On the Finite Element Free Vibration Analysis of Delaminated Layered Beams: A New Assembly Technique

• Main Authors: Nicholas H. Erdelyi, Seyed M. Hashemi
• Format: Article
• Language: English
• Published: Hindawi Limited 2016-01-01
• Series: Shock and Vibration
• Online Access: http://dx.doi.org/10.1155/2016/3707658

The dynamic analysis of flexible delaminated layered beams is revisited. Exploiting Boolean vectors, a novel assembly scheme is developed which can be used to enforce the continuity requirements at the edges of delamination region, leading to a delamination stiffness term. The proposed assembly technique can be used to form various beam configurations with through-width delaminations, irrespective of the formulation used to model each beam segment. The proposed assembly system and the Galerkin Finite Element Method (FEM) formulation are subsequently used to investigate the natural frequencies and modes of 2- and 3-layer beam configurations. Using the Euler-Bernoulli bending beam theory and free mode delamination, the governing differential equations are exploited and two beam finite elements are developed. The free bending vibration of three illustrative example problems, characterized by delamination zones of variable length, is investigated. The intact and defective beam natural frequencies and modes obtained from the proposed assembly/FEM beam formulations are presented along with the analytical results and those available in the literature.