Low-frequency tunable topological interface states in soft phononic crystal cylinders

Abstract

Topological phononic crystals have attracted intensive attention due to their peculiar topologically protected interface or edge states. Their operating frequency, however, is generally fixed once designed and fabricated. Here, we propose to overcome this limitation by utilizing soft topological phononic crystals. In particular, we design a simple one-dimensional periodic system of soft cylindrical waveguides to realize mechanically tunable topological interface states for longitudinal waves. To this end, we employ the nonlinear elasticity theory and its linearized incremental version to fully account for both geometric and material nonlinearities of the system. We derive the dispersion relation for small-amplitude longitudinal motions superimposed on the finitely deformed state. In addition, our analytical results provide information about the corresponding Bloch wave modes, displacement field distributions, and signal transmission coefficients for finite cylindrical waveguides with identical or various unit-cell topologies. Our numerical results illustrate the low-frequency topological interface state occurring at the interface between two topologically distinct soft phononic cylinders. Moreover, we show that the corresponding frequency in the overlapped band gap can be continuously adjusted by an external force. This analytical result is also validated by the finite element simulations. Finally, we provide the topological phase diagrams to demonstrate the tunable position and existence condition of the topological interface states when tuning the external loading. The low-frequency tunable topological interface states with remarkable field enhancement may find a wide range of potential applications such as tunable energy harvesters, low-pass filters and high-sensitivity detectors for biomedical applications.

Wave Manipulation in Intelligent Metamaterials: Recent Progress and Prospects

“…Various implementation schemes have been proposed, including reconfigurable topological MMs and mechanically tunable topological MMs. [246][247][248][249][250][251][252] However, the majority of these topological MMs are composed of passive materials, often constrained within narrow operating frequency ranges and exhibiting clumsy responses to evolving requirements. [253] Additionally, mechanically tunable topological MMs utilize a relatively conventional method of mechanical loading that lacks smart and sophisticated manipulation.…”

“…Another advantage of soft intelligent topological MMs lies in their low working frequency because of the low stiffness of soft materials. [250,252,270,271] Based on the quantum valley Hall effect, Zhou et al [84] designed a soft membrane-type topological MM composite constructed by combining two MM elements different topological properties. Each MM element is formed by spraying metallic particles on the soft DE membrane.…”

Recent advances in topological elastic metamaterials

“…Considering the simplicity and universality of the SSH model, this 1D topological system has been implemented in various elastic wave platforms [62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81]. For instance, Huang et al [77] realized the elastic analogue of the SSH chain in a 1D shear horizontal (SH) guided wave system, which consists of two semi-infinite solid phononic crystal (PC) plates with different Zak phases, connected to each other to form the topological interface modes at the zone-center band gap, or at the zone-boundary band gap, or both.…”

Elastic wave harvesting in piezoelectric-defect-introduced phononic crystal microplates

“…The phononic crystal (PnC) defect results in a high degree of elastic wave localization and provides an efficient way of energy collection in piezoelectric energy harvesting (PEH) devices, which has attracted much attention [1][2][3][4][5][6]. Bandgap is an extraordinary property of PnCs, and elastic waves in the bandgap frequency range decay rapidly and cannot propagate through the PnCs [7][8][9][10][11]. Furthermore, by changing a single unit cell structure to destroy the periodicity of the PnCs (i.e., a defect), flat passbands (i.e., defect bands) usually appear in the bandgap [12][13][14].…”