Modes of vibration of thin cylindrical shells made up of layers with curvilinear fibres (variable stiffness composite laminates (VSCL) shells) are investigated in the linear regime. A p-version finite element type formulation is developed for that purpose; in the absence of data on vibrations of cylindrical VSCL shells, the formulation is verified by comparisons with published data on laminated shells reinforced by straight fibres and on VSCL plates. Parametric studies are performed, in order to investigate how curvilinear fibre paths can influence the modes of vibration. It is found that curvilinear fibre paths can have a very large effect, larger than on plates, on the natural frequencies and natural mode shapes of vibration of cylindrical shells. Factors that strongly influence the modes of vibration of VSCL shells are found; these include the fibre orientation at boundaries and in relation to principal normal sections.
AbdallaMMSetoodehSGürdalZ (2007) Design of variable stiffness composite panels for maximum fundamental frequency using lamination parameters. Composite Structures81: 283–291.
2.
AkhavanHRibeiroP (2011) Natural modes of vibration of variable stiffness composite laminates with curvilinear fibers. Composite Structures93: 3040–3047.
3.
AmabiliM (2008) Nonlinear Vibrations and Stability of Shells and Plates, Cambridge: Cambridge University Press.
4.
AsadiEQatuMS (2013) Free vibration of thick laminated cylindrical shells with different boundary conditions using general differential quadrature. Journal of Vibration and Control19: 356–366.
5.
Blom AW (2010) Structural Performance of Fiber-Placed, Variable-Stiffness Composite Conical and Cylindrical Shells. PhD Thesis, Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands.
6.
BlomAWSetoodehSHolJMAMGürdalZ (2008) Design of variable-stiffness conical shells for maximum fundamental eigenfrequency. Computers and Structures86: 870–878.
7.
BlomAWTattingBFHolJMAMGürdalZ (2009) Fiber path definitions for elastically tailored conical shells. Composites Part B: Engineering40: 77–84.
8.
GürdalZOlmedoR (1993) In-Plane Response of Laminates with Spatially Varying Fiber Orientations: Variable Stiffness Concept. AIAA Journal31: 751–758.
9.
HanWPetytMHsiaoKM (1994) An investigation into geometrically nonlinear-analysis of rectangular laminated plates using the hierarchical finite element method. Finite elements in Analysis and Design18: 273–288.
10.
HanWPetytM (1996) Linear vibration analysis of laminated rectangular plates using the hierarchical finite element method, Part I: Free vibration analysis. Computers and Structures61: 705–712.
11.
HondaSNaritaY (2011) Vibration design of laminated fibrous composite plates with local anisotropy induced by short fibers and curvilinear fibers. Composite Structures93: 902–910.
12.
HondaSNaritaY (2012) Natural frequencies and vibration modes of laminated composite plates reinforced with arbitrary curvilinear fiber shape paths. Journal of Sound and Vibration331: 180–191.
13.
HondaSOonishiYNaritaYSasakiK (2008) Vibration analysis of composite rectangular plates reinforced along curved lines. Journal of System Design and Dynamics2: 76–82.
14.
HosokawaKMurayamaMSakataT (2001) Free vibration analysis of angle-ply laminated shallow cylindrical shell with clamped edges. Journal of Vibrations and Acoustics123: 188–197.
15.
Hyer MW and Charette RF (1990) Innovative design of composite structures: the use of curvilinear fiber format in composite structure design. Report, NASA-CR-186453, Blacksburg.
16.
HyerMWCharetteRF (1991) Use of curvilinear fiber format in composite structure design. AIAA Journal29: 1011–1015.
17.
HyerMWLeeH (1991) The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes. Composite Structures18: 239–261.
18.
LeissaAWNaritaY (1984) Vibrations of completely free shallow shells of rectangular planform. Journal of Sound and Vibration96: 207–218.
19.
LoH-CHyerMW (2012) Fundamental Frequencies of Elliptical Composite Cylinders with Circumferentially Varying Fiber Orientation. AIAA Journal50: 928–937.
20.
NikMAFayazbakhshKPasiniDLessardL (2014) Optimization of variable stiffness composites with embededded defects. Composite Structures107: 160–166.
21.
QatuMSLeissaAW (1991) Free vibrations of completely free doubly curved laminated composite shallow shells. Journal of Sound and Vibration151: 9–29.
22.
QatuMS (2004) Vibration of Laminated Shells and Plates, Amsterdam: Elsevier.
23.
RibeiroP (2003) A hierarchical finite element for geometrically non-linear vibration of doubly curved, moderately thick isotropic shallow shells. International Journal for Numerical Methods in Engineering56: 715–738.
24.
RibeiroP (2004) A p-version, first order shear deformation, finite element for geometrically non-linear vibration of curved beams. International Journal for Numerical Methods in Engineering61: 2696–2715.
25.
RibeiroP (2005) First-order shear deformation, p-version, finite element for laminated plate nonlinear vibrations. AIAA Journal43: 1371–1379.
RibeiroPAkhavanHTeterAWarmińskiJ (2014) A Review on the mechanical behaviour of curvilinear fibre composite laminated panels. Journal of Composite Materials48: 2761–2777.
29.
RibeiroPCochelinBBellizziS (2010) Non-linear vibrations of deep cylindrical shells by the p-version finite element method. Shock and Vibration17: 21–37.
30.
RibeiroPJansenE (2008) Non-linear vibrations of laminated cylindrical shallow shells under thermomechanical loading. Journal of Sound and Vibration315: 626–640.
31.
SinghAVKumarV (1996) Vibration of laminated shallow shells on quadrangular boundary. Journal of Aerospace Engineering9: 52–57.
32.
SzabóBABabuskaI (1991) Finite Element Analysis, New York: John Wiley and Sons.
33.
VentselEKrauthammerT (2001) Thin Plates and Shells. Theory Analysis and Applications, New York: Marcel Dekker.
