Mechanical waves in simply and multiply connected thin-walled beams

In this work, a semi analytical finite element (SAFE) formulation aimed at predicting the stress waves existing in thin-walled waveguides of arbitrary cross-section is proposed. To this purpose, a SAFE shell element, in which the in-plane and the out-of-plane behaviours are coupled, is developed and used to build the guided wave equation by simply interpolating the cross-section mid line. For thin-walled waveguides, the derived SAFE formulation allows enormous computational time and memory needs saving with respect to schemes based on SAFE volume elements. The formulation has been applied to predict the dispersive waves in a beam with simply and multiply connected square cross-section.