SUMMARY

Research in the field of periodic structures and acoustic/elastic metamaterials is dedicated to comprehending and manipulating the propagation of waves in engineered materials characterized by periodic arrangements of unit cells. This organized arrangement governs wave behavior, imparting dispersive characteristics and frequency band structures, thereby inspiring the development of innovative devices and applications with improved functionalities, including wave filtering, acoustic cloaking, energy harvesting, and vibration isolation. Nonlinear periodic structures further advance this research by incorporating geometric or material nonlinearity, resulting in a wide range of amplitude-dependent wave phenomena, such as dispersion shifting, frequency conversion, and non-reciprocal propagations. This dissertation explores these diverse phenomena and interactions in nonlinear periodic structures through a comprehensive approach encompassing analytical, computational, and experimental methods. The research commences with an investigation of the nonreciprocal impulse response in an elastically linked, nonlinear, in-plane rotator unit cell, demonstrating an effective approach for achieving passive targeted energy transfer. Building upon the rotational geometry’s rich dynamics, two types of rotator lattices are designed, showcasing significantly different dispersion characteristics resulting from subtle differences in coupling locations. This leads to amplitude-dependent negative refraction at the interface between these lattices. The dissertation further delves into the morphing of the dispersion relationship through rotational geometry, yielding a stretchable rotator lattice capable of extreme acoustoelastic effects for reconfigurable directivity, refraction steering, on-demand signal time delay, and parametric amplification. Additionally, closed-form perturbation analyses are introduced for two specific cases: nonlinear evanescent waves and nonlinear transmission at the interface of linear-nonlinear periodic structures. The study of nonlinear evanescent waves unveils spatially varying attenuation in the nonlinear evanescent field and predicts an amplitude saturation effect in the presence of softening nonlinearity. The interface study extends the analysis to higher orders, revealing amplitude-dependent self-interaction patterns in the transmitted nonlinear waves, where the fundamental frequency exchanges energy with generated higher harmonics in space. The analytical findings are verified through numerical simulations and/or experimental demonstrations. This dissertation provides valuable insights into nonlinear wave dynamics and periodic structure designs, offering a pathway for next-generation wave-based devices with potential applications in shock isolation, elastic/acoustic imaging, and reconfigurable wave guiding and filtering.