120 research outputs found
Self-induced topological transition in phononic crystals by nonlinearity management
A new design paradigm of topology has recently emerged to manipulate the flow
of phonons. At its heart lies a topological transition to a nontrivial state
with exotic properties. This framework has been limited to linear lattice
dynamics so far. Here we show a topological transition in a nonlinear regime
and its implication in emerging nonlinear solutions. We employ nonlinearity
management such that the system consists of masses connected with two types of
nonlinear springs, "stiffening" and "softening" types, alternating along the
length. We show, analytically and numerically, that the lattice makes a
topological transition simply by changing the excitation amplitude and invoking
nonlinear dynamics. Consequently, we witness the emergence of a new family of
finite-frequency edge modes, not observed in linear phononic systems. We also
report the existence of kink solitons at the topological transition point.
These correspond to heteroclinic orbits that form a closed curve in the phase
portrait separating the two topologically-distinct regimes. These findings
suggest that nonlinearity can be used as a strategic tuning knob to alter
topological characteristics of phononic crystals. These also provide fresh
perspectives towards understanding a new family of nonlinear solutions in light
of topology.Comment: 14 pages, 8 figure
Observation of edge waves in a two-dimensional Su-Schrieffer-Heeger acoustic network
In this work, we experimentally report the acoustic realization the
two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model in a simple network of
air channels. We analytically study the steady state dynamics of the system
using a set of discrete equations for the acoustic pressure, leading to the 2D
SSH Hamiltonian matrix without using tight binding approximation. By building
an acoustic network operating in audible regime, we experimentally demonstrate
the existence of topological band gap. More supremely, within this band gap we
observe the associated edge waves even though the system is open to free space.
Our results not only experimentally demonstrate topological edge waves in a
zero Berry curvature system but also provide a flexible platform for the study
of topological properties of sound waves
Nonlinear resonances and energy transfer in finite granular chains
In the present work we test experimentally and compute numerically the stability and dynamics of harmonically driven monoatomic granular chains composed of an increasing number of particles N(N=1-50). In particular, we investigate the inherent effects of dissipation and finite size on the evolution of bifurcation instabilities in the statically compressed case. The findings of the study suggest that the nonlinear bifurcation phenomena, which arise due to finite size, can be useful for efficient energy transfer away from the drive frequency in transmitted waves
Wave propagation in granular chains with local resonances
We study wave propagation in a chain of spherical particles containing a local resonator. The resonant particles are made of an aluminum outer spherical shell and a steel inner mass connected by a polymeric plastic structure acting as a spring. We characterize the dynamic response of individual particles and the transmitted linear spectra of a chain of particles in contact. A wide band gap is observed both in theoretical and experimental results. We show the ability to tune the acoustic transmission by varying the contact interaction between particles. Higher driving amplitude leads to the generation of nonlinearities both in the response of a single particle and that of the whole chain. For a single resonant particle, we observe experimentally a resonant frequency downshift, which follows a complex nonlinear behavior. In the chain of particles, nonlinearity leads to the generation of nonlinear harmonics and the presence of localized modes inside the band gap
The Impact of Management Practices on Soil Fertility and Foliar Nutrient Concentrations in a Spruce (Picea abies Link) Forest Ecosystem of Rodopi Mountainous Area, in Northern Greece
After forest harvesting, organic matter accumulation and soil nutrient availability are usually negatively influenced, especially during the first years. The hypothesis that 15 years after selective harvesting (15Y) the increased forest biomass, together with the enhanced nutrient recycling rates, compared to 5-years after harvesting (5Y), could restore nutrient availability and organic C accumulation (both in forest floor and soil) to similar levels to the intact site, was tested. The aim of this study was to investigate the effect of the timing of management practices (intact forest-control, 5Y, 15Y) on organic matter content, nutrient concentrations in needles, forest floor and soil, in a forest ecosystem of Picea abies L., in Rodopi mountainous area, in northern Greece. Significant differences between the intact site and the other two treatments were found in: i) soil N, P, C/N and exchangeable Ca, ii) organic matter and nutrient accumulation (basically in the upper 30 cm), iii) foliar K, Fe and Zn concentrations. In conclusion: i) forest management practices clearly influenced soil fertility and organic matter accumulation, ii) 15 years after selective harvesting nutrient and organic C accumulation in forest floor, as well as K and Fe accumulation in soil were restored to similar levels to the intact sites; thus, our hypothesis was partially correct
Locally Resonant Granular Chain
We report the design and testing of a tunable and nonlinear mechanical
metamaterial, called locally resonant granular chain. It consists of a
one-dimensional array of hollow spherical particles in contact, containing
local resonators. The resonant particles are made of an aluminium outer
spherical shell and a steel inner mass connected by a polymeric plastic
structure acting as a spring. We characterize the linear spectra of the
individual particles and of one-dimensional arrays of particles using theory,
numerical analysis, and experiments. A wide band gap is observed as well as
tunability of the dispersive spectrum by changing the applied static load.
Finally, we experimentally explore the nonlinear dynamics of the resonant
particles. By using nonlinear acoustical techniques, we reveal a complex,
nonclassical nonlinear dynamics
Bright and Gap Solitons in Membrane-Type Acoustic Metamaterials
We study analytically and numerically envelope solitons (bright and gap
solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an
air-filled waveguide periodically loaded by clamped elastic plates. Based on
the transmission line approach, we derive a nonlinear dynamical lattice model
which, in the continuum approximation, leads to a nonlinear, dispersive and
dissipative wave equation. Applying the multiple scales perturbation method, we
derive an effective lossy nonlinear Schr\"odinger equation and obtain
analytical expressions for bright and gap solitons. We also perform direct
numerical simulations to study the dissipation-induced dynamics of the bright
and gap solitons. Numerical and analytical results, relying on the analytical
approximations and perturbation theory for solions, are found to be in good
agreement
Modulation instability in nonlinear flexible mechanical metamaterials
In this paper, we study modulation instabilities (MI) in a one-dimensional
chain configuration of a flexible mechanical metamaterial (flexMM). Using the
lumped element approach, flexMMs can be modeled by a coupled system of discrete
equations for the longitudinal displacements and rotations of the rigid mass
units. In the long wavelength regime, and applying the multiple-scales method
we derive an effective nonlinear Schr\"odinger equation for slowly varying
envelope rotational waves. We are then able to establish a map of the
occurrence of MI to the parameters of the metamaterials and the wavenumbers. We
also highlight the key role of the rotation-displacement coupling between the
two degrees of freedom in the manifestation of MI. All analytical findings are
confirmed by numerical simulations of the full discrete and nonlinear lump
problem. These results provide interesting design guidelines for nonlinear
metamaterials offering either stability to high amplitude waves, or conversely
being good candidates to observe instabilities.Comment: 12 pages, 9 figure
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