Variable-width variable-thickness laminated composite beams provide stiffness-tailoring and mass-tailoring design capabilities. They are increasingly and widely being used in engineering applications such as robotic manipulators and helicopter blades and yokes. These structures are subjected to time-varying loadings in service. In practical applications, frequently the supports are not so rigid as idealized by classical boundary conditions such as simple or clamped supports. In the present work, the free vibration of symmetric linear-thickness-and-width-tapered laminated composite beams with elastic supports is considered. Considering a variety of tapered configurations according to different types of plies drop-off two finite element formulations are developed based on the one-dimensional Kirchhoff laminated beam theory. Natural frequencies of different types of internally-tapered composite beams are determined. Elastic supports are modeled using different combinations of translational and rotational springs. Comparison of the finite element solution with the existing results is performed. A comprehensive parametric study is conducted to investigate the effects of taper configurations, stiffnesses of rotational and translational springs, width-ratios and boundary conditions on the free vibration of the composite beams.
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