Damage detection of circular cylindrical shells by Ritz method

Abstract

Shell structures are used extensively in civil, mechanical and aerospace engineering due to their applications in the load support and the energy transfer. External loading, excessive use or corrosion of a shell structure may cause cracks to develop at any stage of its lifetime. These cracks may eventually result in failure, causing loss of human life or other serious consequences. Major studies have been conducted on damage detection of beam and plate structures but few studies have been conducted on shell structures. In the light of current progress in damage detection methodologies described in the available literatures, this study proposes a damage detection technique for circular cylindrical shells based on vibration analysis and wavelet transform. In our study a method for damage detection of thin circular cylindrical shells based on the Ritz method has been developed. Damage in circular cylindrical shells is modelled as the line spring connection along the circumference of the shell in which the stiffness can be varied for simulating different crack severities. By minimising the total potential energy functional of a cylindrical shell, the governing eigenvalue equation and associated stiffness and mass matrices can be derived. The eigenvalue problem is solved to obtain eigenvectors and eigenvalues. The natural frequencies are obtained from eigenvalues and the mode shapes are found from eigenvectors using Ritz functions. Natural frequencies of cylindrical shells with different boundary conditions, crack damage scenarios and length-to-radius ratios are presented. The curvature (second derivative) and wavelet transform of the mode shape are used to detect the crack damage in cylindrical shells. For the verification of the efficiency and accuracy of the algorithm, a convergence study has been conducted and the results are compared with that obtained by other researchers. The validity of the method is confirmed by the close agreement of the results. Different damage scenarios have been modelled on the shell surface with combinations of different boundary conditions to investigate the effect of the crack damage on natural frequencies. The line springs stiffness (Cs) can be varied to simulate different damage scenarios and the derivatives and wavelet transform of the mode shape are used to predict the damage location. The damage location can be identified from the peak of the curvature and wavelet coefficient curve. A recent version of MATLAB has been used for the analyses presented in this study.

Date of Award	2011
Original language	English