Tuning of subwavelength topological interface states in locally resonant metastructures with shunted piezoelectric patches

Abstract

We investigate the propagation behavior of the low-frequency topological interface state of the flexural wave in the locally resonant metastructure and analyze the tunability of the sub-wavelength interface states by the piezoelectric shunting circuit. One homogeneous thin beam is periodically attached with local resonant beams, which connect shunted piezoelectric actuators. The folding band obtained by merging two primitive unit cells into one new element can generate a Dirac point below the low-frequency locally resonant bandgap. This folding point is opened to develop one new bandgap originated from the Bragg scattering effect by breaking the mirror symmetry. Then, topological transitions are demonstrated during the distance variation between two adjacent resonances. The interface state's existence is further confirmed by using steady and transient analysis of the heterostructure, composed of two media with different topological properties. Finally, we show the relationship between the interface frequency and the capacitance ratio and research the influence of the distance parameter on the topological interface state. Because of the tunability of elastic waves by the piezoelectric shunting circuit, our design has potential for applications such as energy harvesters, filters, and physical switches.

Valley Hall Elastic Edge States in Locally Resonant Metamaterials

“…Some researchers have employed the piezoelectric shunt method [39][40][41][42] to manipulate the frequency range of the valley TPES and further realize reconfigurable TIs. Zhou et al [43] developed a tunable QVHE membrane-type metamaterial.…”

Active control of higher-order topological corner states in a piezoelectric elastic plate

“…The x, y and z directions are denoted as 1, 2 and 3 respectively. Since the piezoelectric sheet is subjected to an electric field along the z-axis only, the intrinsic equation of the piezoelectric material in the plane stress state can be expressed as [47,53,54]…”

“…By using the piezoelectric control technique, Li et al controlled the appearance and disappearance of the double Dirac cone by adjusting negative capacitance circuits connected to piezoelectric sheets, and verified the strong robustness of the topological waveguide in the experiments [47]. Piezoelectric shunt technology was first proposed by Forward, as well as being well developed for active control in the field of sound and vibration [48][49][50][51][52][53][54]. By connecting a negative capacitance circuit to the piezoelectric sheet of the metamaterial plate, it can be regarded as an element of adjustable stiffness.…”

“…By connecting a negative capacitance circuit to the piezoelectric sheet of the metamaterial plate, it can be regarded as an element of adjustable stiffness. The local resonant frequency of the resonator can be controlled by adjusting the negative capacitance circuit [50,54]. Following the study of HOTIs for electromagnetic and acoustic waves, the corner states of elastic wave HOTIs have recently begun to be explored as well.…”

Programmable topological interface states in locally resonant piezoelectric metamaterial beams

“…Energy localization is observed for excitations at the interface mode's frequency. Including local resonators enables topological bandgaps in low frequencies and subwavelength topological interface states [6][7][8][9]. In this framework, present-day progress has shown that topological transitions in 1D systems can be obtained by only adjusting the local resonator properties without additional modifications in the host structure [10].…”