Laminated Composite Stiffened Cylindrical Shell Panels with Cutouts under Free Vibration

Notations

• a, b: Length and width of shell in plan

• : Length and width of cutout in plan

• b_st: Width of stiffener in general

• b_sx, b_sy: Width of X and Y stiffeners respectively

• d_st: Depth of stiffener in general

• d_sx, d_sy: Depth of X and Y stiffeners respectively

• {d_e}: Element displacement

• E₁₁, E₂₂: Elastic moduli

• G₁₂, G₁₃, G₂₃: Shear moduli of a lamina with respect to 1, 2 and 3 axes of fibre

• H: Shell thickness

• M_x, M_y: Moment resultants

• M_xy: Torsion resultant

• Np: Number of plies in a laminate

• N₁-N₈: Shape functions

• N_x,, N_y: Inplane force resultants

• N_xy: Inplane shear resultant

• Q_x, Q_y: Transverse shear resultant

• R_y,: Radii of curvature of shell

• u, v, w: Translational degrees of freedom

• x, y, z: Local co-ordinate axes

• X, Y, Z: Global co-ordinate axes

• z_k: Distance of bottom of the kth ply from mid-surface of a laminate

• α,β: Rotational degrees of freedom

• ε_x, ε_y: Inplane strain component

• γ_xy, γ_xz, γ_yz: Shearing strain components

• ν₁₂, ν₂₁: Poisson’s ratios

• ξ, η, τ: Isoperimetric co-ordinates

• ρ: Density of material

• σ_x, σ_y: Inplane stress components

• τ_xy, τ_xz, τ_yz: Shearing stress components

• ω: Natural frequency

• : Non-dimensional natural frequency