A novel straightforward dynamic approach for the evaluation of extensional modes within GBT 'cross-section analysys'

Within the Generalized Beam Theory, the 'cross-section analysis' is a key point to evaluate a suitable basis of modes for the elastic analysis of thin-walled beams. A new dynamic approach is proposed for the evaluation of extensional modes for any possible kind of cross-section (i.e., open, partially closed or closed), using a dual method that perfectly complements and improves the GBT dynamic approach (GBT-D). The method relies on the solution of a very limited number of constrained eigenvalue problems. The emergence of specific hybrid modes for multiply-connected cross-section is pointed out. The proposed approach is much simpler to use than the classic static one, in addition to providing even better results from the point of view of accuracy and symmetry of the displacement fields. An illustrative example shows all the steps of the novel procedure. Several additional examples illustrate the high quality of the results arising from its application.