Wave propagation in space and time modulated structures

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Trainiti, Giuseppe
Ruzzene, Massimo
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This thesis investigates structures with spatial and temporal modulation of the effective mechanical properties, contributing to the state-of-the-art of wave propagation control techniques and to advancements in metamaterials. The first part of the dissertation investigates the effects of periodic geometric undulations on the dispersion properties of 1D and 2D elastic structures. Periodic undulations result from the spatial modulation of the curvature of beams and plates, which leads to the coupling of transverse and in-plane motion. Such coupling induces complete, modal and partial frequency band gaps, along with directional wave motion. Experimental illustration of the band gap behavior of undulated beams, and numerical simulations of wave motion in plates serve as partial validations of the analytical predictions, and as demonstrations of the potential application of the concept for the design of structural components and elastic waveguides with tailored band gap and directional properties. The analysis is extended to undulated square structural lattices, which are 2D reticulates obtained from the tessellation of the plane with curved beams. Periodic undulated structures, in which the undulation is uniform throughout the structure, as well as graded undulated patterns, in which the undulation gradually is varied within the lattice, inhibit wave motion within specified frequency ranges and in specific directions as a result of the undulation-induced anisotropy. The experimental characterization of wave motion in lattice structures is performed through a high speed digital image correlation technique for highly porous structures. Small displacements of the lattice nodes are tracked by centering image subsets about the lattice intersections. The transient response is recorded in the form of full wavefields, which are processed to characterize the properties of a hexagonal lattice. The described optical technique is then applied to experimentally demonstrate the elastic wave filtering properties of graded undulated lattices, which result from the spatial variation of the curvature parameter. The second part of the thesis focuses on periodic structures with time-varying mechanical properties. Specifically, longitudinal and transverse wave propagation in rods and beams with elastic properties that are periodically varying in space and time is first investigated. Spatio-temporal modulation of the elastic properties breaks mechanical reciprocity and leads to one-way wave propagation, which is signaled by directional band gaps in asymmetric dispersion diagrams. The investigation then considers discrete one-dimensional chains of resonators connected by springs with modulated stiffness. Finally, a broadband-to-narrowband elastic wave filter is presented that relies on time-modulation of the effective stiffness. For broadband waves impinging on the time-modulated domain of the system, narrowband reflected waves are induced due to the time periodic modulation of the effective stiffness. The experimental implementation of the stiffness modulation is achieved by using switchable negative capacitance shunts. This work suggests new avenues for the design of structures with unique wave propagation properties, and it does so by providing both a theoretical framework and experimental validation of the proposed concepts.
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