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Topological mechanical metamaterials have been widely explored for their boundary states, which can be robustly isolated or transported in a controlled manner. However, such systems often require pre-configured design or complex active actuation for wave manipulation. Here, we present the possibility of in-situ transfer of topological boundary modes by leveraging the reconfigurability intrinsic in twisted origami lattices. In particular, we employ a dimer Kresling origami system consisting of unit cells with opposite chirality, which couples longitudinal and rotational degrees of freedom in elastic waves. The quasi-static twist imposed on the lattice alters the strain landscape of the lattice, thus significantly affecting the wave dispersion relations and the topology of the underling bands. This in turn facilitates an efficient topological state transfer from one edge to the other. This simple and practical approach of energy transfer in origami-inspired lattices can thus inspire a new class of efficient energy manipulation devices., Comment: 24 pages, 5 figures

We numerically and experimentally study corner states in a continuous elastic plate with em-bedded bolts in a hexagonal pattern. While preserving C6 crystalline symmetry, the system can transition from a topologically trivial to a non-trivial configuration. We create interfacial corners of 60{\deg} and 120{\deg} by adjoining trivial and non-trivial topological configurations. Due to the rich interaction between the bolts and the continuous elastic plate, we find a variety of corner states with and without topological origin. Notably, some of the corner states are highly localized and tunable. By taking advantage of this property, we experimentally demonstrate one-way corner localization in a Z-shaped domain wall., Comment: 6 pages, 5 figures

Spin-1 Weyl point is formed by three bands touching at a single point in the three dimensional (3D) momentum space, with two of which show cone-like dispersion while the third band is flat. Such a triply degenerate point carries higher topological charge $\pm2$2 and can be described by a three-band Hamiltonian. We first propose a tight-binding model of a 3D Lieb lattice with chiral interlayer coupling to form the Spin-1 Weyl point. Then we design a chiral phononic crystal that carries these spin-1 Weyl points and special straight-type acoustic Fermi arcs. We also computationally demonstrate the robust propagation of the topologically protected surface states that can travel around a corner or defect without reflection. Our results pave a new way to manipulate acoustic waves in 3D structures and provide a platform for exploring energy transport properties in 3D spin-1 Weyl systems.

The discovery of topologically non-trivial electronic systems has opened a new age in condensed matter research. From topological insulators to topological superconductors and Weyl semimetals, it is now understood that some of the most remarkable and robust phases in electronic systems (e.g., Quantum Hall or Anomalous Quantum Hall) are the result of topological protection. These powerful ideas have recently begun to be explored also in bosonic systems. Topologically protected acoustic, mechanical, and optical edge states have been demonstrated in a number of systems that recreate the requisite topological conditions. Such states that propagate without backscattering could find important applications in communications and energy technologies. In this work we demonstrate the mechanical analogue of a topologically bound state, a different class of non-propagating protected state that cannot be destroyed by local perturbations. These are well known in electronic systems, such as Majorana bound states in topological superconductors, but remain largely unexplored in a bosonic setting. We implement topological binding by creating a Kekul\'e distortion vortex on a two-dimensional mechanical honeycomb superlattice.

It is recent that the emergence of topological insulators in condensed matter physics has inspired analogous wave phenomena in mechanical systems, mostly in the setting of discrete lattice models. Here we report a numerical and experimental demonstration of topological waveguiding in a continuum plate. We take a ubiquitous design of a bolted elastic plate and show that such a design allows us to invoke the pseudo-spin Hall effect at remarkably low frequencies. We harness the complex interaction of the bolts and the plate to show the existence of a pair of double Dirac cones near the resonant frequency of the bolt. The manipulation of bolted patterns results in the opening of multiple topological bandgaps, including a complete bandgap that forbids all plate modes. We demonstrate that inside this bandgap, the interface between two topologically distinct zones can guide flexural waves crisply around sharp bends., Comment: 9 pages, 5 figures

We report the numerical and experimental study of elastic Wannier-Stark Ladders and Bloch Oscillations in a tunable one-dimensional granular chain consisting of cylindrical particles. The Wannier-Stark Ladders are obtained by tuning the contact angles to introduce a gradient in the contact stiffness along the granular chain. These ladders manifest as resonant modes localized in the space. When excited at the corresponding resonant frequencies, we demonstrate the existence of time-resolved Bloch Oscillations. The direct velocity measurements using Laser Doppler Vibrometry agree well with the numerical simulation results. We also show the possibility of further tailoring these Bloch Oscillations by numerical simulations. Such tunable systems could be useful for applications involving the spatial localization of elastic energy., Comment: Added more references. Updated numerical results

Recently, there have been significant efforts to guide mechanical energy in structures by relying on a novel topological framework popularized by the discovery of topological insulators. Here, we propose a topological metamaterial system based on the design of the Stewart Platform, which can not only guide mechanical waves robustly in a desired path, but also can be tuned in situ to change this wave path at will. Without resorting to any active materials, the current system harnesses bistablilty in its unit cells, such that tuning can be performed simply by a dial-in action. Consequently, a topological transition mechanism inspired by the quantum valley Hall effect can be achieved. We show the possibility of tuning in a variety of topological and traditional waveguides in the same system, and numerically investigate key qualitative and quantitative differences between them. We observe that even though both types of waveguides can lead to significant wave transmission for a certain frequency range, topological waveguides are distinctive as they support robust, back scattering immune, one-way wave propagation.

Inspired by the quantum spin Hall effect shown by topological insulators, we propose a plate structure that can be used to demonstrate the pseudo-spin Hall effect for flexural waves. The system consists of a thin plate with periodically arranged resonators mounted on its top surface. We extend a technique based on the plane wave expansion method to identify a double Dirac cone emerging due to the zone-folding in frequency band structures. This particular design allows us to move the double Dirac cone to a lower frequency than the resonating frequency of local resonators. We then manipulate the pattern of local resonators to open subwavelength Bragg band gaps that are topologically distinct. Building on this method, we verify numerically that a waveguide at an interface between two topologically distinct resonating plate structures can be used for guiding low-frequency, spin-dependent one-way flexural waves along a desired path with bends., Comment: Added more references and Appendix C. A few corrections in the abstract and introduction. The title is more specific now. Figures and equations are better represented

We numerically investigate and experimentally demonstrate an in-situ topological band transition in a highly tunable mechanical system made of cylindrical granular particles. This system allows us to tune its inter-particle stiffness in a controllable way, simply by changing the contact angles between the cylinders. The spatial variation of particles' stiffness results in an in-situ transition of the system's topology. This manifests as the emergence of a boundary mode in the finite system, which we observe experimentally via laser Doppler vibrometry. When two topologically different systems are placed adjacently, we analytically predict and computationally and experimentally demonstrate the existence of a finite-frequency topologically protected mode at their interface.

Origami has recently received significant interest from the scientific community as a building block for constructing metamaterials. However, the primary focus has been placed on their kinematic applications, such as deployable space structures and sandwich core materials, by leveraging the compactness and auxeticity of planar origami platforms. Here, we present volumetric origami cells -- specifically triangulated cylindrical origami (TCO) -- with tunable stability and stiffness, and demonstrate their feasibility as non-volatile mechanical memory storage devices. We show that a pair of origami cells can develop a double-well potential to store bit information without the need of residual forces. What makes this origami-based approach more appealing is the realization of two-bit mechanical memory, in which two pairs of TCO cells are interconnected and one pair acts as a control for the other pair. Using TCO-based truss structures, we present an experimental demonstration of purely mechanical one- and two-bit memory storage mechanisms.