Ondas elásticas em cristais fonônicos aplicadas à engenharia civil

Abstract

This work investigates the propagation of elastic waves in phononic crystals applied to civil engineering, focusing on periodic soil-pile barriers aimed at mitigating vibrations, such as low-frequency vibrations from natural and anthropogenic sources, which can compromise the comfort, functionality, and integrity of sensitive buildings and equipment. In this context, phononic crystals have emerged as a promising passive solution, since they are capable of forming band gaps, defined as frequency ranges in which wave propagation is suppressed due to periodic scattering mechanisms and mechanical impedance contrast. The aim of this study is to evaluate the potential of phononic barriers composed of piles periodically embedded in soil to attenuate low-frequency elastic waves relevant to civil engineering applications (1-100 Hz). To this end, a parametric analysis is carried out considering different lattice geometries (square and triangular) and filling fractions, taking into account mechanical properties (Young’s modulus, Poisson’s ratio, and density) of materials widely used in civil construction, such as concrete, steel, and rubber. The methodology employs numerical simulations based on the Finite Element Method with Bloch–Floquet periodic conditions applied to a bidimensional unit cell, adopting the ω(k) strategy, in which the wave vector k is swept throughout the reciprocal domain and the corresponding frequencies ω are obtained via modal analysis. The model is implemented in COMSOL Multiphysics through an eigenfrequency study, enabling the construction of dispersion diagrams and the identification of band gaps. The results demonstrate that soil–pile barriers can generate complete band gaps within frequency ranges of civil engineering interest, especially when materials with different stiffnesses are combined with high filling fractions. It is also verified that triangular lattices tend to produce wider band gaps than square lattices under equivalent conditions, and that the use of more compliant external layers favors the formation of band gaps at lower frequencies. It is concluded that pile-based phononic crystals represent a viable and promising alternative for passive vibration control in civil engineering, offering potential for applications in foundations, seismic protection, urban vibration control, and structural comfort.