Vibration analysis of tapered composite beams using a higher-order finite element. Part I: Formulation

Tapered composite beams are increasingly being used in various engineering applications such as helicopter yoke, robot arms and turbine blades. The objective of the present work is to conduct an investigation of the free undamped vibration response of such tapered composite beams, using the finite element method. Conventional cubic Hermitian finite element formulation requires a large number of elements to obtain reasonably accurate results in the analysis of tapered laminated beams. Since the continuity of curvature at element interfaces cannot be guaranteed with the use of conventional formulation, the stress distribution across the thickness is not continuous at element interfaces. The material and geometric discontinuities at ply drop-off locations leads to additional discontinuities in stress distributions. As a result, efficient and accurate calculation of natural frequencies becomes very difficult. In order to overcome these limitations, a higher-order finite element formulation is developed in Part I of the present work. The stiffness coefficients of the tapered laminated beam are determined based on the stress and strain transformations and classical laminate theory. In Part II of the present work, the developed formulation is used for the free undamped vibration analysis of various types of tapered composite beams and a parametric study is conducted.