Vibration control via periodic structures from micro- to macro-scale

The study of wave propagation along spatially periodic structures is of great interest in solid state physics: one of the most interesting properties of these structures is the formation of bandgaps, i.e. portions of the frequency response for which an incident wave cannot propagate through the structure. This idea is used in several applications in the electromagnetic domain, one example is the optic fiber, and more recently large interest has been devoted to spatially periodic mechanical structures, named phononic crystals. Depending on dimensions and materials of the periodic structure, applications for mechanical meta-materials range from earthquake protection (seismic metamaterials) to noise isolation and thermal properties control. In all these applications, is undeniable that bandgap width is a key factor to boost performances and robustness, wider bandgap means stronger attenuation around gap central frequency. Another important aspect is the dimension of the unit cell of the periodic structure, which should be comparable to the available space in each field of application. In this thesis periodic structures are studied for vibrations and mechanical wave propagation control from micro to macro-scale engineering problems. Focus is given to theoretical (both analytical and numerical) and experimental study of the periodic structure properties, with particular attention to applications, to shorten the distance between the theoretical study of such structures and the actual implementation in practical engineering problems. For this purpose, several studies are conducted: wave propagation control in micro-sensors, mechanical tunable filters and low frequency ultra-wide 3D mechanical filters with reference to ground-borne vibration reduction in civil engineering problems. A brand new shape optimization algorithm implementation based on Bidirectional Evolutionary Structural Optimization is developed, implemented and numerically tested on a micro-sensor application, showing to be faster in the optimization process than other proposals in the literature. Three-dimensional periodic structures endowed with ultra-wide complete bandgaps are designed and experimentally tested, among which there is the most performing one in the literature. The design strategy is described and a brand new simple analytical model is proposed, which is able to predict the 3D dynamical behaviour of these structures with a 1D spring-mass chain. The good points of these structures are the ultra-wide range of isolation in the frequency spectrum and the low dimension of the unit cell, which is dozens lower than the wavelength of the propagating vibration, enabling the practical use of such structures in actual problems. Combination of auxetic properties and frequency isolation is studied, leading to the design of a 3D meta-material with tuning filtering properties, which is numerically, analytically and experimentally studied. The results described in this thesis are collected in several conference papers, 4 international publications and 2 patents.