Dynamical behavior of disordered rotationally periodic structures: a homogenization approach

This paper put forth a new approach, based on the mathematical theory of homogenization, to study the vibration localization phenomenon in disordered rotationally periodic structures. In order to illustrate the method, a case-study structure is considered, composed of pendula equipped with hinge angular springs and connected one to each other by linear springs. The structure is mistuned due to mass and/or stiffness imperfections. Simple continuous models describing the dynamical behavior of the structure are derived and validated by comparison with a well-known discrete model. The proposed models provide analytical closed-form expressions for the eigenfrequencies and the eigenmodes, as well as for the resonance peaks of the forced response. These expressions highlight how the features of the dynamics of the mistuned structure, e.g. frequency split and localization phenomenon, depend on the physical parameters involved.