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Intrinsic localized modes (ILMs) are concentrations of vibrational energy in periodic systems/ lattices due to the combined influences of nonlinearity and discreteness. Moreover, ILMs can move within the system and may strongly interact with an impurity, such as a stiffness change, mass variation, etc. Numerous scientific fields have uncovered examples and evidence of ILMs, motivating a multidisciplinary pursuit to rigorously understand the underlying principles. In spite of the diverse technical studies, a characterization of ILM interaction behaviors with multiple impurities in dissipative lattices remains outstanding. The insights on such behaviors may be broadly useful when dynamic measurements are the only accessible features of the periodic system. For instance, one may guide an ILM within the lattice using a deliberately applied and steered impurity and harness the observed interaction behaviors with a second, static (immovable) impurity/defect to identify how the underlying lattice is different at the second, defected site, whether or not one knew the position of the defect a priori. In this spirit, this research studies, analyzes, and characterizes the interaction types amongst an ILM and multiple impurities, and devises a method to identify a static defect impurity using quantitatively and qualitatively distinct interaction phenomena. The method is found to be robust to moderate levels of lattice stiffness heterogeneity and is applicable to monitor various property changes that represent impurities. Finally, experimental studies verify that ILMs interact with multiple impurities in unique ways such that defect features may be effectively identified. [ABSTRACT FROM AUTHOR]

A novel design of origami phononic structures with tunable waveguiding features are studied in this research. The structure is formed by attaching cylindrical inclusions on top of origami sheet; in this kind of architecture, folding of the underlying origami sheet can change the periodicity of inclusions. Being periodic in nature, the origami structure exhibits bandgaps features and have the potential to steer wave energy through a path of defects (also known as waveguide) created in the lattice of inclusions. Since the spectral content transmitted through the waveguide depends on the periodicity surrounding it, the folding induced lattice transformation in such origami structures can lead to adaptation in waveguide frequency. In fact, in origami structures that can transform between different Bravais-lattice types, for example between a square and hexagon lattice, the waveguide frequency can be drastically tuned. Such phenomenal adaptation is studied in this research by extracting dispersion diagrams of defective origami structures using the plane wave expansion method. Further, numerical and experimental investigations are performed on finite origami structures with waveguides and the transmission results of different folding configurations demonstrate that waveguide frequency can be significantly altered. Overall, the low effort one-degree-of-freedom (1DOF) folding mechanism combined with the scalable nature of the origami architecture makes the origami phononic structure a novel and effective device for waveguiding applications across a range of frequencies. [ABSTRACT FROM AUTHOR]