Free vibration analysis of delaminated composite pretwisted shells

Abstract

PurposeTo investigate the effects of delamination on free vibration characteristics of graphite‐epoxy composite pretwisted cylindrical shallow shells of various stacking sequences considering length of delamination as a parameter.Design/methodology/approachA multipoint constraint algorithm which leads to unsymmetric elastic stiffness matrix is incorporated into an eight noded isoparametric plate bending finite element to satisfy the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The study is focused upon long, intermediate and short cylindrical shells as defined by Aas‐Jakobsen's parameters and considers symmetric and unsymmetric composite laminates.FindingsThe non‐dimensional fundamental natural frequencies are obtained for angle ply (45/−45/45, 45/−45) and cross ply (0/90/0, 0/90) configurations corresponding to different crack lengths and twist angles. The study implies the importance of the symmetric laminate as well as the long shell.Research limitations/implicationsThe standard eigenvalue computations using QR iteration algorithm for the present analyses take enormous time and hence, an efficient eigen‐solver needs to be employed.Practical implicationsNew vibration modes are exhibited by the delaminated composite structures. The existence of invisible interlaminar cracking can be identified with the help of prior knowledge of natural frequencies for a delaminated composite pretwisted shell which can be idealized as a turbine blade with low aspect ratio.Originality/valueThis paper presents a numerical approach for natural frequency determination of composite pretwisted shallow shells having delamination without taking care of the effect of dynamic contact between delaminated layers. The non‐dimensional frequencies obtained could serve as reference solutions for future investigators.

Finite element analysis of bending-stiff composite conical shells with multiple delamination

“…The numerical results obtained are compared and validated with the results of [Liew et al 1994;Krawczuk et al 1997;Karmakar et al 2005] as furnished in Table 1, Figure 3, and Table 2, respectively. The comparative study shows excellent agreement with the previously published results and hence demonstrates the capability of the code developed and proves the accuracy of the analyses.…”

“…Three delaminations Present FEM [Karmakar et al 2005] Present FEM [Karmakar et al 2005] Table 2. shells under single, double, triple, and quadruple delaminations with different twist angles, as furnished in Table 3.…”

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“…This equation can be considered as a special case for element 1 and Z 1 equal Figure 3. Influence of the relative position of delamination on the first natural frequency of the composite cantilever beam [Krawczuk et al 1997].…”

A simple frequency-based delamination detection and localization method without baseline model

“…[2] studied the effect of delamination on the natural frequencies of a laminated composite beam, results showed that an increase in delamination length increases the reduction in the natural frequency. [3] presented the effect length of delamination on the free vibration of composite pre-twisted shells with different stacking sequences. A finite element model has been presented by [4] to analyse the natural frequencies of delaminated composite beams.…”