Localization in the Vibration of an Axially Loaded Two-span Weakened Column

This paper is devoted to the dynamic analysis of two connected beam columns with a variation of the bending connection and minor perturbations of the length of each span. The point of reduced bending stiffness represented by a rotational spring may result from a crack. This rotational spring can also be associated with a semi-rigid connection in the field of steel or composite structures, for instance. The dynamics of this axially loaded two-span weakened column appears to exhibit strong localization for small values of stiffness of the rotational spring. The vibration mode shapes indicate a strong confinement of the vibration level to a fraction of the column. A quantitative criterion of localization is established and is correlated to well-known phenomena such as curve veering effect or close eigenvalues. Such a result is quite encouraging as localization is strongly associated with the flexibility values of the rotational spring. When considering the open crack analogy, localization only appears for severely damaged columns. It can then be understood as an indicator of the damage level of the global structure.