This study presents an experimentally validated operator-based viscoelastic modelling framework for the dynamic analysis of woven fabric composite rotor shafts. Woven carbon fabric/epoxy composite specimens (20% fabric volume fraction) were characterised using Dynamic Mechanical Analysis (DMA) over a frequency range of 0–100 Hz at 27°C. A standard four-element linear viscoelastic model was identified as the optimum rheological representation, and its parameters were extracted using a Genetic Algorithm–based curve-fitting procedure with minimal deviation from experimental data. The operator parameters where found to be approximately identical due to the woven architecture along the longitudinal and transverse direction. To avoid excessive computational complexity, the resulting higher-order modulus operator was reduced to an equivalent lower-order form without compromising accuracy. The reduced operator was incorporated into a finite element (FE)–based state-space formulation to investigate the rotor dynamic behaviour of the viscoelastic composite shaft. A detailed parametric study revealed a symmetric stability trend with respect to fibre orientation, where the Stability Limit Speed (SLS) decreased from 3690 rpm at 0° to a minimum of 3190 rpm at 45°, and increased again towards 90°. This behaviour is attributed to stiffness redistribution caused by woven fibre orientation. The results demonstrate the critical role of viscoelastic material modelling and fabric orientation in governing the stability and dynamic response of composite rotor shafts.
ArabSBRodriguesJDBouazizS, et al. (2018) Stability analysis of internally damped rotating composite shafts using a finite element formulation. Comptes Rendus Mecanique346(4): 291–307.
2.
BhattacharjeeAGangulyKRoyH (2020) An operator based novel micromechanical model of viscoelastic hybrid woven fiber-particulate reinforced polymer composites. European Journal of Mechanics-A/Solids83: 104044. https://doi.org/10.1016/j.euromechsol.2020.104044
3.
BlandDR (2016) The Theory of Linear Viscoelasticity. Courier Dover Publications.
4.
ChangMYChenJKChangCY (2004) A simple spinning laminated composite shaft model. International Journal of Solids and Structures41(3-4): 637–662. https://doi.org/10.1016/j.ijsolstr.2003.09.043
5.
ChenLWPengWK (1998) The stability behavior of rotating composite shafts under axial compressive loads. Composite Structures41(3-4): 253–263. https://doi.org/10.1016/s0263-8223(98)00022-1
6.
DimentbergFM (1961) Flexural Vibrations of Rotating Shafts. Butterworths.
7.
DuttJKRoyH (2011) Viscoelastic modelling of rotor—shaft systems using an operator-based approach. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science225(1): 73–87. https://doi.org/10.1243/09544062jmes2064
8.
FriswellMIDuttJKAdhikariS, et al. (2010) Time domain analysis of a viscoelastic rotor using internal variable models. International Journal of Mechanical Sciences52(10): 1319–1324. https://doi.org/10.1016/j.ijmecsci.2010.06.007
9.
GangulyKRoyH (2021a) SEREP-based reduced model of higher order viscoelastic propeller shaft considering various asymmetries. Engineering with Computers37(4): 3237–3249. https://doi.org/10.1007/s00366-020-00978-0
10.
GangulyKRoyH (2021b) Modelling and analysis of viscoelastic laminated composite shaft: an operator-based finite element approach. Archive of Applied Mechanics91(1): 343–362. https://doi.org/10.1007/s00419-020-01774-4
11.
GangulyKRoyH (2022) A novel geometric model of breathing crack and its influence on rotor dynamics. Journal of Vibration and Control28(21-22): 3411–3425. https://doi.org/10.1177/10775463211032811
12.
GangulyKRoyHBhattacharjeeA (2024) Establishment and simplification of micromechanical material model for viscoelastic woven fabric/hybrid composite. Archive of Applied Mechanics94(3): 449–468. https://doi.org/10.1007/s00419-023-02528-8
13.
GrybośR (1991) The dynamics of a viscoelastic rotor in flexible bearings. Archive of Applied Mechanics61(6): 479–487. https://doi.org/10.1007/bf00790139
14.
JonesRM (2018) Mechanics of Composite Materials. CRC Press.
MontagnierOHochardC (2014) Dynamics of a supercritical composite shaft mounted on viscoelastic supports. Journal of Sound and Vibration333(2): 470–484. https://doi.org/10.1016/j.jsv.2013.09.021
17.
MoorthyRSMitikuYSridharK (2013) Design of automobile driveshaft using carbon/epoxy and kevlar/epoxy composites. American Journal of Engineering Research2(10): 173–179.
18.
NakraBC (1998) Vibration control in machines and structures using viscoelastic damping. Journal of Sound and Vibration211(3): 449–466. https://doi.org/10.1006/jsvi.1997.1317
19.
ParidaSPJenaPC (2020) Advances of the shear deformation theory for analyzing the dynamics of laminated composite plates: an overview. Mechanics of Composite Materials56(4): 455–484. https://doi.org/10.1007/s11029-020-09896-0
20.
ParidaSPJenaPC (2022) Free and forced vibration analysis of flyash/graphene filled laminated composite plates using higher order shear deformation theory. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science236(9): 4648–4659. https://doi.org/10.1177/09544062211053181
21.
ParidaSPJenaPC (2023) Selective layer-by-layer fillering and its effect on the dynamic response of laminated composite plates using higher-order theory. Journal of Vibration and Control29(11-12): 2473–2488. https://doi.org/10.1177/10775463221081180
22.
ParidaSPJenaPCDashRR (2019) Dynamic analysis of laminated composite beam using Timoshenko beam Theory. International Journal of Engineering and Advanced Technology8(6): 190–196. https://doi.org/10.35940/ijeat.e7159.088619
23.
ParidaSPJenaPCDashRR (2023) Dynamics of rectangular laminated composite plates with selective layer-wise fillering rested on elastic foundation using higher-order layer-wise theory. Journal of Vibration and Control29(23-24): 5598–5615. https://doi.org/10.1177/10775463221138353
24.
ParidaSPJenaPCDasSR, et al. (2024) Transverse vibration of laminated-composite-plates with fillers under moving mass rested on elastic foundation using higher order shear deformation theory. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science238(20): 9878–9888. https://doi.org/10.1177/09544062241256589
25.
RoyHChandrakerS (2017) Dynamic study of viscoelastic rotor: modal analysis of higher order model considering various asymmetries. Mechanism and Machine Theory109: 65–77. https://doi.org/10.1016/j.mechmachtheory.2016.11.003
26.
RoyHChandrakerS (2018) Dynamic study of viscoelastic rotor: a comparative study using analytical and finite element model considering higher-order system. Archive of Applied Mechanics88(8): 1243–1261. https://doi.org/10.1007/s00419-018-1370-1
27.
RoyHDuttJK (2016) Dynamics of polymer and polymer composite rotors–An operator based finite element approach. Applied Mathematical Modelling40(3): 1754–1768. https://doi.org/10.1016/j.apm.2015.08.021
28.
RoyHDuttJKDattaPK (2008) Dynamics of a viscoelastic rotor shaft using augmenting thermodynamic fields—A finite element approach. International Journal of Mechanical Sciences50(4): 845–853. https://doi.org/10.1016/j.ijmecsci.2007.08.007
29.
RoyHChandrakerSDuttJK, et al. (2016) Dynamics of multilayer, multidisc viscoelastic rotor–An operator based higher order classical model. Journal of Sound and Vibration369: 87–108. https://doi.org/10.1016/j.jsv.2015.12.047
30.
SinghSPGuptaK (1994) Free damped flexural vibration analysis of composite cylindrical tubes using beam and shell theories. Journal of Sound and Vibration172(2): 171–190. https://doi.org/10.1006/jsvi.1994.1168
31.
SinghSPGuptaK (1996) Composite shaft rotordynamic analysis using a layerwise theory. Journal of Sound and Vibration191(5): 739–756. https://doi.org/10.1006/jsvi.1996.0153
32.
SinghAVGangulyKDuttJK (2024) Vibration reduction of rotor systems using magneto-rheological elastomeric supports. Journal of Vibration and Control: 10775463241290556. https://doi.org/10.1177/10775463241290556
YangMZhouXZhangW, et al. (2020) A modified transfer matrix method for bending vibration of CFRP/Steel composite transmission shafting. Archive of Applied Mechanics90(3): 603–614. https://doi.org/10.1007/s00419-019-01628-8
35.
ZinbergHSymondsMF (1970) The development of an advanced composite tail rotor driveshaft26th Annual National Forum of the American Helicopter Society, Washington, DC.
