1,578 research outputs found
Pulse propagation in a linear and nonlinear diatomic periodic chain: effects of acoustic frequency band-gap
One-dimensional nonlinear phononic crystals have been assembled from periodic diatomic chains of stainless steel cylinders alternated with Polytetrafluoroethylene spheres. This system allows dramatic changes of behavior (from linear to strongly nonlinear) by application of compressive forces practically without changes of geometry of the system. The relevance of classical acoustic band-gap, characteristic for chain with linear interaction forces and derived from the dispersion relation of the linearized system, on the transformation of single and multiple pulses in linear, nonlinear and strongly nonlinear regimes are investigated with numerical calculations and experiments. The limiting frequencies of the acoustic band-gap for investigated system with given precompression force are within the audible frequency range (20–20,000 Hz) and can be tuned by varying the particle’s material properties, mass and initial compression. In the linear elastic chain the presence of the acoustic band-gap was apparent through fast transformation of incoming pulses within very short distances from the chain entrance. It is interesting that pulses with relatively large amplitude (nonlinear elastic chain) exhibit qualitatively similar behavior indicating relevance of the acoustic band gap also for transformation of nonlinear signals. The effects of an in situ band-gap created by a mean dynamic compression are observed in the strongly nonlinear wave regime
Slow relaxation, confinement, and solitons
Millisecond crystal relaxation has been used to explain anomalous decay in
doped alkali halides. We attribute this slowness to Fermi-Pasta-Ulam solitons.
Our model exhibits confinement of mechanical energy released by excitation.
Extending the model to long times is justified by its relation to solitons,
excitations previously proposed to occur in alkali halides. Soliton damping and
observation are also discussed
Breathers in oscillator chains with Hertzian interactions
We prove nonexistence of breathers (spatially localized and time-periodic
oscillations) for a class of Fermi-Pasta-Ulam lattices representing an
uncompressed chain of beads interacting via Hertz's contact forces. We then
consider the setting in which an additional on-site potential is present,
motivated by the Newton's cradle under the effect of gravity. Using both direct
numerical computations and a simplified asymptotic model of the oscillator
chain, the so-called discrete p-Schr\"odinger (DpS) equation, we show the
existence of discrete breathers and study their spectral properties and
mobility. Due to the fully nonlinear character of Hertzian interactions,
breathers are found to be much more localized than in classical nonlinear
lattices and their motion occurs with less dispersion. In addition, we study
numerically the excitation of a traveling breather after an impact at one end
of a semi-infinite chain. This case is well described by the DpS equation when
local oscillations are faster than binary collisions, a situation occuring e.g.
in chains of stiff cantilevers decorated by spherical beads. When a hard
anharmonic part is added to the local potential, a new type of traveling
breather emerges, showing spontaneous direction-reversing in a spatially
homogeneous system. Finally, the interaction of a moving breather with a point
defect is also considered in the cradle system. Almost total breather
reflections are observed at sufficiently high defect sizes, suggesting
potential applications of such systems as shock wave reflectors
Wave propagation in one-dimensional nonlinear acoustic metamaterials
The propagation of waves in the nonlinear acoustic metamaterials (NAMs) is
fundamentally different from that in the conventional linear ones. In this
article we consider two one-dimensional NAM systems featuring respectively a
diatomic and a tetratomic meta unit-cell. We investigate the attenuation of the
wave, the band structure and the bifurcations to demonstrate novel nonlinear
effects, which can significantly expand the bandwidth for elastic wave
suppression and cause nonlinear wave phenomena. Harmonic averaging approach,
continuation algorithm, Lyapunov exponents are combined to study the frequency
responses, the nonlinear modes, bifurcations of periodic solutions and chaos.
The nonlinear resonances are studied and the influence of damping on
hyper-chaotic attractors is evaluated. Moreover, a "quantum" behavior is found
between the low-energy and high-energy orbits. This work provides an important
theoretical base for the further understandings and applications of NAMs
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