Analysis of nonlinear metamaterials and metastructures for mitigation and control of elastic waves

The mechanical and structural engineering community are increasingly resorting to the use of periodic metamaterials and metastructures to mitigate high amplitude vibrations; and nonlinearities are also an active area of research because they potentially provide different methods for controlling elastic waves. While the theory of propagation of linear elastic waves seems to be fairly complete and has led to remarkable discoveries in a variety of disciplines, there is still much to investigate about nonlinear waves, both in terms of their dispersion analytical description and their numerical characterization. This thesis mainly relies on the latter aspect and focuses on the analysis of nonlinear metamaterials and metastructures for both the mitigation and control of elastic waves. In particular, the thesis covers four main topics, each associated with a different nonlinearity: i) dispersion curves and mechanical parameters identification of a weakly nonlinear cubic 1D locally resonant metamaterial; ii) manipulation of surface acoustic waves (SAWs) through a postbuckling-based switching mechanism; iii) seismic vibration mitigation of a multiple-degrees-of-freedom (MDoF) system, the so-called metafoundation, by means of hysteretic nonlinear lattices; iv) seismic vibration mitigation of a periodic coupled system pipeline-pipe rack (PPR), by means of a vibro-impact system (VIS). To identify the dispersion curves of a cubic nonlinear 1D locally resonant metamaterial, a simple experimentally-informed reference subsystem (RS) which embodies the unit cell is employed. The system identification relies on the Floquet--Bloch (FB) periodic conditions applied to the RS. Instead, the parametric identification is carried out with a revised application of the subspace identification (SSI) method involving harmonic, non-persistent excitation. It is remarkable that the proposed methodology, despite the linearization caused by the FB boundary conditions, is responsive to the amplitude of the excitation that affects the dispersion curves. The FB theorem, in fact, is often adopted to reduce the computational burden in calculating the dispersion curves of metamaterials. In contrast, the experimental dispersion reconstruction requires multiple velocity measurements by means of laser Doppler vibrometers (LDVs), as for the case of SAWs. To manipulate SAWs, a proof-of-concept experiment was performed for a postbuckling-based mechanical switching mechanism. Precompressed beams are periodically arranged on one face of an elastic plate to manipulate the dispersion of the SAWs propagating as edge waves. By compressing the columns over their Euler critical load, in fact, it is possible to manipulate the surface wave dispersion: the dispersion curve’s dispersive branches, originally caused by the beams in the undeformed configuration, are cleared, and the original path of the group velocity is restored. This concept is introduced analytically and numerically in this thesis, and a novel device is proposed for controlling the SAWs. With regard to the mitigation of seismic waves, this thesis presents the application of two nonlinear dissipative devices to periodic components and structures of industrial facilities. Firstly, a finite locally resonant metafoundation of an MDoF fuel storage tank is equipped with fully nonlinear hysteretic devices to mitigate absolute accelerations and displacements in the low-frequency regime. Secondly, for mitigating the vibrations in PPRs, spatial periodicity and internal damping are combined to obtain an enhancement in the attenuation rate of the system. At the same time, the seismic performance of the PPR is improved by means of an external nonlinear VIS. These investigations show the characterization of the structures’ responses due to the stochastic nature of the input; and for the case of the VIS, a chaotic behavior is sometimes observed and demonstrated. In conclusion, this thesis investigates the nonlinear response of different periodic structures and their potential for wave control and mitigation in various applications. The results of this research contribute to the understanding of the nonlinear behavior of these periodic structures and provide insights into the design, the optimization, and the identification of metamaterials and metastructures performance.