Abstract
A family of wavelet-based rod elements based on higher-order rod approximations is developed for modeling dispersive waves in a rod, including Love, Bishop, two-mode, three-mode and four-mode rod elements. The stiffness matrix, mass matrix and generalized force vector are derived by means of Hamilton's variational principle. In addition, simplified crack models of the higher-order rod theories are proposed to consider the reduction of structural stiffness caused by a crack. Based on Castigliano theorem and fracture mechanics, the flexibility of cracked higher-order rods is first formulated in closed form. Numerical examples are performed to compare the computational accuracy and efficiency of different rod models. It is confirmed that wavelet-based higher-order rod elements can be used for realizing the fast and accurate calculation of dispersion waves, and the proposed crack models can well describe the interaction of guided waves and damage.
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