Eur. Phys. J. Plus (2020) 135: 582
https://doi.org/10.1140/epjp/s13360-020-00577-4

Regular Article

Investigation on free vibration and transient response of functionally graded graphene platelets reinforced cylindrical shell resting on elastic foundation

¹ State Key Laboratory of High Performance Complex Manufacturing, Central South University, 410083, Changsha, People’s Republic of China
² Key Laboratory of Traffic Safety on Track, Ministry of Education, School of Traffic and Transportation Engineering, Central South University, 410075, Changsha, People’s Republic of China
³ Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Central South University, 410075, Changsha, People’s Republic of China
⁴ National and Local Joint Engineering Research Center of Safety Technology for Rail Vehicle, Central South University, 410075, Changsha, People’s Republic of China

^d wangqingshan@csu.edu.cn
^e zhongrui@csu.edu.cn

Received: 18 February 2020
Accepted: 29 June 2020
Published online: 18 July 2020

Abstract

This paper is concerned with the free vibration and transient response of graphene platelets reinforced functionally graded (GPL-FG) cylindrical shell resting on elastic foundation by utilizing the Chebyshev–Lagrangian approach. The boundary constraints are realized by setting reasonable values of stiffness of the artificial virtual springs. According to FSDT, the analysis model of GPL-FG cylindrical shell is established. Then, the displacement fields are expanded in terms of the Chebyshev–Lagrangian approach. Based on the work above, Rayleigh–Ritz energy method is employed to solve the unknown coefficients of Chebyshev expansions with purpose to indicate the dynamic characteristics of the analysis model. In addition, the Rayleigh damping coefficients are taken into account to investigate the transient response results from the external excitation. A series of numerical results show the rapid convergence and precision of the present method by comparison with results obtained by the published papers and FEM. Ultimately, the analysis about the effects of parameters and factors on free vibration and transient response are discussed, including geometry and material properties, boundary conditions, stiffness of elastic foundation, loading types and Rayleigh damping coefficients.