Vibration of composite beams with two overlapping delaminations

Abstract

Delaminations in composite laminates may develop from small cracks due to fabrication and impact loading, or from places of high stress concentration. The locations of the delaminations are not determinate. In this research, an analytical solution for the free vibration of a composite beam with two overlapping delaminations is presented. The delaminated beam is analyzed as seven interconnected beams using the delaminations as their boundaries. The continuity and equilibrium conditions are satisfied between the adjoining regions of the beams. Classical beam theory is applied to each of the beams. Complex vibration behaviors emerge for different sizes and locations of the delaminations. Comparison with analytical results reported in the literature verifies the validity of the present solution.

Dynamics of a generally layered composite beam with single delamination based on the shear deformation theory

“…Della and Shu have presented the analytical solutions to the free vibration of composite beams with two nonoverlapping [7], two overlapping [8,9], and double [10,11] delaminations. Both the free mode and constrained mode models have been used in these papers.…”

“…Thus, shear deformation is also another important aspect in the analysis of such multilayered composite structures. During the past decades, the free vibrations of the delaminated composite beams based on the classical theory have received considerable attentions by many researchers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], but only few publications were devoted to include partially the Poisson's effects and the influences of the couplings, shear deformation, and rotary inertia for beams [16][17][18][19][20][21][22][23][24][25][26][27].…”

Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams

“…Based on the continuity conditions of both delaminated tips, the small-amplitude vibration of the delaminated beam plate with respect to a postbuckled state has been studied. An analytical solution to the free vibrations of a beam with two overlapping delaminations has been presented by Della et al [ 5 , 6 ]. The delaminated beam has been analyzed as seven interconnected Euler-Bernoulli beams.…”

Coupled bending-torsion vibration of a homogeneous beam with a single delamination subjected to axial loads and static end moments

“…Nonlinear interaction, due piecewise linear spring models between the delaminated sub-laminates, were also included. Della et al [14][15][16] used the "free mode" and "constrained mode" assumptions to study beams with several delamination configurations. Liu and Shu [17] conducted free vibration analysis of rotating Timoshenko beams with multiple delaminations.…”

“…The effects of delaminations on the natural frequencies are consequently influenced by the presence of different loadings at the boundary [15]. End moments are commonly exerted on beams by the connections, which are expected to transmit axial force, shear and moment between connecting members [18].…”