Nonlinear dynamics of higher-dimensional system for an axially accelerating viscoelastic beam with in-plane and out-of-plane vibrations

2010 ◽  
Vol 329 (25) ◽  
pp. 5321-5345 ◽  
Author(s):  
L.H. Chen ◽  
W. Zhang ◽  
F.H. Yang
Keyword(s):  
Nonlinear Dynamics ◽  
Dimensional System ◽  
Viscoelastic Beam ◽  
Higher Dimensional ◽  
Out Of Plane

scholarly journals Inverse-square law between time and amplitude for crossing tipping thresholds

2019 ◽  
Vol 475 (2222) ◽  
pp. 20180504 ◽  
Author(s):  
Paul Ritchie ◽  
Özkan Karabacak ◽  
Jan Sieber
Keyword(s):  
Dynamical System ◽  
Feedback Loop ◽  
Tipping Point ◽  
Dimensional System ◽  
Stochastic Forcing ◽  
Inverse Square Law ◽  
System A ◽  
Asymptotic Expressions ◽  
Higher Dimensional ◽  
Random Disturbances

A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold. For the case when the dynamical system is subject to stochastic forcing we give an approximation to the probability of tipping if a parameter changing in time reverses near the tipping point. The derived approximations are valid if the parameter change in time is sufficiently slow. We demonstrate for a higher-dimensional system, a model for the Indian summer monsoon, how numerically observed escape from the equilibrium converge to our asymptotic expressions. The inverse-square law between peak of the parameter forcing and the time the parameter spends above a given threshold is also visible in the level curves of equal probability when the system is subject to random disturbances.

scholarly journals Revealing topology with transformation optics

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Lizhen Lu ◽  
Kun Ding ◽  
Emanuele Galiffi ◽  
Xikui Ma ◽  
Tianyu Dong ◽  
...  
Keyword(s):  
Physical Space ◽  
Real Space ◽  
Virtual Space ◽  
Transformation Optics ◽  
Coordinate Space ◽  
Dimensional System ◽  
Edge States ◽  
And Topology ◽  
Higher Dimensional ◽  
Insight Into

AbstractSymmetry deepens our insight into a physical system and its interplay with topology enables the discovery of topological phases. Symmetry analysis is conventionally performed either in the physical space of interest, or in the corresponding reciprocal space. Here we borrow the concept of virtual space from transformation optics to demonstrate how a certain class of symmetries can be visualised in a transformed, spectrally related coordinate space, illuminating the underlying topological transitions. By projecting a plasmonic system in a higher-dimensional virtual space onto a lower-dimensional system in real space, we show how transformation optics allows us to construct a topologically non-trivial system by inspecting its modes in the virtual space. Interestingly, we find that the topological invariant can be controlled via the singularities in the conformal mapping, enabling the intuitive engineering of edge states. The confluence of transformation optics and topology here can be generalized to other wave realms beyond photonics.

Non-Standard Reduction of Noisy Structural Systems: Shallow Arches

2000 ◽  
Author(s):  
Lalit Vedula ◽  
N. Sri Namachchivaya
Keyword(s):  
Markov Process ◽  
Random Perturbation ◽  
Exit Time ◽  
Stochastic Averaging ◽  
Dimensional System ◽  
Shallow Arches ◽  
Higher Dimensional ◽  
Mean Exit Time ◽  
Stationary Probability Density Function ◽  
Low Dimensional

Abstract The dynamics of a shallow arch subjected to small random external and parametric excitation is invegistated in this work. We develop rigorous methods to replace, in some limiting regime, the original higher dimensional system of equations by a simpler, constructive and rational approximation – a low-dimensional model of the dynamical system. To this end, we study the equations as a random perturbation of a two-dimensional Hamiltonian system. We achieve the model-reduction through stochastic averaging and the reduced Markov process takes its values on a graph with certain glueing conditions at the vertex of the graph. Examination of the reduced Markov process on the graph yields many important results such as mean exit time, stationary probability density function.

Targeting Applying ε-Bounded Orbit Correction Perturbations

1998 ◽  
Vol 08 (07) ◽  
pp. 1575-1584 ◽  
Author(s):  
M. S. Baptista
Keyword(s):  
Dimensional System ◽  
Fast Computation ◽  
Orbit Correction ◽  
Higher Dimensional ◽  
Starting Point

A low-sized chaotic trajectory is used to compute epsilon-bounded orbit correction perturbations in order to rapidly target a trajectory from the vicinity of a starting point to a target. An algorithm that allows fast computation of a set of perturbations to be applied is presented, and its performance is tested in a higher-dimensional system, the kicked double rotor.

Application of HDQM for the Analysis of Two-Dimensional Nonlinear Dynamics of Axially Accelerating Beam

2014 ◽  
Author(s):  
Dong-Mei Wang ◽  
Wei Zhang ◽  
Mu-Rong Li ◽  
Qian Wang
Keyword(s):  
Nonlinear Dynamics ◽  
Nonlinear Vibrations ◽  
Numerical Solutions ◽  
Differential Quadrature Method ◽  
Nonlinear Partial Differential Equations ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Chaotic Motions ◽  
Nonlinear Dynamical ◽  
Out Of Plane

In this paper, the two-dimensional nonlinear dynamics are investigated for the nonplanar nonlinear vibrations of an axially accelerating moving viscoelastic beam with in-plane and out-of-plane vibrations by the harmonic differential quadrature method (HDQM). The coupled nonlinear partial differential equations for the two-dimensional nonplanar nonlinear vibrations are discretized in space and time domains using HDQM and Runge-Kutta-Fehlberg methods respectively. Based on the numerical solutions, the nonlinear dynamical behaviors such as bifurcations and chaotic motions of the nonlinear system are investigated by using of the phase portrait and the bifurcation diagrams. The bifurcation diagrams for the in-plane and out-of-plane displacements via the mean axial velocity and the amplitude of velocity fluctuation are respectively presented while other parameters are fixed.

Distinguishing quantum operations: LOCC versus separable operators

2016 ◽  
Vol 14 (06) ◽  
pp. 1640028 ◽  
Author(s):  
Indrani Chattopadhyay ◽  
Debasis Sarkar
Keyword(s):  
Dimensional System ◽  
Quantum Operation ◽  
Initial State ◽  
Quantum Operations ◽  
Higher Dimensional

In this paper, we discuss the issue of distinguishing a pair of quantum operation in general. We use Krause theorem for representing the operations in unitary form. This supports the existence of pair of quantum operations that are not locally distinguishable, but distinguishable in asymptotic sense in some higher dimensional system. The process can even be successful without any use of the entangled initial state.

Nonlinear Dynamics of Flexible L-Shaped Beam Based on Exact Modes Truncation

2017 ◽  
Vol 27 (03) ◽  
pp. 1750035 ◽  
Author(s):  
Tian-Jun Yu ◽  
Wei Zhang ◽  
Xiao-Dong Yang
Keyword(s):  
Nonlinear Dynamics ◽  
Linear Equations ◽  
Elliptic Functions ◽  
Governing Equations ◽  
Modal Interactions ◽  
Partial Differential ◽  
Shaped Beam ◽  
Higher Dimensional ◽  
Theoretical Predictions ◽  
Energy Exchanges

Nonlinear dynamics of flexible multibeam structures modeled as an L-shaped beam are investigated systematically considering the modal interactions. Taking into account nonlinear coupling and nonlinear inertia, Hamilton’s principle is employed to derive the partial differential governing equations of the structure. Exact mode functions are obtained by the coupled linear equations governing the horizontal and vertical beams and the results are verified by the finite element method. Then the exact modes are adopted to truncate the partial differential governing equations into two coupled nonlinear ordinary differential equations by using Galerkin method. The undamped free oscillations are studied in terms of Jacobi elliptic functions and results indicate that the energy exchanges are continual between the two modes. The saturation and jumping phenomena are then observed for the forced damped multibeam structure. Further, a higher-dimensional, Melnikov-type perturbation method is used to explore the physical mechanism leading to chaotic behaviors for such an autoparametric system. Numerical simulations are performed to validate the theoretical predictions.

scholarly journals Nonlinear dynamics of a base-isolated beam under turbulent wind flow

2021 ◽  
Author(s):  
Simona Di Nino ◽  
Angelo Luongo
Keyword(s):  
Nonlinear Dynamics ◽  
Hopf Bifurcation ◽  
Perturbation Methods ◽  
Wind Flow ◽  
Viscoelastic Beam ◽  
Static Theory ◽  
Isolation System ◽  
Turbulent Wind ◽  
Nonlinear Viscoelastic ◽  
Mechanical Performances

AbstractA homogeneous continuous viscoelastic beam, describing the dynamics of a base-isolated tower, exposed to a uniformly distributed turbulent wind flow, is studied. The beam is constrained at the bottom end by a nonlinear viscoelastic device, and it is free at the top end. Aeroelastic forces are computed by the quasi-static theory. The steady component of wind is responsible for a Hopf bifurcation, and the turbulent component induces parametric excitation. The interaction between the two bifurcations is investigated. Critical and post-critical behavior is analyzed by perturbation methods. The mechanical performances of the structure are discussed to assess the effectiveness of the viscoelastic isolation system.

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