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

Abstract

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.

A Finite Element Formulation for Bending-Torsion Coupled Vibration Analysis of Delaminated Beams under Combined Axial Load and End Moment

“…e un-prestressed defective beam, in this case, is assumed to be clamped-clamped and isotropic, with P 0 � 0, M zz � 0, H 2 /H � 0.3, and L 2 /L � 0.4. To validate the present FE solution method, the first two nondimensional natural frequencies, λ 2 , of a defective clamped-clamped beam with a through-the-width delamination occurring symmetrically about the midsection (L 1 � L 4 ) on the midplane (H 2 � H 3 ) for various delamination lengths are compared with the analytical results reported by Wang et al [4], as well as the DSM [18] and FEM data [19] by Erdelyi and Hashemi, where…”

“…Later, they developed an analytical model using coupled linear layerwise laminate theory and a FE model to investigate both static and dynamic response of flexible defective composite beams, including delaminations and active piezoelectric sensors [15]. Della and Shu [16,17] reported an analytical solution method, and more recently, Erdelyi and Hashemi used Dynamic Stiffness Matrix (DSM) [18] and presented a FEM-based novel assembly technique [19] to investigate the behaviour of a delaminated slender beam and compared their results with those reported by Wang et al [4] and Lee [20]. In a recent work, Szekrényes [21] performed stability analysis on delaminated composite beams undergoing coupled flexurallongitudinal vibration.…”

“…In two recent publications, the authors exploited the classical [24] and frequency-dependent (dynamic) FEM [25] formulations for the free vibration of intact prestressed beams. e free vibration/buckling of intact and delaminated axially-loaded beams has also been investigated before (e.g., [17][18][19][20][21][22][23]). However, to the authors' best knowledge, the vibration of prestressed delaminated beams, subjected to combined axial load and end moment, has not been reported in the open literature.…”

Linear and Nonlinear Dynamic Analyses of Sandwich Panels with Face Sheet-to-Core Debonding

“…Some recent advanced studies point at the need to use models accounting for coupling between normal and flexural actions in vibrations [34]. As found, it is a reason of parametrically induced vibration of delaminated beams and plates [35][36][37]. Other studies confirmed the efficiency of the LW-based finite element models compared to those using the ESL approach [38,39] and showed that such models provide a stress recovery for localized effects [40].…”

A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

“…For a plate with 3 sides simply supported and one side free (SS-SS-SS-F) boundary condition, modeled using a single DFE, the determinant matrix is plotted in Figure 3. The determinant function also produces undefined regions, known as poles [41], where the determinant value approaches infinity. These regions represent the denominator of the determinant function [12].…”