Asynchronous Modes of Vibration

This work provides a comprehensive discussion about the modal asynchronicity (or localisation) phenomenon applied to structural systems. Departing from a Ziegler’s column with two degrees of freedom (DOF)–which nicely illustrates that even simple systems can display asynchronous modes—admissibility conditions for modal asynchronicity are discussed in a series of linear systems, namely a 3DOF Ziegler’s column, two planar frames, heavy chains with three and many DOF, a continuous model of a simply-supported beam with a cantilever extension and finally a buckled Ziegler’s column. Then, modal asynchronicity is discussed in the non-linear realm: nearly-asynchronous modes in a 3DOF heavy chain and in beams on elastic foundation, one of these with unilateral contact; and exactly-asynchronous modes in a 2DOF heavy chain. To conclude, the technological potentiality of modal asynchronicity for vibration control and energy harvesting is illustrated for a 3DOF heavy chain coupled to a piezoelectric element.