Rajesh Chaunsali

Estimating material viscoelastic properties based on surface wave measurements: A comparison of techniques and modeling assumptions

Previous studies of the first author and others have focused on low audible frequency (<1 kHz) shear and surface wave motion in and on a viscoelastic material comprised of or representative of soft biological tissue. A specific case considered has been surface (Rayleigh) wave motion caused by a circular disk located on the surface and oscillating normal to it. Different approaches to identifying the type and coefficients of a viscoelastic model of the material based on these measurements have been proposed. One approach has been to optimize coefficients in an assumed viscoelastic model type to match measurements of the frequency-dependent Rayleigh wave speed. Another approach has been to optimize coefficients in an assumed viscoelastic model type to match the complex-valued frequency response function (FRF) between the excitation location and points at known radial distances from it. In the present article, the relative merits of these approaches are explored theoretically, computationally, and experimentally. It is concluded that matching the complex-valued FRF may provide a better estimate of the viscoelastic model type and parameter values; though, as the studies herein show, there are inherent limitations to identifying viscoelastic properties based on surface wave measurements.

Stress Wave Isolation by Purely Mechanical Topological Phononic Crystals

We present an active, purely mechanical stress wave isolator that consists of short cylindrical particles arranged in a helical architecture. This phononic structure allows us to change inter-particle stiffness dynamically by controlling the contact angles of the cylinders. We use torsional travelling waves to control the contact angles, thereby imposing a desired spatio-temporal stiffness variation to the phononic crystal along the longitudinal direction. Such torsional excitation is a form of parametric pumping in the system, which results in the breakage of the time-reversal symmetry. We report that, in quasi-static sense, the system shows topologically non-trivial band-gaps. However, in a dynamic regime where the pumping effect is significant, these band-gaps become asymmetric with respect to the frequency and wavenumber domains in the dispersion relationship. By using numerical simulations, we show that such asymmetry has a direct correspondence to the topological invariant, i.e., Chern number, of the system. We propose that this asymmetry, accompanied by selective inter-band transition, can be utilized for directional isolation of the stress wave propagating along the phononic crystal.

Extreme control of impulse transmission by cylinder-based nonlinear phononic crystals

Abstract 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 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 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-to-high frequency 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.

Dial-in Topological Metamaterials Based on Bistable Stewart Platform

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.

Elastic Wannier-Stark ladders and Bloch oscillations in 1D granular crystals

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.

Demonstration of accelerating and decelerating nonlinear impulse waves in functionally graded granular chains

We propose a tunable cylinder-based granular system that is functionally graded in its stiffness distribution in space. With no initial compression given to the system, it supports highly nonlinear waves propagating under an impulse excitation. We investigate analytically, numerically and experimentally the ability to accelerate and decelerate the impulse wave without a significant scattering in the space domain. Moreover, the gradient in stiffness results in the scaling of contact forces along the chain. We envision that such tunable systems can be used for manipulating highly nonlinear impulse waves for novel sensing and impact mitigation purposes. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

Experimental demonstration of topological waveguiding in elastic plates with local resonators

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.

Topologically tunable metamaterial based on bi-stable Stewart platform (Conference Presentation)

The discovery of topological insulators in materials science revolutionized the concept of wave propagation by giving rise to the existence of edge modes that are immune to backscattering. Similarly, the tunability in waveguiding – including in-situ frequency modifications and path designation – can be highly useful in manipulating energy flow, which still remains an open challenge. Here we investigate topologically tunable mechanical metamaterials based on the quantum valley hall effect (QVHE) by utilizing the bi-stable Stewart platform (SP). Generally, topologically protected wave propagation can leverage two physical mechanisms: the quantum hall effect (QHE) and the quantum spin hall effect (QSHE). Compared to the QHE and the QSHE, the QVHE exploited in this study maintains the time reversal symmetry and can be achieved by using a relatively simple, passive system with one degree-of-freedom. The tunable system we propose and investigate in this study is made of a two-dimensional hexagon crystal and is composed of SPs at nodes connected by linear springs. Each building block can exhibit one of the two stable states of the SP, so that the C6 inversion symmetry of the lattice is broken while C3 symmetry is reserved. By changing the sequence of the bi-stable state in the SP, we can formulate two kinds of unit cells – marked as A and B – with different topological properties. Berry curvatures as well as corresponding eigenmodes are obtained to demonstrate the topological conversion between the two lattices. Then we conduct super-cell analysis by forming a 1-by-20 array of A and B unit cells. Band structure of the super-cell indicates the existence of edge modes over the while band gap, which appear at the interface of A and B unit cells. Based on this tunable property of bi-stable SP, we can easily form S-type and L-type (60 and 120 degree bents) topological paths in the 40-by-40 lattices without breaking the original geometry parameters. We then conduct the numerical simulations with these topological wave guides to verify the topological protection of the valley hall edge states from backscattering. The tunable system we proposed in this paper may pave a possible way to achieving tunability of topological metamaterials.

Linear and nonlinear dynamics of isospectral granular chains

We study the dynamics of isospectral granular chains that are highly tunable due to the nonlinear Hertz contact law interaction between the granular particles. The system dynamics can thus be tuned easily from being linear to strongly nonlinear by adjusting the initial compression applied to the chain. In particular, we introduce both discrete and continuous spectral transformation schemes to generate a family of granular chains that are isospectral in their linear limit. Inspired by the principle of supersymmetry in quantum systems, we also introduce a methodology to add or remove certain eigenfrequencies, and we demonstrate numerically that the corresponding physical system can be constructed in the setting of one-dimensional granular crystals. In the linear regime, we highlight the commonalities and differences in the elastic wave transmission characteristics of such isospectral systems, and emphasize that the presented mathematical framework allows one to suitably tailor the wave transmission through a general class of granular chains. Moreover, we show how the dynamic response of these structures deviates from its linear limit as we introduce Hertzian nonlinearity in the chain and how nonlinearity breaks the notion of linear isospectrality.