Rotating laminated shells are widely used in engineering structures, where their vibration behavior is jointly affected by material anisotropy, centrifugal stiffening, gyroscopic coupling, and boundary flexibility. For moderately thick and thick shells, these effects become more complicated and may not be captured accurately by equivalent single-layer models. Accordingly, this paper presents a semi-analytical formulation for the traveling-wave vibration analysis of rotating laminated cylindrical shells with general elastic end restraints based on a full layerwise shell theory and the boundary spring technique. The governing equations are derived from Hamilton’s principle, in which the Fourier series and one-dimensional finite elements are employed to discretize the circumferential displacement field and axial domain, respectively, while a mass-weighted modal assurance criterion is introduced to track the continuous modal branches under rotation. The validity of the proposed method is verified through convergence studies, comparison with experimental results, and benchmark solutions available in the literature. The results show that the present formulation can accurately capture the forward and backward traveling-wave branches, together with the associated frequency splitting and mode veering phenomena induced by rotation. The effects of elastic end restraints and stacking sequence on the traveling-wave vibration characteristics are further clarified. The proposed method provides an efficient and accurate tool for the vibration analysis of rotating laminated cylindrical shells under general elastic support conditions.
ReddyJN. Mechanics of laminated composite plates and shells: theory and analysis. CRC Press, 2003.
2.
QatuMS. Vibration of laminated shells and plates. Elsevier, 2004.
3.
SoedelW. Vibrations of shells and plates. CRC Press, 2004.
4.
AmabiliM. Nonlinear vibrations and stability of shells and plates. Cambridge University Press, 2008.
5.
CarreraEBrischettoSNaliP. Plates and shells for smart structures: classical and advanced theories for modeling and analysis. John Wiley & Sons, 2011, vol 36.
6.
LeKC. Vibrations of shells and rods. Springer Science & Business Media, 2012.
7.
QuYChenYLongX, et al.A modified variational approach for vibration analysis of ring-stiffened conical-cylindrical shell combinations. Eur J Mech Solid2013; 37: 200–215. https://doi.org/10.1016/j.euromechsol.2012.06.006
8.
ZouMSLiuSXQiLB. An analytical formulation for the underwater acoustic radiation of a cylindrical shell with an internal flexural floor based on the reciprocity theorem. Appl Acoust2019; 154: 18–27. https://doi.org/10.1016/j.apacoust.2019.04.017
9.
KolarevićNNefovska-DanilovićM. Dynamic stiffness-based free vibration study of open circular cylindrical shells. J Sound Vib2020; 486: 115600. https://doi.org/10.1016/j.jsv.2020.115600
10.
ZhuHZWuJH. Free vibration of partially fluid-filled or fluid-surrounded composite shells using the dynamic stiffness method. Acta Mech2020; 231(9): 3961–3978. https://doi.org/10.1007/s00707-020-02734-3
11.
TalezadehlariA. Free vibration analysis of perforated composite cylindrical shell and panel using multi-domain generalized differential quadrature (GDQ) method. Compos Struct2022; 287: 115337. https://doi.org/10.1016/j.compstruct.2022.115337
12.
LiZJinGYeT, et al.A unified vibration modeling of open cylindrical shell-rectangular plate coupling structures based on the dynamic stiffness method. J Sound Vib2023; 563: 117870. https://doi.org/10.1016/j.jsv.2023.117870
ZhaoXWangSMeiZ, et al.Jacobi-Ritz method for free vibration analysis of medium-thickness sandwich cylindrical shells utilizing the layerwise theory and domain decomposition method. Ocean Eng2025; 342: 123065. https://doi.org/10.1016/j.oceaneng.2025.123065
15.
GuenanouAHoumatAHachemiM, et al.Geometrically nonlinear free vibration analysis of shear deformable laminated composite elliptic plates using the p-version FEM. J Compos Mater2025; 59(26): 2991–3020. https://doi.org/10.1177/00219983251340016
16.
WangYWuD. Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory. Aerosp Sci Technol2017; 66: 83–91. https://doi.org/10.1016/j.ast.2017.03.003
17.
SunWZhuMWangZ. Free vibration analysis of a hard-coating cantilever cylindrical shell with elastic constraints. Aerosp Sci Technol2017; 63: 232–244. https://doi.org/10.1016/j.ast.2017.01.002
18.
NinhDGBichDH. Characteristics of nonlinear vibration of nanocomposite cylindrical shells with piezoelectric actuators under thermo-mechanical loads. Aerosp Sci Technol2018; 77: 595–609. https://doi.org/10.1016/j.ast.2018.04.008
19.
CaoYWuBChenW. Three-dimensional free vibrations of piezoelectric spherical shells filled with Non-Newtonian fluids. J Sound Vib2025; 618: 119294. https://doi.org/10.1016/j.jsv.2025.119294
20.
ÇetinAKurtaranH. Large amplitude free vibration of hemp fiber-reinforced laminated composite plates using generalized differential quadrature method. J Compos Mater2025; 59(26): 2957–2980. https://doi.org/10.1177/00219983251341619
21.
QinZChuFZuJ. Free vibrations of cylindrical shells with arbitrary boundary conditions: a comparison study. Int J Mech Sci2017; 133: 91–99. https://doi.org/10.1016/j.ijmecsci.2017.08.012
22.
JinGYeTJiaX, et al.A general Fourier solution for the vibration analysis of composite laminated structure elements of revolution with general elastic restraints. Compos Struct2014; 109: 150–168. https://doi.org/10.1016/j.compstruct.2013.10.052
23.
ZhangCJinGMaX, et al.Vibration analysis of circular cylindrical double-shell structures under general coupling and end boundary conditions. Appl Acoust2016; 110: 176–193. https://doi.org/10.1016/j.apacoust.2016.03.038
24.
ChoeKWangQTangJ, et al.Vibration analysis for coupled composite laminated axis-symmetric doubly-curved revolution shell structures by unified Jacobi-Ritz method. Compos Struct2018; 194: 136–157. https://doi.org/10.1016/j.compstruct.2018.03.095
25.
LiHPangFChenH, et al.Vibration analysis of functionally graded porous cylindrical shell with arbitrary boundary restraints by using a semi analytical method. Compos B Eng2019; 164: 249–264. https://doi.org/10.1016/j.compositesb.2018.11.046
26.
ZhangCJinGWangZ, et al.Dynamic stiffness formulation and vibration analysis of coupled conical-ribbed cylindrical-conical shell structure with general boundary condition. Ocean Eng2021; 234: 109294. https://doi.org/10.1016/j.oceaneng.2021.109294
27.
GuoDChuFLZhengZC. The influence of rotation on vibration of a thick cylindrical shell. J Sound Vib2001; 242(3): 487–505. https://doi.org/10.1006/jsvi.2000.3356
SunSChuSCaoD. Vibration characteristics of thin rotating cylindrical shells with various boundary conditions. J Sound Vib2012; 331(18): 4170–4186. https://doi.org/10.1016/j.jsv.2012.04.018
33.
DongYLiuHHuH, et al.Semi-analytical and experimental studies on travelling wave vibrations of a moderately thick cylindrical shell subject to a spinning motion. J Sound Vib2022; 535: 117095. https://doi.org/10.1016/j.jsv.2022.117095
ShariyatMMohammadjaniR. Three-dimensional stress field analysis of rotating thick bidirectional functionally graded axisymmetric annular plates with nonuniform loads and elastic foundations. J Compos Mater2014; 48(23): 2879–2904. https://doi.org/10.1177/0021998313503389
36.
SongXZhaiJChenY, et al.Traveling wave analysis of rotating cross-ply laminated cylindrical shells with arbitrary boundaries conditions via Rayleigh-Ritz method. Compos Struct2015; 133: 1101–1115. https://doi.org/10.1016/j.compstruct.2015.08.015
37.
MalekzadehPHeydarpourY. Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment. Compos Struct2012; 94(9): 2971–2981. https://doi.org/10.1016/j.compstruct.2012.04.011
38.
ShengGGWangX. The non-linear vibrations of rotating functionally graded cylindrical shells. Nonlinear Dyn2017; 87(2): 1095–1109. https://doi.org/10.1007/s11071-016-3100-y
39.
DongYHLiYHChenD, et al.Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion. Compos B Eng2018; 145: 1–13. https://doi.org/10.1016/j.compositesb.2018.03.009
40.
QinZPangXSafaeiB, et al.Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions. Compos Struct2019; 220: 847–860. https://doi.org/10.1016/j.compstruct.2019.04.046
41.
XuHWangYXuZ, et al.Gegenbauer-Ritz method for free vibration analysis of rotating functionally graded graphene reinforced porous composite stepped cylindrical shells with arbitrary boundary conditions. Eng Struct2024; 303: 117555. https://doi.org/10.1016/j.engstruct.2024.117555
42.
XuZWangYZhaiJ, et al.Analytical analysis of traveling wave vibration for rotating bi-directional dual-functionally graded carbon nanotube reinforced composite stepped thin cylindrical shells. Thin-Walled Struct2025; 210: 112956. https://doi.org/10.1016/j.tws.2025.112956
43.
JianZWangYZhaiJ, et al.Traveling wave vibration characteristic analysis of FRC sandwich cylindrical shells with FGP-GPLRC core under discontinuous elastic boundary conditions. Compos Struct2024; 348: 118487. https://doi.org/10.1016/j.compstruct.2024.118487
44.
XuPYangYLiH, et al.Free vibration characteristics analysis of rotating composite fiber-reinforced honeycomb cylindrical shells with arbitrary boundary conditions. Compos Struct2025; 380: 119986. https://doi.org/10.1016/j.compstruct.2025.119986
45.
QinZYangZZuJ, et al.Free vibration analysis of rotating cylindrical shells coupled with moderately thick annular plates. Int J Mech Sci2018; 142–143: 127–139. https://doi.org/10.1016/j.ijmecsci.2018.04.044
46.
DuDSunWMaH, et al.Vibration characteristics analysis for rotating bolted joined cylindrical shells considering the discontinuous variable-stiffness connection. Thin-Walled Struct2022; 177: 109422. https://doi.org/10.1016/j.tws.2022.109422
47.
ZangJLiYWangZJ, et al.Vibration analysis of hole-containing laminated composite combined structures in electric aircraft using an area scan-fitting approach. J Sound Vib2025; 619: 119399. https://doi.org/10.1016/j.jsv.2025.119399
48.
DuDYanXLiuH, et al.Veering of frequency loci and nonlinear coupling vibration analysis between traveling waves of rotational hard-coated cylindrical shells. J Sound Vib2022; 536: 117152. https://doi.org/10.1016/j.jsv.2022.117152
49.
GuXLiSZhaoB, et al.Nonlinear dynamic analysis of a viscoelastic rotating cantilever beam under stochastic perturbation. J Sound Vib2025; 619: 119428. https://doi.org/10.1016/j.jsv.2025.119428
50.
SongXChaiZWangC, et al.Vibration performance of rotating thin-walled cylindrical shell with tip-rubbing excitation between drum and stator vane segment of aero-engine. J Sound Vib2022; 525: 116759. https://doi.org/10.1016/j.jsv.2022.116759
51.
SunLHaoYXZhangW, et al.Traveling wave vibration and critical rotating speed of rotating porous metal conical shell with elastic boundary conditions. Aerosp Sci Technol2024; 148: 109091. https://doi.org/10.1016/j.ast.2024.109091
52.
WanRLiuWChengL, et al.Traveling wave vibration analysis of rotating reinforced functionally graded conical shells. J Mech Sci Technol2025; 39(5): 2417–2429. https://doi.org/10.1007/s12206-025-0402-3
53.
WangPWangYZhaiJ, et al.Modeling and traveling wave vibration analysis of rotating multi-ring hard coating double thin-walled cylindrical shells coupled structure considering connection mistuning. J Sound Vib2025; 594: 118668. https://doi.org/10.1016/j.jsv.2024.118668
54.
DongYHuHWangL, et al.Nonlinear coupled multi-mode vibrations of simply-supported cylindrical shells: Comparison studies. Commun Nonlinear Sci Numer Simul2024; 128: 107667. https://doi.org/10.1016/j.cnsns.2023.107667
55.
ZhaoXSunSChuS, et al.Multi-mode vibration control and optimization of smart rotating cylindrical shells subjected to circumferential moving loads. Thin-Walled Struct2025; 211: 113094. https://doi.org/10.1016/j.tws.2025.113094
56.
LiuYQinZChuF. Nonlinear forced vibrations of FGM sandwich cylindrical shells with porosities on an elastic substrate. Nonlinear Dyn2021; 104(2): 1007–1021. https://doi.org/10.1007/s11071-021-06358-7
57.
LiuYQinZChuF. Nonlinear forced vibrations of rotating cylindrical shells under multi-harmonic excitations in thermal environment. Nonlinear Dyn2022; 108(4): 2977–2991. https://doi.org/10.1007/s11071-022-07449-9
58.
LiuYQinZChuF. Investigation of magneto-electro-thermo-mechanical loads on nonlinear forced vibrations of composite cylindrical shells. Commun Nonlinear Sci Numer Simul2022; 107: 106146. https://doi.org/10.1016/j.cnsns.2021.106146
59.
LiuYVellaDQinZ, et al.A review of nonlinear dynamics and vibration in lightweight composite structures: recent advances and challenges. Eng Struct2026; 360: 122835. https://doi.org/10.1016/j.engstruct.2026.122835
60.
LamKYLoyCT. Analysis of rotating laminated cylindrical shells by different thin shell theories. J Sound Vib1995; 186(1): 23–35. https://doi.org/10.1006/jsvi.1995.0431
61.
CarreraE. Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Arch Comput Methods Eng2003; 10(3): 215–296. https://doi.org/10.1007/bf02736224
62.
CarreraE. Historical review of zig-zag theories for multilayered plates and shells. Appl Mech Rev2003; 56(3): 287–308. https://doi.org/10.1115/1.1557614
63.
ReddyJNStarnesJHJr. General buckling of stiffened circular cylindrical shells according to a layerwise theory. Comput Struct1993; 49(4): 605–616. https://doi.org/10.1016/0045-7949(93)90065-l
