Tapered laminated composite beams provide stiffness-tailoring and mass-tailoring design capabilities. They are increasingly and widely being used in engineering applications including robotic manipulators, aircraft wings, space structures, helicopter blades and yokes, turbine blades, and civil infrastructure. In the present work, the free and the forced vibration response of symmetric linear-thickness-and-width-tapered laminated composite beams are considered. Considering a variety of tapered configurations according to different types of plies drop-off configurations both conventional and hierarchical finite element formulations are developed based on cylindrical laminated beam bending theory. Natural frequencies, mode shapes and forced vibration response of different types of internally-tapered composite beams are determined. Comparison of the hierarchical finite element solution with the Rayleigh-Ritz and a higher-order finite element solution is performed. A parametric study is conducted to investigate the effects of boundary conditions, width-ratio, taper configurations, thickness-tapering angle, laminate configuration, compressive axial force and damping on the free and forced vibration response of thickness- and width-tapered laminated composite beams.
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