Detect damages in conical shells using curvature mode shape and wavelet finite element method

The curvature mode shape and natural frequency of a damaged structure will change. Based on this, the damage-induced curvature mode shape and natural frequency changes are taken into account to form a hybrid damage detection approach to detect locations and severities of damages on the surface of conical shell. This approach includes two steps, i.e., the first is to detect damage locations using wavelet transform to decompose a curvature mode shape and the second is to determine damage severities using support vector machine (SVM) to seek from damage severities evaluation database calculated by wavelet-based elements. Of particular interest is the damaged conical shell modeled by wavelet-based elements to gain precise displacement mode shape and natural frequencies. Similar to the construction of wavelet-based thin truncated conical shell element, the wavelet-based thick truncated conical shell element is proposed for the vibration analysis of conical shell. The scaling functions of B-spline wavelet on the interval (BSWI) is employed as the multi-scale interpolating bases. Numerical simulations verify the main advantage of the wavelet-based method is the time savings due to the reduction of degrees of freedom (DOFs). To investigate the robustness and accuracy of the proposed damage detection approach, numerical examples of damaged conical shell are conducted. It is found that the approach is capable of detecting damages on the surface of conical shell. The comparison investigation between the curvature mode shape and displacement mode shape also indicate that the proposed approach performed reasonably well at certain level of noise. ► Wavelet-based vibration analysis method proposed to solve thick conical shell. ► A new damage detection approach using curve mode shape is investigated. ► The performance of the new method and damage detection approach are verified. ► The method can be extended to analyze dynamic response.