On Localised Modes in Bio-inspired Hierarchically Organised Oscillatory Chains

This study is concerned with bio-inspired hierarchically organised oscillatory chains from the viewpoint of a localisation phenomenon, when only certain parts of the chain oscillate. The chain consists of block masses attached mutually via tension-extension Hookean springs. The first- and second-order hierarchy are considered to determine their modes and modal frequencies, with the focus on localised modes. Then, a chain with an arbitrary number of masses is dealt with. A theorem is presented that defines the number of its localised modes in terms of the order of hierarchy.