Approximate Mode Shape for Damped Structures

Mode shape is very important in dynamic analysis of the structures. It can be employed to assess dynamic interaction between a structure and its supports to avoid sudden failure. However, unlike undamped structures, exact mode shapes for damped structures are difficult to obtain due to the eigenvectors complexity. In practice, damped structures cannot be shunned and they are available in many engineering applications. Some undamped structures may become damped structures during the operations. Such structures include pipes conveying fluid and because of their roles globally, their dynamic analysis becomes vital to check their integrity to prevent abrupt failures. In this paper, different methods of obtaining approximate mode shapes of composite pipe conveying fluid were investigated. The pipe is modeled using the extended Hamilton’s theory and discretized using wavelet-based finite element method. The pipe complex modal characteristics were obtained by solving the generalized eigenvalue problem and its mode shapes were computed.