This study is concerned with the stability analysis for various vibrational motions of tow-steered variable angle fibres based composite rotating beam with time varying speed. The formulation combines a higher order theory introducing sine function along with finite element methodology. It satisfies the plane stress condition in width direction of beam. The displacement kinematics are generic in the sense it includes various possible vibrational motions like chord and flap wise motions, torsional and axial vibration behaviours. The equilibrium equations for the proposed problem evolved adopting virtual dynamic work are then transformed into the equations of Mathieu-Hill type considering time varying harmonic rotational speed. Using Bolotin’s procedure coupled with C1 continuity-based beam element, the parametric resonance zones along with boundary limits are numerically evaluated. The eigenvalue type of solution methodology applied for the detailed study is validated for accuracy and computational efficiency against the time domain dynamic response analysis. Based on in-depth analysis, dynamic instability characteristics in terms of resonance range and origin of instability of composite beam subjected to the chord and flap wise, torsional and axial motions are studied considering curvilinear fibre path angles, beam cross section, hub radius, thickness ratio and mean rotary speed.
RafieeMNitzscheFLabrosseM. Dynamics, vibration and control of rotating composite beams and blades: a critical review. J Thin-walled Struct2017; 119: 795–819. DOI: 10.1016/j.tws.2017.06.018.
3.
BrasingtonASaccoCHalbritterJ, et al.Automated fiber placement: a review of history, current technologies, and future paths forward. J Compos C: Open Access2021; 6: 100182. DOI: 10.1016/j.jcomc.2021.100182.
4.
WaldhartC, Analysis of tow-placed variable stiffness laminates. Master’s thesis, Virginia Polytechnic Institute and State University, 1996.
5.
BolotinVV. The dynamic stability of elastic systems. San Francisco: Holden-Day Inc, 1964.
6.
RoutT. On the dynamic stability of functionally graded material beams under parametric excitation. PhD Thesis. India: National Institute of Technology Rourkela, 2012.
7.
TanTHLeeHPLengGSB. Dynamic stability of a radially rotating beam subjected to base excitation. J Comput Methods Appl Mech Eng1997; 146(3–4): 265–279. DOI: 10.1016/S0045-7825(96)01238-8.
8.
ChungJJungDYooHH. Stability analysis for the flapwise motion of a cantilever beam with rotary oscillation. J Sound Vib2004; 273(4–5): 1047–1062. DOI: 10.1016/S0022-460X(03)00521-2.
9.
ParidaRDashP. Dynamic stability analysis of a circularly tapered rotating beam subjected to axial pulsating load and thermal gradient under various boundary conditions. Int J Acoust; Vib2016; 21(2): 137–144. DOI: 10.20855/ijav.2016.21.2402.
10.
PradhanMMishraMKDashP. Static and dynamic stability analysis of a rotating taper beam having elliptical cross section subjected to pulsating axial load with thermal gradient. Int J Acoust Vib2019; 24(3): 440–450. DOI: 10.20855/ijav.2019.24.31250.
11.
LinCYChenLW. Dynamic stability of rotating pre-twisted blades with a constrained damping layer. J Compos Struct2003; 61(3): 235–245. DOI: 10.1016/S0263-8223(03)00048-5.
12.
ArvinHTangYNadooshanAA. Dynamic stability in principal parametric resonance of rotating beams: method of multiple scales versus differential quadrature method. Int J Non-Linear Mech2016; 85: 118–125. DOI: 10.1016/j.ijnonlinmec.2016.06.007.
13.
LinCYChenLW. Dynamic stability of rotating composite beams with a viscoelastic core. J Compos Struct2002; 58(2): 185–194. DOI: 10.1016/S0263-8223(02)00127-7.
14.
SerajSGanesanR. Dynamic instability of rotating doubly-tapered laminated composite beams under periodic rotational speeds. J Compos Struct2018; 200: 711–728. DOI: 10.1016/j.compstruct.2018.05.133.
15.
ZhouYZhangYYaoG. Higher-order stability analysis of a rotating BDFG tapered beam with time-varying velocity. J Compos Struct2021; 267: 113858. DOI: 10.1016/j.compstruct.2021.113858.
16.
GuXJHaoYXZhangW, et al.Dynamic stability of rotating cantilever composite thin-walled twisted plate with initial geometric imperfection under in-plane load. J Thin-walled Struct2019; 144: 106267. DOI: 10.1016/j.tws.2019.106267.
17.
SankarANatrajanSManickamG. Dynamic instability analysis of sandwich plates with CNT reinforced facesheets. J Compos Struct2016; 146: 187–200. DOI: 10.1016/j.compstruct.2016.03.026.
18.
HaddadpourHZamaniZ, Curvilinear fiber optimization tools for aeroelastic design of composite wings. J Fluid Struct2012; 33(2012): 180–190. DOI: 10.1016/j.jfluidstructs.2012.05.008.
19.
AkhavanHRebeiroP. Natural modes of vibration of variable stiffness composite laminates with curvilinear fibers. J Compos Struct2011; 93(11): 3040–3047. DOI: 10.1016/j.compstruct.2011.04.027.
20.
BarathanVRajamohanVHaboussiM, et al.Variable stiffness composite laminated beams – nonlinear free flexural vibration behaviour using a sinusoidal based shear flexible structural theory accounting for Poisson’s effect. Int. J. Non-Linear Mech2022; 146: 104146. DOI: 10.1016/j.ijnonlinmec.2022.104146.
21.
FarsadiT. Enhancement of static and dynamic performance of composite tapered pretwisted rotating blade with variable stiffness. J Vib Acoust2021; 143(2). DOI: 10.1115/1.4048333.
22.
VenkatachariANatarajanSHaboussiM, et al.Environmental effects on the free vibration of curvilinear fibre composite laminates with cutouts. J Compos B Eng2016; 88: 131–138. DOI: 10.1016/j.compositesb.2015.10.017.
23.
DaraeiBShojaeeSHamzehei-JavaranS. Free vibration analysis of composite laminated beams with curvilinear fibers via refined theories. J Mech Adv. Mater Struct2022; 29(6): 840–849. DOI: 10.1080/15376494.2020.1797959.
24.
ManickamGPolitOBalajiL, et al.Variable-stiffness curved laminated-beams by curvilinear fibers with arbitrarily layup-vibrational features by sine-based higher-order beam model with renewed-constitutive relations and improved-kinematics. J Compos Struct2023; 324: 117514. DOI: 10.1016/j.compstruct.2023.117514.
25.
SamukhamSVyasarayaniCPRajuG. Implicit Floquet analysis for parametric instabilities in a variable angle tow composite panel. J Compos Struct2020; 233: 111637. DOI: 10.1016/j.compstruct.2019.111637.
26.
ChenXNieGWuZ. Dynamic instability of variable angle tow composite plates with delamination. J Compos Struct2018; 187: 294–307. DOI: 10.1016/j.compstruct.2017.12.042.
27.
KhalafiVFazilatiJ. Parametric instability behaviour of tow steered laminated quadrilateral plates using isogeometric analysis. J Thin-Walled Struct2018; 133: 96–105. DOI: 10.1016/j.tws.2018.09.035.
28.
FilippiMAzzaraRCarreraE. Rotordynamic analyses with variable-kinematic beam and shell finite elements. Mech Adv Mater Struct2023; 31: 2246221. DOI: 10.1080/15376494.2023.2246221.
29.
FilippiMGiusaDPaganiA, et al.Assessment of classical, advanced, and layer-wise theories for the vibration of rotating composite anisotropic blades. Compos Struct2020; 245: 112315. DOI: 10.1016/j.compstruct.2020.112315.
30.
BalajiLManickamGPolitO, et al.Variable angle tow-steered curvilinear fibres-based rotating arbitrarily layered composite beams- a coupled vibration of chordwise-flapwise-torsional motions by higher-order beam theory. Compos Struct2024; 340: 118199. DOI: 10.1016/j.compstruct.2024.118199.
31.
TouratierM. An efficient standard plate theory. Int J Eng Sci1991; 29(8): 901–916. DOI: 10.1016/0020-7225(91)90165-Y.
32.
PolitOMerzoukiTManickamG. Elastic stability of curved nanobeam based on higher-order shear deformation theory and nonlocal analysis by finite element approach. J. Finite Elem. Anal. Des2018; 146: 1–15. DOI: 10.1016/j.finel.2018.04.002.
Jafari-TalookolaeiR-AAbediMAttarM. In-plane and out-of-plane vibration modes of laminated composite beams with arbitrary lay-ups. Aero Sci Technol2017; 66: 366–379. DOI: 10.1016/j.ast.2017.02.027.
35.
RiberioPAkhavanHTeterA, et al.A review on the mechanical behaviour of curvilinear fibre composite laminated panels. J Compos Mater2014; 48(22): 2761–2777. DOI: 10.1177/0021998313502066.
36.
VenkatachariANatarajanSManickamG. Variable stiffness laminated composite shells – free vibration characteristics based on higher-order structural theory. J. Compos. Struct2018; 188: 407–414. DOI: 10.1016/j.compstruct.2018.01.025.
37.
VenkatachariANatarajanSManickamG, et al.Mechanical buckling of curvilinear fibre composite laminate with material discontinuities and environmental effects. J Compos Struct2015; 131: 790–798. DOI: 10.1016/j.compstruct.2015.05.080.
