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In the classic realm of impact mitigation, targeting different impact scenarios with a universally designed device still remains an unassailable challenge. In this study, we delve into the untapped potential of Resch-patterned origami for impact mitigation, specifically considering the adaptively reconfigurable nature of the Resch origami structure. Our unit-cell-level analyses reveal two distinctive modes of deformation, each characterized by contrasting mechanical responses: the folding mode that displays monostability coupled with strain-hardening, and the unfolding mode that manifests bistability, facilitating energy absorption through snap-through dynamics. Drop tests further unveil a novel dynamic bifurcation phenomenon, where the origami switches between folding and unfolding depending on impact speed, thereby showcasing its innate self-reconfigurability in a wide range of dynamic events. The tessellated meter-scale Resch structure mimicking an automotive bumper inherits this dynamically bifurcating behavior, demonstrating the instantaneous morphing into favorable deformation mode to minimize the peak acceleration upon impact. This suggests a self-adaptive and universally applicable impact-absorbing nature of the Resch-patterned origami system. We believe that our findings pave the way for developing smart, origami-inspired impact mitigation devices capable of real-time response and adaptation to external stimuli, offering insights into designing universally protective structures with enhanced performance in response to various impact scenarios.

In this study, we present a method for generating a synthetic gauge field in origami metamaterials with continuously varying geometrical parameters. By modulating the mass term in the Dirac equation linearly, we create a synthetic gauge field in the vertical direction, which allows for the quantization of Landau levels through the generated pseudomagnetic field. Furthermore, we demonstrate the existence and robustness of the chiral zeroth Landau level. The unique elastic snake state is realized using the coupling between the zeroth and the first Landau levels. Our results, supported by theory and simulations, establish a feasible framework for generating pseudomagnetic fields in origami metamaterials with potential applications in waveguides and cloaking., Comment: 6 pages, 4 figures

Despite the extensive studies of topological systems, the experimental characterizations of strongly nonlinear topological phases have been lagging. To address this shortcoming, we design and build elliptically geared isostatic metamaterials. Their nonlinear topological transitions can be realized by collective soliton motions, which stem from the transition of nonlinear Berry phase. Endowed by the intrinsic nonlinear topological mechanics, surface polar elasticity and dislocation-bound zero modes can be created or annihilated as the topological polarization reverses orientation. Our approach integrates topological physics with strongly nonlinear mechanics and promises multi-phase structures at the micro and macro scales., Comment: 5+19 pages, 4+20 figures

Origami structures often serve as the building block of mechanical systems due to their rich static and dynamic behaviors. Experimental observation and theoretical modeling of origami dynamics have been reported extensively, whereas the data-driven modeling of origami dynamics is still challenging due to the intrinsic nonlinearity of the system. In this study, we show how the dynamic mode decomposition (DMD) method can be enhanced by integrating geometry information of the origami structure to model origami dynamics in an efficient and accurate manner. In particular, an improved version of DMD with control, that we term geometry-informed dynamic mode decomposition~(giDMD), is developed and evaluated on the origami chain and dual Kresling origami structure to reveal the efficacy and interpretability. We show that giDMD can accurately predict the dynamics of an origami chain across frequencies, where the topological boundary state can be identified by the characteristics of giDMD. Moreover, the periodic intrawell motion can be accurately predicted in the dual origami structure. The type of dynamics in the dual origami structure can also be identified. The model learned by the giDMD also reveals the influential geometrical parameters in the origami dynamics, indicating the interpretability of this method. The accurate prediction of chaotic dynamics remains a challenge for the method. Nevertheless, we expect that the proposed giDMD approach will be helpful towards the prediction and identification of dynamics in complex origami structures, while paving the way to the application to a wider variety of lightweight and deployable structures., Comment: 11 pages, 7 figures

In this study, we experimentally and numerically investigate the evolution of the tensile material properties of Discontinuous Fiber Composites (DFCs) with an increasing average number of platelets through the thickness for two different platelet widths. The results show that both the number of platelets and the platelet width have significant effects on the tensile modulus and strength. We find that not only the average mechanical properties but also their coefficients of variation change according to the different DFC mesostructures. To understand the relationship between material morphology at the mesoscale and corresponding material properties, we developed a random platelet mesostructure generation algorithm combined with explicit finite element models. Leveraging the computational tools, we find that moduli and strength increase with increasing average number of platelets through the thickness. The increasing trend continues until reaching an asymptotic limit at about 45 layers through the thickness for the narrow platelets and 27 layers for the square platelets. In the study, we address the importance of having accurate simulations of the mesostructure to match not only the average modulus and strength but also their associated coefficients of variation. We show that it is possible to accurately predict the tensile material properties of DFCs, including their B-basis design values. This is a quintessential condition for the adoption of DFCs in structural applications.

We investigate the effect of disorder on topologically nontrivial states in a two dimension (2D) mechanical system. We first propose a quantum spin Hall (QSH) insulator based on an out-of-plane spring-mass model and analytically study the interplay between the disorder and topology in both topologically trivial and nontrivial systems. We adopt the spin Bott index to characterize the topological property in disordered mechanical systems. By tracking the evolution of the spin Bott index with the increase of disorders, we quantitatively demonstrate the disorder induced transition from a topologically nontrivial QSH insulator to a trivial insulator. We then validate the topological phase transition through transient analysis in discrete lattices. Finally, we design a phononic crystal based on the discrete spring-mass model and numerically verify the topologically protected states along the boundary between the trivial insulator and disordered topological QSH insulator in a continuous system. This work puts a step forward in understanding the role of disorder in a 2D topological classical system.

Elastic topological states have been receiving increased intention in numerous scientific and engineering fields due to their defect-immune nature, resulting in applications of vibration control and information processing. Here, we present the data-driven discovery of elastic topological states using dynamic mode decomposition (DMD). The DMD spectrum and DMD modes are retrieved from the propagation of the relevant states along the topological boundary, where their nature is learned by DMD. Applications such as classification and prediction can be achieved by the underlying characteristics from DMD. We demonstrate the classification between topological and traditional metamaterials using DMD modes. Moreover, the model enabled by the DMD modes realizes the prediction of topological state propagation along the given interface. Our approach to characterizing topological states using DMD can pave the way towards data-driven discovery of topological phenomena in material physics and more broadly lattice systems., Comment: 32 pages, 10 figures

We propose an efficient method to build a simple discrete element model (DEM) that accurately simulates the oscillation of a continuum beam. The DEM is based on the Timoshenko beam theory of slender cylindrical members and their corresponding wave dynamics in assembly. This physics-informed DEM accounts for multiple vibration modes of the constituting beam elements in wide frequency ranges. We construct various DEMs mimicking cylinder chains and compare their wave dynamics with those measured in experiments to validate the proposed method. Furthermore, we construct a graded woodpile chain of slender cylinders. We experimentally and numerically investigate the frequency bandgaps of the system and demonstrate the possibility of constructing a wide bandgap by consecutively superposing multiple stop bands generated from cylinders of various lengths. This system is highly efficient in blocking propagating waves by leveraging the vibration isolation effect stemming from the local resonance of the cylinders. The proposed DEM method can be useful for investigating and designing complex vibration systems in an efficient and accurate manner. Moreover, the design approach of manipulating the frequency bandgap can be exploited for developing vibration filters and impact mitigation devices., Comment: 42 pages, 11 figures

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

In this work we present an analytical and numerical study of rogue and solitary waves in a coupled one-dimensional nonlinear lattice that involves both axial and rotational degrees of freedom. Using a multiple-scale analysis we derive a system of coupled nonlinear Schr\"odinger type equations in order to approximate solitary waves and rogue waves of the coupled lattice model. Numerical simulations are found to agree with the analytical approximations. We also consider generic initialization data in the form of a Gaussian profile and observe that they can result in the spontaneous formation of rogue wave-like patterns in the lattice. The solitary and rogue waves in the lattice demonstrate both energy isolation and exchange between the axial and rotational degrees of freedom of the system. This suggests that the studied coupled lattice has the potential to be an efficient energy isolation, transfer, and focusing medium., Comment: 11 pages, 6 figures

Origami-based mechanical metamaterials have recently received significant scientific interest due to their versatile and reconfigurable architectures. However, it is often challenging to account for all possible geometrical configurations of the origami assembly when each origami cell can take multiple phases. Here, we investigate the reconfigurability of a tessellation of origami-based cellular structures composed of bellows-like unit cells, specifically Tachi-Miura Polyhedron (TMP). One of the unique features of the TMP is that a single cell can take four different phases in a rigid foldable manner. Therefore, the TMP tessellation can achieve various shapes out of one originally given assembly. To assess the geometrical validity of the astronomical number of origami phase combinations, we build a graph-theoretical framework to describe the connectivity of unit cells and to analyze the reconfigurability of the tessellations. Our approach can pave the way to develop a systematic computational tool to design origami-based mechanical metamaterials with tailored properties., Comment: 20 pages and 8 figures

We numerically investigate the topological phase transition induced purely by disorder in a spring-mass chain. We employ two types of disorders - chiral and random types - to explore the interplay between topology and disorder. By tracking the evolution of real space topological invariants, we obtain the topological phase diagrams and demonstrate the bilateral capacity of disorder to drive topological transitions, from topologically nontrivial to trivial and vice versa. The corresponding transition is accompanied by the realization of a mechanical Topological Anderson Insulator. The findings from this study hint that the combination of disorder and topology can serve as an efficient control knob to manipulate the transfer of mechanical energy.

Elastic valley metamaterials offer an excellent platform to manipulate elastic waves and have potential applications in energy harvesting and elastography. Here we introduce a series of strategies to realize topological transition in spiral elastic valley metamaterials by parameter modulations. We show the evolution of Berry curvature and valley Chern number as a function of inherent parameters of spiral, which further results in a general scheme to achieve topological valley edge states. Our strategy leverages multiple degrees of freedom in spiral elastic valley metamaterials to provide enhanced opportunities for desired topological states.

The leaf-like origami structure was inspired by geometric patterns found in nature, exhibiting unique transitions between open and closed shapes. With a bistable energy landscape, leaf-like origami is able to replicate the autonomous grasping of objects observed in biological systems like the Venus flytrap. We show uniform grasping motions of the leaf-like origami, as well as various non-uniform grasping motions which arise from its multi-transformable nature. Grasping motions can be triggered with high tunability due to the structure's bistable energy landscape. We demonstrate the self-adaptive grasping motion by dropping a target object onto our paper prototype, which does not require an external power source to retain the capture of the object. We also explore the non-uniform grasping motions of the leaf-like structure by selectively controlling the creases, which reveals various unique grasping configurations that can be exploited for versatile, autonomous, and self-adaptive robotic operations.

Coral reef ecosystems support significant biological activities and harbor huge diversity, but they are facing a severe crisis driven by anthropogenic activities and climate change. An important behavioral trait of the coral holobiont is coral motion, which may play an essential role in feeding, competition, reproduction, and thus survival and fitness. Therefore, characterizing coral behavior through motion analysis will aid our understanding of basic biological and physical coral functions. However, tissue motion in the stony scleractinian corals that contribute most to coral reef construction are subtle and may be imperceptible to both the human eye and commonly used imaging techniques. Here we propose and apply a systematic approach to quantify and visualize subtle coral motion across a series of light and dark cycles in the scleractinian coral Montipora capricornis. We use digital image correlation and optical flow techniques to quantify and characterize minute coral motions under different light conditions. In addition, as a visualization tool, motion magnification algorithm magnifies coral motions in different frequencies, which explicitly displays the distinctive dynamic modes of coral movement. We quantified and compared the displacement, strain, optical flow, and mode shape of coral motion under different light conditions. Our approach provides an unprecedented insight into micro-scale coral movement and behavior through macro-scale digital imaging, thus offering a useful empirical toolset for the coral research community.

We examine the role of strong nonlinearity on the topologically-robust edge state in a one-dimensional system. We consider a chain inspired from the Su-Schrieffer-Heeger model, but with a finite-frequency edge state and the dynamics governed by second-order differential equations. We introduce a cubic onsite-nonlinearity and study this nonlinear effect on the edge state's frequency and linear stability. Nonlinear continuation reveals that the edge state loses its typical shape enforced by the chiral symmetry and becomes generally unstable due to various types of instabilities that we analyze using a combination of spectral stability and Krein signature analysis. This results in an initially-excited nonlinear-edge state shedding its energy into the bulk over a long time. However, the stability trends differ both qualitatively and quantitatively when softening and stiffening types of nonlinearity are considered. In the latter, we find a frequency regime where nonlinear edge states can be linearly stable. This enables high-amplitude edge states to remain spatially localized without shedding their energy, a feature that we have confirmed via long-time dynamical simulations. Finally, we examine the robustness of frequency and stability of nonlinear edge states against disorder, and find that those are more robust under a chiral disorder compared to a non-chiral disorder. Moreover, the frequency-regime where high-amplitude edge states were found to be linearly stable remains intact in the presence of small amount of disorder of both types., Comment: 13 pages, 8 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

Automated Fiber Placement (AFP) technology provides a great ability to efficiently produce large carbon fiber reinforced composite structures with complex surfaces. AFP has a wide range of tow placement angles, and the users can design layup angles so that they can tailor the performance of the structure. However, despite the design freedom, the industry generally adopts a layering of 0 deg, 90 deg, and plus-minus 45 deg ply-drop angles. Here, we demonstrate the optimization of ply-drop angles of non-conventional composites. Specifically, we use classical laminate theory and Bayesian optimization to achieve better layup angles in terms of stiffness, Tsai-Wu failure criteria, and manufacturing time. Our approach shows its effectiveness in designing carbon fiber composite structures using unconventional angles in terms of both mechanical properties and production efficiency. Our method has the potential to be used for more complex scenarios, such as the production of curved surfaces and the utilization of finite element analysis.

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.

Advances in machine learning have revolutionized capabilities in applications ranging from natural language processing to marketing to health care. Here, we demonstrate the efficacy of machine learning in predicting chaotic behavior in complex nonlinear mechanical systems. Specifically, we use quasi-recurrent neural networks to predict extremely chaotic time series data obtained from multistable origami systems. Additionally, while machine learning is often viewed as a "black box", in this study we conduct hidden layer analysis to understand how the neural network can process not only periodic, but also chaotic data in an accurate manner. Also, our approach shows its effectiveness in characterizing and predicting chaotic dynamics in a noisy environment of vibrations without relying on a mathematical model of origami systems. Therefore, our method is fully data-driven and has the potential to be used for complex scenarios, such as the nonlinear dynamics of thin-walled structures and biological membrane systems.

The study of Weyl points in electronic systems has inspired many recent researches in classical systems such as photonic and acoustic lattices. Here we show how the Weyl physics can also inspire the design of novel elastic structures. We construct a single-phase 3D structure, an analogue of the AA-stacked honeycomb lattice, and predict the existence of Weyl points with opposite topological charges (${\pm 1}$), elastic Fermi arcs, and the associated gapless topologically protected surface states. We employ full-scale numerical simulations on the elastic 3D structure, and present a clear visualization of topological surface states that are directional and robust. Such designed lattices can pave the way for novel vibration control and energy harvesting on structures that are ubiquitous in many engineering applications.

We present a gradient-index crystal that offers extreme tunability in terms of manipulating the propagation of elastic waves. For small-amplitude excitations, we achieve control over wave transmission depth into the crystal. We numerically and experimentally demonstrate a boomerang-like motion of wave packet injected into the crystal. For large-amplitude excitations on the same crystal, we invoke nonlinear effects. We numerically and experimentally demonstrate asymmetric wave transmission from two opposite ends of the crystal. Such tunable systems can thus inspire a novel class of designed materials to control linear and nonlinear elastic wave propagation in multi-scales., Comment: 9 pages with Supporting Information, 7 figures

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.

Valley, as a new degree of freedom, raises the valleytronics in fundamental and applied science. The elastic analogs of valley states have been proposed by mimicking the symmetrical structure of either two-dimensional materials or photonic valley crystals. However, the asymmetrical valley construction remains unfulfilled. Here, we present the valley anisotropy by introducing asymmetrical design into elastic metamaterials. The elastic valley metamaterials are composed of bio-inspired hard spirals and soft materials. The anisotropic topological nature of valley is verified by asymmetrical distribution of the Berry curvature. We show the high tunability of the Berry curvature both in magnitude and sign enabled by our anisotropic valley metamaterials. Finally, we demonstrate the creation of valley topological insulators and show topologically protected propagation of transverse elastic waves relying on operating frequency. The proposed topological properties of elastic valley metamaterials pave the way to better understanding the valley topology and to creating a new type of topological insulators enabled by an additional valley degree of freedom., Comment: 22 pages, 7 figures

In this study, we investigate experimentally and numerically the mode I intra-laminar fracture and size effect of Discontinuous Fiber Composites (DFCs) as a function of the structure thicknesses. By testing geometrically-scaled Single Edge Notch Tension (SENT) specimens a notable structure size effect on the nominal strength of DFCs is identified. As the specimen size increases, the nominal strength decreases. For small specimens, we find a limited size effect with enhanced pseudo-ductility and a strong divergence from Linear Elastic Fracture Mechanics (LEFM). For sufficiently large specimen sizes, the scaling of the nominal strength follows closely LEFM with a strong brittle failure. As the thickness increases, the size effect decreases. We identify the fracture energy and the effective size of the fracture process zone as a function of the thickness of the structure. To do so, we integrate equivalent fracture mechanics and stochastic finite element modeling. Experimentally, we collect the nominal strength of geometrically-scaled Single Edge Notch Tension (SENT) specimens. The numerical stochastic model captures the complex, inhomogeneous mesostructure of DFCs by explicitly generating the platelets. From the integrated analysis, it is found that the fracture energy depends significantly on the structure thickness. It is shown to increase gradually up to 2 mm and saturates after 3 mm to a value of 57.77 N/mm, which is 4.81 times larger than a typical aluminum alloy.

This study investigates the mode I intra-laminar fracture and size effect in Discontinuous Fiber Composites (DFCs). Towards this goal, the results of fracture tests on geometrically-scaled Single Edge Notch Tension (SENT) specimens are presented and critically discussed for three platelet sizes. The results clearly show a decrease in nominal strength as the specimen size increases. This effect becomes more important as the structure size increases. It is found that, when the specimen is sufficiently large, the structural strength scales according to Linear Elastic Fracture Mechanics (LEFM) and the failure occurs in a very brittle way. In contrast, small specimens exhibit a more pronounced pseudo-ductility with a limited scaling effect and a significant deviation from LEFM. To characterize the fracture energy and the effective length of the fracture process zone, an approach combining equivalent fracture mechanics and stochastic finite element modeling is proposed. The model accounts for the complex random mesostructure of the material by modeling the platelets explicitly. Thanks to this theoretical framework, the mode I fracture energy of DFCs is estimated for the first time and it is shown to depend significantly on the platelet size. In particular, the fracture energy is shown to increase linearly with the platelet size in the range investigated in this work., Comment: 42 pages, 16 figures

We study the Bloch oscillation of elastic waves in a chain composed of hollow elliptical cylinders (HECs). These HECs are 3D-printed in different wall thicknesses and are arranged to form a graded chain. We find that the frequency band structure of this lattice can be manipulated in a way to create a narrow strip of transmission range sandwiched between slanted stop bands. This enables the trapping of elastic waves at a specific location of the chain, which depends on the input frequency of the propagating elastic waves. This elastic Bloch oscillation in a tailorable 3D-printed system enables the control of energy localization in solids, potentially leading to engineering applications for vibration filtering, energy harvesting, and structural health monitoring., Comment: 18 pages, 8 figures, 2 appendices

We propose a 3D-printed graded lattice made of hollow elliptical cylinders (HECs) as a new way to design impact mitigation systems. We observe asymmetric dynamics in the graded HEC chains with increasing and decreasing stiffness. Specifically, the increasing stiffness chain shows an acceleration of the propagating waves, while the decreasing stiffness chain shows the opposite. From the standpoint of impact mitigation, the decreasing stiffness chain combined with the strain-softening behavior of HECs results in an order-of-magnitude improvement in force attenuation compared to the increasing stiffness chain. We extend this finding to the graded 2D arrays and demonstrate a similar trend of wave transmission efficiency contrast between the increasing and decreasing stiffness lattices. The 3D-printed HEC lattices shown in this study can lead to the development of a new type of impact mitigating and shock absorbing structures., Comment: 22 pages, 11 figures, 4 appendices

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

The principles underlying the art of origami paper folding can be applied to design sophisticated metamaterials with unique mechanical properties. By exploiting the flat crease patterns that determine the dynamic folding and unfolding motion of origami, we are able to design an origami-based metamaterial that can form rarefaction solitary waves. Our analytical, numerical and experimental results demonstrate that this rarefaction solitary wave overtakes initial compressive strain waves, thereby causing the latter part of the structure to feel tension first instead of compression. This counter-intuitive dynamic mechanism can be used to create a highly efficient--yet reusable--impact mitigating system without relying on material damping, plasticity or fracture.

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 present a novel device that can offer two extremes of elastic wave propagation --- nearly complete transmission and strong attenuation under impulse excitation. The mechanism of this highly tunable device relies on intermixing effects of dispersion and nonlinearity. The device consists of identical cylinders arranged in a chain, which interact with each other as per nonlinear Hertz's contact law. For a `dimer' configuration, i.e., two different contact angles alternating in the chain, we analytically, numerically, and experimentally show that impulse excitation can either propagate as a localized wave, or it can travel as a highly dispersive wave. Remarkably, these extremes can be achieved in this periodic arrangement simply by \textit{in-situ} control of contact angles between cylinders. We close the discussion by highlighting the key characteristics of the mechanisms that facilitate strong attenuation of incident impulse. These include low frequency to high frequency (LF-HF) scattering, and turbulence-like cascading in a periodic system. We thus envision that these adaptive, cylinder-based nonlinear phononic crystals, in conjunction with conventional impact mitigation mechanisms, could be used to design highly tunable and efficient impact manipulation devices.

The study of energy transport properties in heterogeneous materials has attracted scientific interest for more than a century, and it continues to offer fundamental and rich questions. One of the unanswered challenges is to extend Anderson theory for uncorrelated and fully disordered lattices in condensed-matter systems to physical settings in which additional effects compete with disorder. Specifically, the effect of strong nonlinearity has been largely unexplored experimentally, partly due to the paucity of testbeds that can combine the effect of disorder and nonlinearity in a controllable manner. Here we present the first systematic experimental study of energy transport and localization properties in simultaneously disordered and nonlinear granular crystals. We demonstrate experimentally that disorder and nonlinearity --- which are known from decades of studies to individually favor energy localization --- can in some sense "cancel each other out", resulting in the destruction of wave localization. We also report that the combined effect of disorder and nonlinearity can enable the manipulation of energy transport speed in granular crystals from subdiffusive to superdiffusive ranges., Comment: main text + supplementary information

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.

In the present work motivated by generalized forms of the Hertzian dynamics associated with granular crystals, we consider the possibility of such models to give rise to both shock and rarefaction waves. Depending on the value $p$ of the nonlinearity exponent, we find that both of these possibilities are realizable. We use a quasi-continuum approximation of a generalized inviscid Burgers model in order to predict the solution profile up to times near the shock formation, as well as to estimate when it will occur. Beyond that time threshold, oscillations associated with the discrete nature of the underlying model emerge that cannot be captured by the quasi-continuum approximation. Our analytical characterization of the above features is complemented by systematic numerical computations.

We investigate wave mixing effects in a phononic crystal that couples the wave dynamics of two channels -- primary and control ones -- via a variable stiffness mechanism. We demonstrate analytically and numerically that the wave transmission in the primary channel can be manipulated by the control channel's signal. We show that the application of control waves allows the selection of a specific mode through the primary channel. We also demonstrate that the mixing of two wave modes is possible whereby a modulation effect is observed. A detailed study of the design parameters is also carried out to optimize the switching capabilities of the proposed system. Finally, we verify that the system can fulfill both switching and amplification functionalities, potentially enabling the realization of an acoustic transistor.

We study scattering of waves by impurities in strongly precompressed granular chains. We explore the linear scattering of plane waves and identify a closed-form expression for the reflection and transmission coefficients for the scattering of the waves from both a single impurity and a double impurity. For single-impurity chains, we show that, within the transmission band of the host granular chain, high-frequency waves are strongly attenuated (such that the transmission coefficient vanishes as the wavenumber $k\rightarrow \pm\pi$), whereas low-frequency waves are well-transmitted through the impurity. For double-impurity chains, we identify a resonance --- enabling full transmission at a particular frequency --- in a manner that is analogous to the Ramsauer--Townsend (RT) resonance from quantum physics. We also demonstrate that one can tune the frequency of the RT resonance to any value in the pass band of the host chain. We corroborate our theoretical predictions both numerically and experimentally, and we directly observe complete transmission for frequencies close to the RT resonance frequency. Finally, we show how this RT resonance can lead to the existence of reflectionless modes even in granular chains (including disordered ones) with multiple double impurities., Comment: 12 pages, 9 figures