Wave Propagation in Undulated Structures

The work presented in this proposal investigates wave propagation in mechanical metamaterials obtained by periodically modulating the geometry of their structural components. The structures studied herein realize a superior control on wave phenomena, with a specific focus on mitigation, insulation and beaming of mechanical waves.

The objective of this research is to understand the role of geometry modulation in affecting the dispersion properties of simple and architected structures. Specifically, geometry modulation is realized by imposing a spatial variation of the curvature. This variation generates structures that show undulated patterns. The first step of the study is to build a general framework for the description of the behavior of 2D structural components subjected to a spatial variation of the curvature, namely undulated plates. Of interest for this proposal is the analysis of 1D periodic system only, namely undulated beams, obtained as a special case of undulated plates. The main goal of the investigation is to study role of the non-zero measure of local curvature in coupling longitudinal and transverse motion, resulting in band gap formation. The dependence of the band gap location and amplitude is related to the geometrical parameters defining the character of the curvature modulation. The second step of the study is the analysis of wave propagation properties of arrays of undulated beams defining undulated lattice structures. In such 2D structures, band gaps are studies as well as wave directionality. The understanding of the behavior of periodic undulated lattices is employed to explore graded configurations, which are not only able to provide interesting combinations of responses associated to the generating periodic configurations, but also to display unique features. Among others, graded lattice structures realize wave splitting based on mode conversion.

The ability of structural metamaterials to control wave propagation is of particular relevance in scenarios where the energy associated to violent phenomena, such as impacts or blasts, has to be properly contained and managed to ensure structural integrity. Moreover, structural metamaterials find application in vibration insulation due to their broadband filtering capabilities.

Investigation of wave propagation in periodic undulated beams is performed analytically through a plane wave expansion method (PWEM), then validated both numerically and experimentally. The behavior of reticulates of undulated beams, both periodic and graded, is explored numerically by a FE-based implementation of the Bloch theory. Future investigations will concentrate on the extension of the study to 3D undulated lattice structures and the experimental validation of relevant wave phenomena in 2D lattices, mainly focusing on the assessment of their filtering and wave directionality properties. In order to do that, an innovative optical approach for the measurement of in-plane wave propagation through high speed cameras and digital image correlation will be used. Among the future developments, the new optical technique will be improved to tackle a more general set of problems.

Committee: Dr. Massimo Ruzzene (advisor), Dr. Julian J. Rimoli, Dr. Graeme J. Kennedy, Dr. Alper Erturk, Dr. Karim G. Sabra