Abstract
The natural dynamic characteristics of a circular cylindrical tube made of three-directional (3D) functional graded material (FGM) based on the Timoshenko beam theory are investigated. Hamilton’s principle is utilized to derive the novel motion equations of the tube, considering the interactions among the longitudinal, transverse, and rotation deformations. By dint of the differential quadrature method (DQM), the governing equations are discretized to conduct the analysis of natural dynamic characteristics. The Ritz method, in conjunction with the finite element method (FEM), is introduced to verify the present results. It is found that the asymmetric modes in the tube are controlled by the 3D FGM, which exhibit more complicated shapes compared with the unidirectional (1D) and bi-directional (2D) FGM cases. Numerical examples illustrate the effects of the axial, radial, and circumferential FGM indexes as well as the supported edges on the natural dynamic characteristics in detail. It is notable that the obtained results are beneficial for accurate design of smart structures composed from multi-directional FGM.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
GUPTA, A. and TALHA, M. Recent development in modeling and analysis of functionally graded materials and structures. Progress in Aerospace Sciences, 79, 1–14 (2015)
SHAW, L. L. The crack driving force of functionally graded materials. Journal of Materials Science Letters, 17, 65–67 (1998)
MA, L. S. and LEE, D. W. Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading. European Journal of Mechanics-A/Solids, 31, 13–20 (2012)
BANERJEE, J. R. and ANANTHAPUVIRAJAH, A. Free vibration of functionally graded beams and frameworks using the dynamic stiffness method. Journal of Sound and Vibration, 422, 34–47 (2018)
RAD, A. B. Thermo-elastic analysis of functionally graded circular plates resting on a gradient hybrid foundation. Applied Mathematics and Computation, 256, 276–298 (2015)
SHEN, H., PAÏDOUSSIS, M. P., WEN, J., YU, D., and WEN, X. The beam-mode stability of periodic functionally-graded-material shells conveying fluid. Journal of Sound and Vibration, 333, 2735–2749 (2014)
TANG, Y. and YANG, T. Post-buckling behavior and nonlinear vibration analysis of a fluid-conveying pipe composed of functionally graded material. Composite Structures, 185, 393–400 (2018)
ZHEN, Y., GONG, Y., and TANG, Y. Nonlinear vibration analysis of a supercritical fluid-conveying pipe made of functionally graded material with initial curvature. Composite Structures, 268, 113980 (2021)
JIANG, Q., ZHOU, Z., and YANG, F. The transient response of hollow electrostrictive cylinder subjected to the electrical shock. Archive of Applied Mechanics, 91, 4039–4051 (2021)
LI, Z. M. and LIU, T. A new displacement model for nonlinear vibration analysis of fluid-conveying anisotropic laminated tubular beams resting on elastic foundation. European Journal of Mechanics-A/Solids, 86, 104172 (2021)
KADOLI, R. and GANESAN, N. Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition. Journal of Sound and Vibration, 289, 450–480 (2006)
FU, Y., ZHONG, J., SHAO, X., and CHEN, Y. Thermal postbuckling analysis of functionally graded tubes based on a refined beam model. International Journal of Mechanical Sciences, 96, 58–64 (2015)
LU, L., SHE, G. L., and GUO, X. M. Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection. International Journal of Mechanical Sciences, 199, 106428 (2021)
LU, L., WANG, S., LI, M., and GUO, X. M. Free vibration and dynamic stability of functionally graded composite microtubes reinforced with graphene platelets. Composite Structures, 272, 114231 (2021)
GHATAGE, P. S., KAR, V. R., and SUDHAGAR, P. E. On the numerical modelling and analysis of multi-directional functionally graded composite structures: a review. Composite Structures, 236, 111837 (2020)
NEJAD, M. Z., HADI, A., OMIDVARI, A., and RASTGOO, A. Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen’s non-local elasticity theory. Structural Engineering and Mechanics, 67, 417–425 (2018)
LAL, R. and AHLAWAT, N. Buckling and vibrations of two-directional functionally graded circular plates subjected to hydrostatic in-plane force. Journal of Vibration and Control, 23, 2111–2127 (2017)
LAL, R. and DANGI, C. Dynamic analysis of bi-directional functionally graded Timoshenko nanobeam on the basis of Eringen’s nonlocal theory incorporating the surface effect. Applied Mathematics and Computation, 395, 125857 (2021)
TANG, Y., LV, X. F., and YANG, T. Z. Bi-directional functionally graded beams: asymmetric modes and nonlinear free vibration. Composites Part B: Engineering, 156, 319–331 (2019)
CHEN, X. C. and LI, Y. H. Size-dependent post-buckling behaviors of geometrically imperfect microbeams. Mechanics Research Communications, 88, 25–33 (2018)
TANG, Y. and DING, Q. Nonlinear vibration analysis of a bi-directional functionally graded beam under hygro-thermal loads. Composite Structures, 225, 111076 (2019)
TANG, Y., MA, Z. S., DING, Q., and WANG, T. Dynamic interaction between bi-directional functionally graded materials and magneto-electro-elastic fields: a nano-structure analysis. Composite Structures, 264, 113746 (2021)
TANG, Y., WANG, T., MA, Z. S., and YANG, T. Magneto-electro-elastic modelling and nonlinear vibration analysis of bi-directional functionally graded beams. Nonlinear Dynamics, 105, 2195–2227 (2021)
HADI, A., NEJAD, M. Z., and HOSSEINI, M. Vibrations of three-dimensionally graded nanobeams. International Journal of Engineering Science, 128, 12–23 (2018)
SHU, C. and CHEW, Y. T. On the equivalence of generalized differential quadrature and highest order finite difference scheme. Computer Methods in Applied Mechanics and Engineering, 155, 249–260 (1998)
Acknowledgements
The current study is funded by the Middle-aged Top-notch Talent and Innovative Team Support Programs of Anhui Polytechnic University of China.
Funding
Project supported by the National Natural Science Foundation of China (Nos. 11902001 and 12072221), the China Postdoctoral Science Foundation (No. 2018M641643), and the Anhui Provincial Natural Science Foundation of China (Nos. 1908085QA13 and 1808085ME128)
Author information
Authors and Affiliations
Corresponding author
Additional information
Citation: TANG, Y., XU, J. Y., and YANG, T. Z. Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material. Applied Mathematics and Mechanics (English Edition), 43(4), 479–496 (2022) https://doi.org/10.1007/s10483-022-2839-6
Rights and permissions
About this article
Cite this article
Tang, Y., Xu, J. & Yang, T. Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material. Appl. Math. Mech.-Engl. Ed. 43, 479–496 (2022). https://doi.org/10.1007/s10483-022-2839-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-022-2839-6
Key words
- circular cylindrical tube
- three-directional (3D) functionally graded material (FGM)
- asymmetric mode
- natural dynamic characteristic
- differential quadrature method (DQM)