Free vibration analysis of delaminated composite pretwisted shells

Amit Karmakar (Mechanical Engineering Department, Jadavpur University, Kolkata, India Department of Mechanical and Control Engineering, Tokyo Institute of Technology, Tokyo, Japan)
Haraprasad Roy (Mechanical Engineering Department, Jadavpur University, Kolkata, India)
Kikuo Kishimoto (Department of Mechanical and Control Engineering, Tokyo Institute of Technology, Tokyo, Japan)

Aircraft Engineering and Aerospace Technology

ISSN: 0002-2667

Publication date: 1 December 2005



To 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.


A 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.


The 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/implications

The 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 implications

New 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.


This 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.



Karmakar, A., Roy, H. and Kishimoto, K. (2005), "Free vibration analysis of delaminated composite pretwisted shells", Aircraft Engineering and Aerospace Technology, Vol. 77 No. 6, pp. 486-490.

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