Mode Localization in Quasi Periodic Cyclic Structures

Resumo

In this work, we study the phenomenon of localization of vibration modes in quasi-periodic cyclic
structures with linear behavior. They are composed of nominally identical substructures loosely coupled together,
taking into account possible small imperfections. Such linear systems in the face of the disorder caused by small
imperfections, can lead to the confinement of vibrational energy in certain regions of the structure, a phenomenon
known as Mode Localization. This phenomenon can cause catastrophic failure due to high vibration amplitude and
fatigue. The identification and study of the location effect from a modal perspective, as well as the response of the
structure and its components to dynamic requests is of fundamental importance, as it is a diagnostic tool for
possible preventive mitigation actions or even use of this phenomenon in damping of the system. Through the
implementation of computer simulation via MATLAB® software, based on the Finite Element Method, the
distribution, interference and consequence of vibrational energy on the adopted model are analyzed with reference
to the periodic and ordered or aperiodic and disordered dynamic characteristics. The so-called “real case” considers
the small variations in characteristics (length, stiffness, attack angle), resulting from manufacturing tolerances or
FOD (Foreign Object Debris) impact. This work presents graphically the amplitude of normalized vibration
amplitude resulting from the appearance of the phenomenon of localization of vibration modes in the substructures,
which can be restricted to one or a few of them.