arXiv subjects

Weijian Jiao

Publications and source records attributed to Weijian Jiao.

9 recordsLinked to original sources

arXiv2025

Opening and closing a bandgap via alternating softening and hardening nonlinearities

Recent studies have shown some unusual nonlinear dispersion behaviors that are disconnected from the linear regime. However, existing analytical techniques, such as perturbation methods, fail to correctly capture these behaviors. Here we propose a general theoretical approach that converts the nonlinear wave equation to an equivalent linear eigenvalue problem, which directly gives the nonlinear dispersion relation and modal vectors. The theoretical approach is employed to 1D phononic chains and 2D hexagonal lattices with alternating softening and hardening nonlinearities, revealing amplitude-induced bandgap opening and closing phenomena. The theoretical results are validated via full-scale simulations with periodic boundary conditions, in which steady-state nonlinear plane wave responses are numerically obtained. Moreover, we leverage these nonlinear phenomena to achieve tunable frequency splitting and focusing effects. Thus, our work opens new paradigms for understanding nonlinear wave physics and for achieving novel wave control capabilities.

cond-mat.soft↗

arXiv2024

A theoretical framework for physically-realizable kagome metamaterials and its implications on dualities and topological edge modes

Since the discovery of topological modes in idealized ball-and-spring kagome lattices, significant efforts have been devoted to realizing mechanical analogues of these ideal lattices via practical fabrication techniques. While numerical and experimental characterizations of these mechanical analogues have been reported, theoretical modeling that accounts for realistic structural effects (e.g., the bending behavior of thin ligaments-a departure from ideal hinges allowing free rotation) has been lacking. Here we propose a theoretical framework to investigate the dynamic properties of physically-realizable kagome metamaterials consisting of solid triangles and ligaments, in which triangles and ligaments are modeled as rigid bodies and elastic springs, respectively. By applying the framework, validated through finite element analysis, to twisted and deformed kagome metamaterials, we theoretically show the required conditions for achieving certain unique dynamic properties, including dispersion dualities and topological edge modes. The presented study unequivocally reveals the effects of structural components on these properties, which could enable new design strategies for wave propagation manipulation in kagome-based metamaterials.

physics.app-ph↗

arXiv2023

Nucleation of transition waves via collisions of elastic vector solitons

In this work, we show that collisions of one type of nonlinear wave can lead to generation of a different kind of nonlinear wave. Specifically, we demonstrate the formation of topological solitons (or transition waves) via collisions of elastic vector solitons, another type of nonlinear wave, in a multi-stable mechanical system with coupling between translational and rotational degrees of freedom. We experimentally observe the nucleation of a phase transformation arising from colliding waves, and we numerically investigate head-on and overtaking collisions of solitary waves with vectorial properties (i.e., elastic vector solitons). Unlike KdV-type solitons, which maintain their shape despite collisions, our system shows that collisions of two vector solitons can cause nucleation of a new phase via annihilation of the vector soltions, triggering the propagation of transition waves. The propagation of these depends both on the amount of energy carried by the vector solitons and on their respective rotational directions. The observation of the initiation of transition waves with collisions of vector solitons in multistable mechanical systems serves as an example of new fundamental nonlinear wave interactions, and could also prove useful in applications involving reconfigurable structures.

physics.app-ph↗

arXiv2023

Phase transitions in 2D multistable mechanical metamaterials via collisions of soliton-like pulses

In this work, we report observations of phase transitions in 2D multistable mechanical metamaterials that are initiated by collisions of soliton-like pulses in the metamaterial. Analogous to first-order phase transitions in crystalline solids, we experimentally and numerically observe that the multistable metamaterials support phase transitions if the new phase meets or exceeds a critical nucleus size. If this criterion is met, the new phase subsequently propagates in the form of transition waves, converting the rest of the metamaterial to the new phase. More interestingly, we observe that the critical nucleus can be formed via collisions of soliton-like pulses. Moreover, the rich direction-dependent behavior of the nonlinear pulses enables control of the location of nucleation and the spatio-temporal shape of the growing phase.

nlin.PS↗

arXiv2021

Wavenumber-space band clipping in nonlinear periodic structures

In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent correction of the dispersion relation. This phenomenon can manifest either as a frequency shift or as a wavenumber shift depending on whether the excitation is prescribed as a initial condition or as a boundary condition, respectively. Several models have been proposed to capture the frequency shifts observed when the system is subjected to harmonic initial excitations. However, these models are not compatible with harmonic boundary excitations, which represent the conditions encountered in most practical applications. To overcome this limitation, we present a multiple scales framework to analytically capture the wavenumber shift experienced by dispersion relation of nonlinear monatomic chains under harmonic boundary excitations. We demonstrate that the wavenumber shifts result in an unusual dispersion correction effect, which we term wavenumber-space band clipping. We then extend the framework to locally-resonant periodic structures to explore the implications of this phenomenon on bandgap tunability. We show that the tuning capability is available if the cubic nonlinearity is deployed in the internal springs supporting the resonators.

nlin.PS↗

arXiv2021

Tunable bandgaps and symmetry breaking in magneto-mechanical metastructures inspired by multi-layer 2D materials

In this Letter, we introduce a paradigm to realize magneto-mechanical metastructures inspired by multi-layer 2D materials, such as graphene bilayers. The metastructures are intended to capture two aspects of their nanoscale counterparts. One is the multi-layer geometry, which is implemented by stacking hexagonal lattice sheets. The other is the landscape of weak inter-layer forces, which is mimicked by the interactions between pairs of magnets located at corresponding lattice sites on adjacent layers. We illustrate the potential of this paradigm through a three-layer prototype. The two rigid outer lattices serve as control layers, while the thin inner layer is free to experience flexural motion under the confining action of the magnetic forces exchanged with the outer ones, thus behaving as a lattice on elastic foundation. The inner layer is free to rotate relatively to the others, giving rise to a rich spectrum of inter-layer interaction patterns. Our objective is to determine how the dynamical response can be tuned by changing the twist angle between the layers. Specifically, we demonstrate experimentally that switching between different stacking patterns has profound consequences on the phonon landscape, opening and closing bandgaps in different frequency regimes.

cond-mat.mtrl-sci↗

arXiv2020

Dynamics of interacting particle systems: Modeling implications of the repulsive interactions and experiments on magnetic prototypes

In this work, we investigate the dynamics of interacting particle systems subjected to repulsive forces, such as lattices of magnetized particles. To this end, we first develop a general model capable of capturing the complete dynamical behavior of interacting particle systems governed by arbitrary potentials. The model elucidates the important role played by the static repulsive forces exchanged between particles in the initial equilibrium configuration, which is distilled and mathematically captured by a dedicated component of the stiffness matrix. The implications of the model are then examined through the simple illustrative example of a magnetic particle oscillator, by which we show that the effect associated with the initial static forces is germane to two- or higher-dimensional particle systems and vanishes for 1D chains. In the context of wave propagation, we show that this type of effect manifests as modal-selective corrections of the dispersion relation of 2D repulsive lattices. To corroborate these findings, we perform laser vibrometry experiments on a lattice prototype consisting of a triangular grid of magnets supported by an elastic foundation of thin pillars. The tests unequivocally confirm the emergence of distinctive dispersive regimes in quantitative accordance to the model.

physics.app-ph↗

arXiv2020

Nonlinear harmonic generation in two-dimensional lattices of repulsive magnets

In this Letter, we provide experimental evidence of nonlinear wave propagation in a triangular lattice of repulsive magnets supported by an elastic foundation of thin pillars and we interpret all the individual features of the nonlinear wavefield through the lens of a phonon band calculation that precisely accounts for the inter-particle repulsive forces. We confirm the co-existence of two spectrally distinct components (homogeneous and forced) in the wave response that is induced via second harmonic generation (SHG), a well-known effect of quadratic nonlinearity (here embedded in the magnetic interaction). We show that the modal and spatial characteristics of the second harmonic components are complementary to those exhibited by the fundamental harmonic. This endows the lattice with a functionality enrichment capability, whereby additional modes and directivity patterns can be triggered and tuned by merely increasing the amplitude of excitation.

nlin.PS↗

arXiv2019

Doubly-nonlinear waveguides with self-switching functionality selection capabilities

In this article, we investigate the effects of the interplay between quadratic and cubic nonlinearities on the propagation of elastic waves in periodic waveguides. Through this framework, we unveil an array of wave control strategies that are intrinsically available in the response of doubly-nonlinear systems and we infer some basic design principles for tunable elastic metamaterials. The objective is to simultaneously account for two sources of nonlinearity that are responsible for distinct and complementary phenomena and whose effects are therefore typically discussed separately in the literature. Our study explicitly targets the intertwined effects that the two types of nonlinearity exert on each other, which modify the way in which their respective signatures are observed in the dynamic response. Through two illustrative examples we show how the dispersion correction caused by cubic nonlinearity can be used as an internal switch, or mode selector, capable of tuning on/off certain high-frequency response features that are generated through quadratic mechanisms.

nlin.PS↗