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We realize an elastic second-order topological insulator hosting both one-dimensional gapped edge states and zero-dimensional in-gap corner modes in the double-sided pillared phononic crystal plates with square lattice. Changing the width of two neighbor pillars breaks the inversion symmetry and induces the band inversion to emulate the quantum spin Hall effect where the gapless edge states are obtained. Further breaking the space-symmetry at interface, the gapless edge states are gapped and inducing the edge topological transitions and then giving rise to the zero-dimensional in-gap corner modes. Our work offers a novel way for elastic wave trapping and robustly guiding.

Topological phononic insulators (TPnIs) show promise for application in the manipulation of acoustic waves for the design of low-loss transmission and perfectly integrated communication devices. Since solid phononic crystals exist as a transverse polarization mode and a mixed longitudinal-transverse polarization mode, the realization of topological edge states for both out-of-plane and in-plane bulk elastic waves is desirable to enhance the controllability of the edge waves in solid systems. In this paper, a two-dimensional (2D) solid/solid hexagonal-latticed phononic system that simultaneously supports the topologically protected edge states for out-of-plane and in-plane bulk elastic waves is investigated. Firstly, two pairs of two-fold Dirac cones, respectively corresponding to the out-of-plane and in-plane waves, are obtained at the same frequency by tuning the crystal parameters. Then, a strategy of zone folding is invoked to form double Dirac cones. By shrinking and expanding the steel scatterer, the lattice symmetry is broken, and band inversions induced, giving rise to an intriguing topological phase transition. Finally, the topologically protected edge states for both out-of-plane and in-plane bulk elastic waves, which can be simultaneously located at the frequency range from 1.223 to 1.251 MHz, are numerically observed. Robust pseudospin-dependent elastic edge wave propagation along arbitrary paths is further demonstrated. Our results will significantly broaden its practical application in the engineering field.

In this paper, we realize the topological edge modes of a shear horizontal (SH) guided wave in the one-dimensional (1D) composite structure that exist at the phononic band gaps opened at the center of the Brillouin zone (BZ), or at the zone boundary, or both. Furthermore, we investigate the topological edge modes in periodic acoustic systems result from both Bragg scattering and local resonances. In particular, we find and demonstrate that, in our system where topological and trivial defect states coexist, these results provide a new paradigm for manipulating the existence of the interface states in a set of prescribed band gaps that can have potential applications in the design of novel acoustic devices.

The shear horizontal (SH) guided wave band structures and transmission coefficients in a homogenous plate with periodic tapered surface, whose width is gradually decreases from the lower base to the upper base, are calculated based on the eigen-mode matching theory (EMMT) method. The finite element method (FEM) is also employed to calculate the band structures, which is in good agreement with the results by EMMT method. Numerical results show that the SH guided wave band structures in reduced frequency keep unchanged even if the whole homogenous plate with periodic tapered surface is filled with different materials. We also present the numerical investigations of the geometrical factors' effect on the band structures, including the upper base width, the lower base width, the tapered surface thickness and the plate thickness. These properties of SH guided wave can potentially be utilized to design acoustic sensors, tune band gaps and generate filters.

The Lamb wave band structure of a one-dimensional thin plate with periodic Gaussian surfaces is calculated based on the eigen-mode matching theory (EMMT) method. The finite element method is also employed to calculate the transmission power spectra and the band structure, which are both in good agreement with the results of the EMMT method. In contrast with the straight stubs, the low-frequency band gap of the system with the Gaussian surfaces is wider, when the Gaussian domain's height and area are equal to those of the stub, and the two systems' main plate size and materials are the same. This can be confirmed by the ‘spring–mass' model, which can be used to estimate the resonant frequency. We also investigate the effects of the geometrical parameters on band structure, including the height of the Gaussian domain, the plate thickness and the filling fraction. The results suggest that the band gaps have a close relevance to them.

We investigate the band structures in a homogeneous plate with periodic truncated cones for the square lattice based on finite element method (FEM). The radius of the truncated cone is gradually reduced from the lower base to the upper base. Compared to the classical stubbed phononic plates, a considerable enlargement of the bandwidth by a factor of 2.04 is obtained by varying the semiangle of the truncated cone, while the truncated cone's weight is only 65.19% of that of the cylinder of the stubbed case. Moreover the relative bandwidth is also enlarged by a factor of 1.68. We show that this band gap enlargement is due to the acoustic waves of different wavelengths is localized at the different parts of the truncated cone. These characteristics of elastic or acoustic waves suggest potential applications in aerospace.