Vibration analysis of composite beams using hierarchical finite element method

The conventional finite element formulation has limitations in performing the dynamic analysis of composite beams. The discretization necessary for obtaining solutions with acceptable accuracy in the determination of dynamic response parameters leads to discontinuities in stress and strain distributions. The hierarchical finite element formulation provides us with the advantages of using fewer elements and obtaining better accuracy in the calculation of natural frequencies, displacements and stresses. The hierarchical finite element formulation for uniform and variable-thickness composite beams is developed in the present work. Two sub-formulations of hierarchical finite element method viz. polynomial and trigonometric sub-formulations have been developed. The efficiency and accuracy of the developed formulation are established in comparison with closed-form solutions for uniform composite beams. The static response of uniform composite beams is evaluated using the hierarchical finite element method. The dynamic response of variable-thickness composite beams is calculated based on the developed formulation. A detailed parametric study encompassing the influences of boundary conditions, laminate configuration, taper angle and the type of taper on the dynamic response of the beam is performed. The NCT-301 graphite-epoxy composite material is considered in the analysis and in the parametric study.