Natural Frequencies Of Internally-Doubly-Tapered Laminated Composite Beams

In the present study, the free vibration response of symmetric thickness-and-width-tapered (doubly-tapered) laminated composite beams is investigated. Considering the continuous-plies-interspersed ply drop-off configuration, called herein as taper configuration D, both conventional and hierarchical finite element formulations are developed based on the cylindrical bending theory of laminated beam. Natural frequencies of different types of internally-tapered composite beams are determined. Comparison of the hierarchical finite element solution with the Rayleigh-Ritz solution and a higherorder finite element solution is performed. A parametric study is conducted to investigate the effects of width-taper-ratio and the thickness-taper-ratio (or equivalently thickness-tapering angle) on the free vibration response of doubly-tapered laminated composite beams.