862Search in Google Scholar

[38] F. Tornabene, N. Fantuzzi, M. Bacciocchi, R. Dimitri, Free vibrations of composite oval and elliptic cylinders by the generalized differential quadrature method, Thin-Walled Struct., 97 (2015) 114-129.10.1016/j.tws.2015.08.023Search in Google Scholar

[39] M.S. Qatu, Vibration of laminated shells and plates, Elsevier, 2004. 10.1016/B978-008044271-6/50006-5Search in Google Scholar

[40] G. Jin, X. Ma, S. Shi, T. Ye, Z. Liu, A modified Fourier series solution for vibration analysis of truncated conical shells with general boundary conditions, Applied Acoustics, 85 (2014) 82-96.10.1016/j.apacoust.2014.04.007Search in Google Scholar

[41] T. Ye, G. Jin, Z. Su, Y. Chen, A modified Fourier solution for vibration analysis of moderately thick laminated plates with general boundary restraints and internal line supports, International Journal of Mechanical Sciences, 80 (2014) 29-46.10.1016/j.ijmecsci.2014.01.001Search in Google Scholar

[42] W.L. Li, Free vibrations of beams with general boundary conditions, J. Sound Vibrat., 237 (2000) 709-725.10.1006/jsvi.2000.3150Search in Google Scholar

[43] Q. Wang, D. Shi, Q. Liang, X. Shi, A unified solution for vibration analysis of functionally graded circular, annular and sector plates with general boundary conditions, Composites Part B: Engineering, 88 (2016) 264-294.10.1016/j.compositesb.2015.10.043Search in Google Scholar

[44] H. Zhang, D. Shi, S. Zha, Q.Wang, Vibro-acoustic analysis of the thin laminated rectangular plate-cavity coupling system, Composite Structures, 189 (2018) 570-585.10.1016/j.compstruct.2018.01.099Search in Google Scholar

[45] Q.Wang, D. Shao, B. Qin, A simple first-order shear deformation shell theory for vibration analysis of composite laminated open cylindrical shells with general boundary conditions, Composite Structures, 184 (2018) 211-232.10.1016/j.compstruct.2017.09.070Search in Google Scholar

[46] Q. Wang, K. Choe, D. Shi, K. Sin, Vibration analysis of the coupled doubly-curved revolution shell structures by using Jacobi- Ritz method, International Journal of Mechanical Sciences, 135 (2018) 517-531.10.1016/j.ijmecsci.2017.12.002Search in Google Scholar

[47] J. Guo, D. Shi, Q. Wang, J. Tang, C. Shuai, Dynamic analysis of laminated doubly-curved shells with general boundary conditions by means of a domain decomposition method, International Journal of Mechanical Sciences, 138-139 (2018) 159-186.10.1016/j.ijmecsci.2018.02.004Search in Google Scholar

[48] J. Guo, D. Shi, Q. Wang, F. Pang, Q. Liang, A domain decomposition approach for static and dynamic analysis of composite laminated curved beam with general elastic restrains, Mechanics of Advanced Materials and Structures, (2018) 1-13.10.1080/15376494.2018.1432810Search in Google Scholar

[49] X. Guan, J. Tang, Q. Wang, C. shuai, Application of the differential quadrature finite element method to free vibration of elastically restrained plate with irregular geometries, Engineering Analysis with Boundary Elements, 90 (2018) 1-16.10.1016/j.enganabound.2018.02.005Search in Google Scholar

[50] Y. Zhou, Q. Wang, D. Shi, Q. Liang, Z. Zhang, Exact solutions for the free in-plane vibrations of rectangular plates with arbitrary boundary conditions, International Journal of Mechanical Sciences, 130 (2017) 1-10.10.1016/j.ijmecsci.2017.06.004Search in Google Scholar

[51] H. Zhang, D. Shi, Q. Wang, B. Qin, Free vibration of functionally graded parabolic and circular panels with general boundary conditions, Curved and Layered Structures, 4 (2017) 52-84.10.1515/cls-2017-0006Search in Google Scholar

[52] H. Zhang, D. Shi, Q. Wang, An improved Fourier series solutionfor free vibration analysis of the moderately thick laminated composite rectangular plate with non-uniform boundary conditions, International Journal of Mechanical Sciences, 121 (2017)1-20.10.1016/j.ijmecsci.2016.12.007Search in Google Scholar

[53] Q. Wang, D. Shi, Q. Liang, F. Pang, Free vibration of fourparameter functionally graded moderately thick doubly-curved panels and shells of revolution with general boundary conditions, Appl. Math. Model., 42 (2017) 705-734.10.1016/j.apm.2016.10.047Search in Google Scholar

[54] Q. Wang, D. Shi, Q. Liang, F. Pang, Free vibrations of composite laminated doubly-curved shells and panels of revolution with general elastic restraints, Appl. Math. Model., 46 (2017) 227-262.10.1016/j.apm.2017.01.070Search in Google Scholar

[55] Q. Wang, D. Shi, Q. Liang, F. Pang, A unified solution for vibration analysis of moderately thick functionally graded rectangular plates with general boundary restraints and internal line supports, Mechanics of Advanced Materials and Structures, 24 (2017) 943-961.10.1080/15376494.2016.1196797Search in Google Scholar

[56] Q. Wang, B. Qin, D. Shi, Q. Liang, A semi-analytical method for vibration analysis of functionally graded carbon nanotube reinforced composite doubly-curved panels and shells of revolution, Composite Structures, 174 (2017) 87-109.10.1016/j.compositesb.2016.02.044Search in Google Scholar

[57] Q. Wang, F. Pang, B. Qin, Q. Liang, A unified formulation for free vibration of functionally graded carbon nanotube reinforced composite spherical panels and shells of revolution with general elastic restraints by means of the Rayleigh-Ritz method, Polymer Composites, (2017) n/a-n/a.10.1002/pc.24339Search in Google Scholar

[58] Q. Wang, X. Cui, B. Qin, Q. Liang, J. Tang, A semi-analytical method for vibration analysis of functionally graded (FG) sandwich doubly-curved panels and shells of revolution, International Journal of Mechanical Sciences, 134 (2017) 479-499.10.1016/j.ijmecsci.2017.10.036Search in Google Scholar

[59] Q. Wang, X. Cui, B. Qin, Q. Liang, Vibration analysis of the functionally graded carbon nanotube reinforced composite shallowshellswith arbitrary boundary conditions, Composite Structures, 182 (2017) 364-379.10.1016/j.compstruct.2017.09.043Search in Google Scholar

[60] Q.Wang, D. Shi, F. Pang, Q. Liang, Vibrations of Composite Laminated Circular Panels and Shells of Revolution with General Elastic Boundary Conditions via Fourier-Ritz Method, Curved and Layered Structures, 3 (2016) 105-136.10.1515/cls-2016-0010Search in Google Scholar

Received: 2018-03-31
Accepted: 2018-04-06
Published Online: 2018-05-24

© 2018 Qingshan Wang, published by De Gruyter

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Downloaded on 3.5.2024 from https://www.degruyter.com/document/doi/10.1515/cls-2018-0008/html
Scroll to top button