Abstract
Free vibration of conical shells of variable thickness is analysed under shear deformation theory with simply supported and clamped free boundary conditions by applying collocation with spline approximation. Sinusoidal thickness variation of layers is assumed in axial direction. Displacements and rotational functions are approximated by Bickley-type splines of order three and a generalized eigenvalue problem is obtained. This problem is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration of composite conical shells consisting of three layers and five layers where each layer is made up of different materials is analysed. Parametric studies are made for analysing the frequencies of the shell with respect to the coefficients of thickness variations, length ratio, cone angle, circumferential node number, and different ply angles with different combinations of the materials. The results are presented in terms of tables and graphs.
Highlights
Laminated composite materials are widely used in engineering applications, since they have the ability to achieve desired weight as they have higher specific modulus and specific strength
A novel vibrational numerical method was used by Ansari et al [5] to investigate the free vibration of composite conical shells. 2D-FGM truncated conical shell resting on Winkler–Pasternak foundations was studied by Asanjarani et al [6] using the differential quadrature method for different boundary conditions
Frequency of symmetric angle-ply conical shells is analysed with respect to the circumferential node number, length ratio, cone angle, sinusoidal thickness variation and different number of lay ups, material combinations, and ply angles for C-F and Simply supported (S-S) boundary conditions. ree materials, AS4/3501-6 graphite/epoxy (GE), E-glass/epoxy (EGE), and Kevlar-49/epoxy (KE), are considered to analyse the problem
Summary
Laminated composite materials are widely used in engineering applications, since they have the ability to achieve desired weight as they have higher specific modulus and specific strength. The generalized differential quadrature method was used by Bacciocchi et al [4] to analyse the vibration of plates of variable thickness and shells. Fluid loaded ring-stiffened conical shells of variable thickness were analysed for their free vibration using the transfer matrix method by Liu et al [8]. Since the thickness is assumed to be varying along the axial direction, one can define the elastic coefficients Aij, Bij, and Dij (extensional, bending-extensional coupling, and bending stiffnesses) corresponding to layers of uniform thickness with superscript “c” as. E governing differential equations characterising the vibration of conical shell frusta of variable thickness including first-order shear deformation theory are derived in terms of displacement functions u0(x, θ, t), v0(x, θ, t), and w0(x, θ, t) and shear rotational functions ψx(x, θ, t) and ψθ(x, θ, t) using stress-strain and strain-displacement relations of the conical shell
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