Multifield nested metafilters for wave propagation control

The present work proposes a novel class of multifield nested tunable metadevices that serve as high performance acoustic metafilters. The designed metafilter is characterized by a multiscale, hierarchical structure. At the mesoscale, the metamaterial consists of a sequence of two different periodically alternating layers: a polymeric homogeneous layer, which exhibits a viscoelastic constitutive response, and a microstructured one. The latter is based on the periodic repetition of a multiphase microscale cell that is composed by a stiff elastic external coating, a viscoelastic phase and an internal disk of piezoelectric material shunted by an external electrical circuit having a tunable impedance/admittance This tuning parameter affects the constitutive elastic properties of the piezoelectric phase and, in turn, the overall response of the microscale cell, thereby ultimately enabling to achieve an optimal filtering performance for the metadevice. Due to the periodicity of the multiphase cell at the microscale, a two-scale variational-asymptotic homogenization technique is exploited in the frequency domain in order to obtain the frequency-dependent overall constitutive properties of the microstructured layer. Subsequently, in-plane free wave propagation inside the periodic multilayered metamaterial at the mesoscale is investigated by means of Floquet–Bloch theory, together with the transfer matrix method. By triggering the shunting effect, a stiffening of the piezoelectric phase can be achieved, which is demonstrated to open low frequency band gaps in the metamaterial frequency spectrum. The filtering capability of the metadevice has been assessed as a function of its geometrical features and the tuning parameter, thus paving the way towards the design of sophisticated and topologically optimized acoustic filters.