182 research outputs found
Nonlinear Generalization of Den Hartog's Equal-Peak Method
This study addresses the mitigation of a nonlinear resonance of a mechanical
system. In view of the narrow bandwidth of the classical linear tuned vibration
absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber
(NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is
that the mathematical form of its restoring force is tailored according to the
nonlinear restoring force of the primary system. The NLTVA parameters are then
determined using a nonlinear generalization of Den Hartog's equal-peak method.
The mitigation of the resonant vibrations of a Duffing oscillator is considered
to illustrate the proposed developments
High-Intensity Discharge Lamp and Duffing Oscillator - Similarities and Differences
The processes inside the arc tube of high-intensity discharge lamps are
investigated by finite element simulations. The behavior of the gas mixture
inside the arc tube is governed by differential equations describing mass,
energy and charge conservation as well as the Helmholtz equation for the
acoustic pressure and the Navier-Stokes equation for the flow driven by the
buoyancy and the acoustic streaming force. The model is highly nonlinear and
requires a recursion procedure to account for the impact of acoustic streaming
on the temperature and other fields. The investigations reveal the presence of
a hysteresis and the corresponding jump phenomenon, quite similar to a Duffing
oscillator. The similarities and, in particular, the differences of the
nonlinear behavior of the high-intensity discharge lamp to that of a Duffing
oscillator are discussed. For large amplitudes the high-intensity discharge
lamp exhibits a stiffening effect in contrast to the Duffing oscillator.Comment: 14 pages, 8 figure
Nonlinear damping in mechanical resonators based on graphene and carbon nanotubes
Carbon nanotubes and graphene allow fabricating outstanding nanomechanical
resonators. They hold promise for various scientific and technological
applications, including sensing of mass, force, and charge, as well as the
study of quantum phenomena at the mesoscopic scale. Here, we have discovered
that the dynamics of nanotube and graphene resonators is in fact highly exotic.
We propose an unprecedented scenario where mechanical dissipation is entirely
determined by nonlinear damping. As a striking consequence, the quality factor
Q strongly depends on the amplitude of the motion. This scenario is radically
different from that of other resonators, whose dissipation is dominated by a
linear damping term. We believe that the difference stems from the reduced
dimensionality of carbon nanotubes and graphene. Besides, we exploit the
nonlinear nature of the damping to improve the figure of merit of
nanotube/graphene resonators.Comment: main text with 4 figures, supplementary informatio
Impulsive perturbations to differential equations: stable/unstable pseudo-manifolds, heteroclinic connections, and flux
State-dependent time-impulsive perturbations to a two-dimensional autonomous
flow with stable and unstable manifolds are analysed by posing in terms of an
integral equation which is valid in both forwards- and backwards-time. The
impulses destroy the smooth invariant manifolds, necessitating new definitions
for stable and unstable pseudo-manifolds. Their time-evolution is characterised
by solving a Volterra integral equation of the second kind with discontinuous
inhomogeniety. A criteria for heteroclinic trajectory persistence in this
impulsive context is developed, as is a quantification of an instantaneous flux
across broken heteroclinic manifolds. Several examples, including a kicked
Duffing oscillator and an underwater explosion in the vicinity of an eddy, are
used to illustrate the theory
Vibrational energy transfer in coupled mechanical systems with nonlinear joints
Acknowledgement This work was supported by National Natural Science Foundation of China under Grant number 12172185, by Zhejiang Provincial Natural Science Foundation of China under Grant number LY22A020006, and by Ningbo Municipal Natural Science Foundation under Grant number 2022J174.Peer reviewedPostprin
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