The elastic wave attenuation in artificial composites, known as phononic crystals (PnCs), is an important topic in the context of wave manipulation. However, there is a lack of knowledge in the obtainment of the wave attenuation of PnCs when the viscoelastic effect of different polymers is considered. In this study, the complex band structure of longitudinal waves in 1-D viscoelastic PnC (VPnC) rods composed by steel inclusions (elastic material) in a polymeric matrix (viscoelastic material) is investigated. The viscoelastic effect is modelled by the standard linear solid model (SLSM), which can be used to closely model the behavior of polymers for practical applications. It is also studied the influence of different polymers (i.e., epoxy, nylon, silicon rubber, natural rubber, and low density polyethylene (LDPE)) on the complex band structure of 1-D VPnC rods. The improved plane wave expansion (IPWE) and extended plane wave expansion (EPWE) are used to compute the band structure. It is observed that the viscoelastic effect influences significantly both the propagating and evanescent waves. The viscoelasticity increases the unit cell wave attenuation for most range of frequency considering all polymeric matrices. The highest unit cell wave attenuation is for the polymeric matrix of natural rubber.

Plate structures are widely used in civil engineering, for instance, as slabs, foundations, and retaining walls. In structural acoustics, flexural wave control becomes an important parameter for the safety of engineering thin structures. Metaconcrete is a new type of concrete where conventional aggregates are replaced by resonant aggregates, made of a solid core coated with a compliant material, which presents wave attenuation properties. Hence, the aim of this paper is to evaluate the band structure of flexural waves in a metaconcrete, using the thin plate theory associated with the improved plane wave expansion (IPWE) method. The effect of aggregate geometry, core density, Young's modulus of the coating, and number of layers are analyzed. Complete bandgaps are observed for almost all inclusions. The results reveal the possibility of adjusting the desired frequency range according to the configuration of the resonators for flexural vibration management through metaconcrete thin plates. instance slabs foundations walls acoustics material properties Hence IPWE (IPWE method geometry density Youngs Young s coating analyzed inclusions plates

We study the band structure of elastic waves propagating in a nano-piezoelectric phononic crystal consisting of a polymeric matrix reinforced by BaTiO3 inclusions in square, rectangular, triangular, honeycomb and Kagomé lattices. We also investigate the influence of inclusion cross section geometry - circular, hollow circular, square and rotated square with a 45º angle of rotation with respect to x and y axes. Plane wave expansion method is used to solve the governing equations of motion of a piezoelectric solid based on classical elasticity theory, ignoring nanoscopic size effects, considering two-dimensional periodicity and wave propagation in the xy plane. Complete band gaps between XY and Z modes are observed for all inclusions and the best performance is for circular inclusion in a triangular lattice. Piezoelectricity influences significantly the band gaps for hollow circular inclusion in lower frequencies. We suggest that nano-piezoelectric phononic crystals are feasible for elastic vibration management in GHz.

We investigate theoretically and experimentally the forced response of flexural waves propagating in a 1D phononic crystal (PC) Euler-Bernoulli beam, composed by steel and polyethylene, and its band structure. The finite element, spectral element, wave finite element, wave spectral element, conventional and improved plane wave expansion methods are applied. We demonstrate that the vibration attenuation of the unit cell can be improved choosing correctly the polyethylene and steel quantities and we suggest the best percentages of these materials, considering different unit cell lengths. An experiment with a 1D PC beam is proposed and the numerical results can localize the band gap position and width close to the experimental results. A small Bragg-type band gap with low attenuation is observed between 405 Hz - 720 Hz. The 1D PC beam with unit cells of steel and polyethylene presents potential application for vibration control.