A numerical study of 1D self-similar waveguides: Relationship between localization, integrated density of state and the distribution of scatterers

The vibrational behaviour of 1D mechanical structures locally loaded with additional masses according to a self-similar pattern is considered. An analysis of the multiple scattering problem is proposed to point out the existence of strongly localized modes. The eigenfrequency distribution is investigated through the vibrational integrated density of state (integrated DOS). The features of this distribution allow one to predict the mode shapes and give an indication of the additional masses number and weight. Finally, the role played by the distribution of the additional masses in the vibrational behaviour of the structure is discussed.