Instrument for in situ study of rolling under normal load and torque.

Instabilities that develop at the contact interface of solid rollers or airless tires while in motion can lead to increased energy losses and reduced service life. This manuscript describes an instrument that can give better insight into the origin of such instabilities by monitoring both local and global roller mechanics. This is done by simultaneously obtaining force and displacement data from sensors as well as optical measurements and local deformation fields across two different planes, extracted from images taken by a high-speed camera. Multiple loading configurations are possible, ranging from static normal loading of the roller to free rolling and rolling with a propulsive or a braking torque. Instrument functions, elements, and design are presented in detail and its capabilities are demonstrated by obtaining measurements such as width of the contact interface under normal loading, strain fields of the roller sidewall and contact interface under normal loading, and the roller's resistance to motion for free and forced rolling.

Perturbation analysis of nonlinear evanescent waves in a one-dimensional monatomic chain.

This paper investigates evanescent waves in one-dimensional nonlinear monatomic chains using a first-order Lindstedt-Poincaré approach. Perturbation approaches applied to traveling waves in similar chains have predicted weakly nonlinear phenomena such as dispersion shifts and amplitude-dependent stability. However, nonlinear evanescent waves have received sparse attention, even though they are expected to serve a critical role in nonlinear interface problems. To aid in their analysis, the nonlinear evanescent waves are categorized herein as either complete or transitional evanescent waves. Complete evanescent waves, including linear evanescent waves, attenuate to zero amplitude in the far field. Transitional evanescent waves, only occurring in softening systems, attenuate to a nontrivial amplitude in the far field, regardless of the initial amplitude, resulting in a saturation effect. For both cases, the presented perturbation approach reveals that the imaginary wave number in the evanescent field is a function of space, rather than a constant value as in its linear counterpart. It also reveals that hardening and softening nonlinearity slow and accelerate the near-field decay, respectively. The predictions obtained from the perturbation approach are verified using numerical simulations with both initial-condition and boundary-continuous excitation, documenting strong agreement.

Additive manufacturing of channeled acoustic topological insulators.

We propose and fabricate an acoustic topological insulator to channel sound along statically reconfigurable pathways. The proposed topological insulator exploits additive manufacturing to create unit cells with complex geometry designed to introduce topological behavior while reducing attenuation. We break spatial symmetry in a hexagonal honeycomb lattice structure composed of a unit cell with two rounded cylindrical chambers by altering the volume of each chamber, and thus, observe the quantum valley Hall effect when the Dirac cone at the K-point lifts to form a topologically protected bandgap. Moderately protected edge states arise at the boundary between two regions with opposite orientations. The resulting propagation of a topologically protected wave along the interface is predicted computationally and validated experimentally. This represents a first step towards creating reconfigurable, airborne topological insulators that can lead to promising applications, such as four-dimensional sound projection, acoustic filtering devices, or multiplexing in harsh environments.

Experimental realization of a reconfigurable electroacoustic topological insulator.

A substantial challenge in guiding elastic waves is the presence of reflection and scattering at sharp edges, defects, and disorder. Recently, mechanical topological insulators have sought to overcome this challenge by supporting back-scattering resistant wave transmission. In this paper, we propose and experimentally demonstrate a reconfigurable electroacoustic topological insulator exhibiting an analog to the quantum valley Hall effect (QVHE). Using programmable switches, this phononic structure allows for rapid reconfiguration of domain walls and thus the ability to control back-scattering resistant wave propagation along dynamic interfaces for phonons lying in static and finite-frequency regimes. Accordingly, a graphene-like polyactic acid (PLA) layer serves as the host medium, equipped with periodically arranged and bonded piezoelectric (PZT) patches, resulting in two Dirac cones at the K points. The PZT patches are then connected to negative capacitance external circuits to break inversion symmetry and create nontrivial topologically protected bandgaps. As such, topologically protected interface waves are demonstrated numerically and validated experimentally for different predefined trajectories over a broad frequency range.

Isolated frequencies at which nonlinear materials behave linearly.

In this Rapid Communication, we demonstrate that specific frequencies in weakly nonlinear lattices avoid the generation of higher harmonics, and thus the lattices behave linearly. Using a multiple scales analysis, we present plane-wave solutions that persist at only a single frequency and wave number; i.e., whose spatiotemporal production of higher harmonics is remarkably small. We study monatomic and diatomic chains with quadratic and cubic stiffness nonlinearities as example systems. Direct numerical integration of the equations of motion confirms that finite amplitude plane waves assigned to these special frequencies produce negligible higher harmonics when injected into the lattices. Such findings provide new considerations for the operating frequency of nonlinear communications devices, sensors, and transducers for enhanced signal-to-noise ratios.

Internally resonant wave energy exchange in weakly nonlinear lattices and metamaterials.

This paper presents a multiple-scales analysis approach capable of capturing internally resonant wave interactions in weakly nonlinear lattices and metamaterials. Example systems considered include a diatomic chain and a locally resonant metamaterial-type lattice. At a number of regions in the band structure, both the frequency and wave number of one nonlinear plane wave may relate to another in a near-commensurate manner (such as in a 2:1 or 3:1 ratio) resulting in an internal resonance mechanism. As shown herein, nonlinear interactions in the lattice couple these waves and enable energy exchange. Near such internal resonances, previously derived higher-order dispersion corrections for single plane wave propagation may break down, leading to singularities in the predicted nonlinear dispersion relationships. Using the presented multiple-scales approach and the two example systems, this paper examines internal resonance occurring (i) within the same branch and (ii) between different branches of the band structure, resolving the aforementioned singularity issue while capturing energy exchange. The multiple-scales evolution equations, together with a local stability analysis, uncover multiple stable fixed points associated with periodic energy exchange between internally resonant propagating modes. Response results generated using direct numerical simulation verify the perturbation-based predictions for amplitude-dependent dispersion corrections and slow-scale energy exchange; importantly, these comparisons verify the exchange frequency predicted by the multiple-scales approach.

Reconfigurable topological insulator for elastic waves.

Inspired by the quantum valley Hall effect, a mechanical topological insulator (TI) purposely built for reconfigurability is proposed and experimentally demonstrated. An aluminum plate serves as the host medium with periodically arranged voids and fixed inclusions used to break mirror symmetry. Reconfigurability is derived from the ability to easily alter the imperfection type (void or fixed inclusion) in any unit cell. The corresponding band structure of the proposed hexagonal unit cell is obtained using numerical means, which documents double-folded Dirac cones at the K-points. The breaking of mirror symmetry results in a topologically protected bandgap. Furthermore, topologically protected edge states (TPES) at the interface of two structures with opposite Chern numbers have been demonstrated numerically, and verified experimentally, for different desired trajectories. These TPES are robust against backscattering at defect locations and sharp bends. The proposed reconfigurable TI can be a stepping-stone platform toward building mechanical logic and circuits, which have advantages over electronic equivalents in harsh operating conditions, or to replace wireless systems near dead-zones of metallic and carbon fiber structures.

Experimental Demonstration of an Ultrabroadband Nonlinear Cloak for Flexural Waves.

Broadband cloaking of flexural waves is a major challenge since the governing equation is not form invariant under coordinate transformations. We fabricate a flexural cloaking structure using only a single material composed of homogeneous and isotropic layers, and then present experimental evidence of the first near-ideal broadband cloak in thin plates. The 3D-printed structure is shown to effectively disguise an object over a broad frequency range (2 kHz-11 kHz). The proposed cloak has potential applications in shielding sensors and sensitive components from vibrations in bridges, automobiles, and aircraft.

Broadband Bending of Flexural Waves: Acoustic Shapes and Patterns.

Directing and controlling flexural waves in thin plates along a curved trajectory over a broad frequency range is a significant challenge that has various applications in imaging, cloaking, wave focusing, and wireless power transfer circumventing obstacles. To date, all studies appeared controlling elastic waves in structures using periodic arrays of inclusions where these structures are narrowband either because scattering is efficient over a small frequency range, or the arrangements exploit Bragg scattering bandgaps, which themselves are narrowband. Here, we design and experimentally test a wave-bending structure in a thin plate by smoothly varying the plate's rigidity (and thus its phase velocity). The proposed structures are (i) broadband, since the approach is frequency-independent and does not require bandgaps, and (ii) capable of bending elastic waves along convex trajectories with an arbitrary curvature.

Amplitude-dependent Lamb wave dispersion in nonlinear plates.

The paper presents a perturbation approach for calculating amplitude-dependent Lamb wave dispersion in nonlinear plates. Nonlinear dispersion relationships are derived in closed form using a hyperelastic stress-strain constitutive relationship, the Green-Lagrange strain measure, and the partial wave technique integrated with a Lindstedt-Poincaré perturbation approach. Solvability conditions are derived using an operator formalism with inner product projections applied against solutions to the adjoint problem. When applied to the first- and second-order problems, these solvability conditions lead to amplitude-dependent, nonlinear dispersion corrections for frequency as a function of wavenumber. Numerical simulations verify the predicted dispersion shifts for an example nonlinear plate. The analysis and identification of amplitude-dependent, nonlinear Lamb wave dispersion complements recent research focusing on higher harmonic generation and internally resonant waves, which require precise dispersion relationships for frequency-wavenumber matching.

Acoustic scattering from phononic crystals with complex geometry.

This work introduces a formalism for computing external acoustic scattering from phononic crystals (PCs) with arbitrary exterior shape using a Bloch wave expansion technique coupled with the Helmholtz-Kirchhoff integral (HKI). Similar to a Kirchhoff approximation, a geometrically complex PC's surface is broken into a set of facets in which the scattering from each facet is calculated as if it was a semi-infinite plane interface in the short wavelength limit. When excited by incident radiation, these facets introduce wave modes into the interior of the PC. Incorporation of these modes in the HKI, summed over all facets, then determines the externally scattered acoustic field. In particular, for frequencies in a complete bandgap (the usual operating frequency regime of many PC-based devices and the requisite operating regime of the presented theory), no need exists to solve for internal reflections from oppositely facing edges and, thus, the total scattered field can be computed without the need to consider internal multiple scattering. Several numerical examples are provided to verify the presented approach. Both harmonic and transient results are considered for spherical and bean-shaped PCs, each containing over 100 000 inclusions. This facet formalism is validated by comparison to an existing self-consistent scattering technique.

A three-dimensional Bloch wave expansion to determine external scattering from finite phononic crystals.

External scattering from a finite phononic crystal (PC) is studied using the Helmholtz-Kirchhoff integral theorem integrated with a Bloch wave expansion (BWE). The BWE technique is used to describe the internal pressure field of a semi-infinite or layered PC subject to an incident monochromatic plane wave. Following the BWE solution, the Helmholtz-Kirchhoff integral is used to determine the external scattered field. For cubic PCs, the scattered results are compared to numerical treatments in both the frequency and time domain. The presented approach is expected to be valid when the PC size is larger than the acoustic wavelength. However, very good agreement in the spatial beam pattern is also documented for both large and small (with respect to the wavelength) PCs. The result of this work is a fully-analytical, efficient, and verified approach for accurately predicting external scattering from finite, three-dimensional PCs.

Bloch-wave expansion technique for predicting wave reflection and transmission in two-dimensional phononic crystals.

In this paper acoustic wave reflection and transmission are studied at the interface between a phononic crystal (PC) and a homogeneous medium using a Bloch wave expansion technique. A finite element analysis of the PC yields the requisite dispersion relationships and a complete set of Bloch waves, which in turn are employed to expand the transmitted pressure field. A solution for the reflected and transmitted wave fields is then obtained using continuity conditions at the half-space interface. The method introduces a group velocity criterion for Bloch wave selection, which when not enforced, is shown to yield non-physical results. Following development, the approach is applied to example PCs and results are compared to detailed numerical solutions, yielding very good agreement. The approach is also employed to uncover bands of incidence angles whereby perfect acoustic reflection from the PC occurs, even for frequencies outside of stop bands.

Locomotion of Mexican jumping beans.

The Mexican jumping bean, Laspeyresia saltitans, consists of a hollow seed housing a moth larva. Heating by the sun induces movements by the larva which appear as rolls, jumps and flips by the bean. In this combined experimental, numerical and robotic study, we investigate this unique means of rolling locomotion. Time-lapse videography is used to record bean trajectories across a series of terrain types, including one-dimensional channels and planar surfaces of varying inclination. We find that the shell encumbers the larva's locomotion, decreasing its speed on flat surfaces by threefold. We also observe that the two-dimensional search algorithm of the bean resembles the run-and-tumble search of bacteria. We test this search algorithm using both an agent-based simulation and a wheeled Scribbler robot. The algorithm succeeds in propelling the robot away from regions of high temperature and may have application in biomimetic micro-scale navigation systems.

Reflection of compressional and Rayleigh waves on the edges of an elastic plate with quadratic nonlinearity.

Previous ultrasonic studies have demonstrated that measurements of material nonlinearities can provide a means for detecting early signs of fatigue damage using both compressional (P) and Rayleigh (R) surface waves. However, these experimental studies have typically been limited to the direct wave arrival between the source and receiver in simple geometries where no reflection occurs. In particular, the degree of material nonlinearity is often quantified by the ratio of the cumulative amplitude of the first harmonic to that of the fundamental for the direct arrival only. Hence a practical question arises over the interpretation of ultrasonic measurements of material nonlinearities in the presence of reflected nonlinear waves. Thus, this article investigates the reflection problem of P or R waves at the edge of a homogeneous plate with quadratic nonlinearity using both a theoretical formulation, based on perturbation analysis, and direct numerical simulations using a Cellular Automata formulation. The numerical approach is first validated against an existing theoretical formulation for reflecting nonlinear P waves. It is then used to simulate the nonlinear reflection of R waves at a plate's edge for which no closed-form formulation is presently available.

Computation of acoustic absorption in media composed of packed microtubes exhibiting surface irregularity.

A multi-scale homogenization technique and a finite element-based solution procedure are employed to compute acoustic absorption in smooth and rough packed microtubes. The absorption considered arises from thermo-viscous interactions between the fluid media and the microtube walls. The homogenization technique requires geometric periodicity, which for smooth tubes is invoked using the periodicity of the finite element mesh; for rough microtubes, the periodicity invoked is that associated with the roughness. Analysis of the packed configurations, for the specific microtube radii considered, demonstrates that surface roughness does not appreciably increase the overall absorption, but instead shifts the peaks and values of the absorption curve. Additionally, the effect of the fluid media temperature on acoustic absorption is also explored. The results of the investigation are used to make conclusions about tailored design of acoustically absorbing microtube-based materials.

Acoustic absorption calculation in irreducible porous media: a unified computational approach.

A critical task in predicting and tailoring the acoustic absorption properties of porous media is the calculation of the frequency-dependent effective density and compressibility tensors, which are explicitly related to the micro-scale permeability properties. Although these two quantities exhibit strong sensitivity to physics occurring at complex micro-scale geometries, most of the existing literature focuses on employing very limited in-house and oftentimes multiple numerical analysis tools. In order to predict these parameters and acoustic absorption efficiently and conveniently, this article synthesizes multiple disparate approaches into a single unified formulation suitable for incorporation into a commercial analysis package. Numerical results computed herein for four close-packed porous media are compared to similar results available in the literature. These include simple cubic, body-centered cubic, and face-centered cubic structures, and also hexagonal close-packed, which has not appeared in the literature. Together with critical comparisons of a hybrid versus direct numerical approaches, the close agreement demonstrates the capabilities of the unified formulation to analyze and control the acoustic absorption properties at the microscopic level.