Divergence-driven oscillations in a flexible-channel flow with fixed upstream flux

2013 ◽  
Vol 723 ◽  
pp. 706-733 ◽  
Author(s):  
Feng Xu ◽  
John Billingham ◽  
Oliver E. Jensen
Keyword(s):  
Low Frequency ◽  
Rigid Wall ◽  
Inertial Effects ◽  
One Dimensional ◽  
Channel One ◽  
Uniform State ◽  
Steady Solutions ◽  
Dissipative Hamiltonian System ◽  
Oscillatory Instabilities ◽  
Linear Pressure Distribution

AbstractWe consider flow in a finite-length channel, one wall of which contains a membrane under longitudinal tension. The upstream flux and downstream pressure are prescribed and an external linear pressure distribution is applied to the membrane such that the system admits uniform Poiseuille flow as a steady solution. The system is described using a one-dimensional model that accounts for viscous and inertial effects. A linear stability analysis reveals that the uniform state is unstable to static (or divergent) and oscillatory instabilities. Asymptotic analysis in the neighbourhood of a Takens–Bogdanov bifurcation point shows how, when the downstream rigid section of the channel is not substantially longer than the membrane, an oscillatory mode arises through an interaction between two static eigenmodes. Perturbations to the uniform state exhibit the dynamics of a weakly dissipative Hamiltonian system for which low-frequency self-excited oscillations are forced by the divergent instability of two nearby steady solutions, before ultimately growing to large amplitudes. Simulations show that the subsequent dynamics can involve slamming motion in which the membrane briefly comes into near-contact with the opposite rigid wall over short length scales.

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

2021 ◽  
pp. 108128652110238
Author(s):  
Barış Erbaş ◽  
Julius Kaplunov ◽  
Isaac Elishakoff
Keyword(s):  
Ad Hoc ◽  
Moving Load ◽  
Low Frequency ◽  
Elastic Beam ◽  
Winkler Foundation ◽  
One Dimensional ◽  
Beam Equations ◽  
Dimensional Equation ◽  
Phase And Group Velocities ◽  
Group Velocities

A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.

scholarly journals MULTIDIMENSIONAL REPRESENTATION OF AUTOMATIC DOSING DEVICE SIGNALS

2018 ◽  
pp. 26-32
Author(s):  
Denis Borisovich Fedosenkov ◽  
Anna Alekseevna Simikova ◽  
Boris Andreevich Fedosenkov ◽  
Stanislav Matveevich Kulakov
Keyword(s):  
Fourier Transform ◽  
Wigner Distribution ◽  
Low Frequency ◽  
Stationary Flow ◽  
Complex Model ◽  
Signal Spectrum ◽  
One Dimensional ◽  
Time Frequency ◽  
Cohen's Class ◽  
Discrete Values

The article describes the development of a special approach based on using multidimensional wavelet distributions principle to monitor and control the feed dozing processes in the mix preparation unit. As a key component, this approach uses the multidimensional time-frequency Wigner-Ville distribution, which is the part of Cohen's class distributions. The research focuses on signals characterizing mass transfer processes in the form of material flow measuring signals in relevant points of the unit. Wigner-Ville distribution has been shown in time terms as Fourier transform of products of multiplied parts of the signal under consideration for past and future time moments; corresponding distribution for the frequency spectrum is shown as Fourier transform of the products of signal parts for high-frequency and low-frequency fragments of the signal spectrum. It has been noted that when using a complex model of a dozing signal, discrete values (samples) of the latter are considered as its real values. The description of the signal parameters (amplitude, phase, frequency) has been carried out with the help of Hilbert transform. In Cohen's class distributions which represent one-dimensional non-stationary flow signals, the concept of ‘instantaneous frequency’ has been introduced. A graphical explanation for the transformation of a process flow signal from a one-dimensional time domain to a time-frequency 2 D/ 3 D -space is presented. The technology of developing a multidimensional image in the form of Wigner distribution for one-dimensional signals of continuous spiral or screw-type feeders has been examined in detail. There have been considered the features to support Wigner distribution, which allow to guess the presence or absence of time-frequency distribution elements in the interval of signal recording. There has been demonstrated how Wigner distribution can be obtained for a continuous-intermittent feeding signal. It has been concluded that for a certain types of the signal for zero fragments of the latter, non-zero time-frequency elements (i.e. virtual, anomalous ones) appear on the distribution. In addition to Wigner distribution, two other distributions - of Rihachek and Page - are considered. They display the same signal and also contain virtual elements, but in different domains of the time-frequency space. A generalized multidimensional compound signal distribution with a so-called distribution kernel available in it is presented, which includes a correction parameter that allows controlling the intensity of the virtual signal energy.

scholarly journals Tunable Omnidirectional Band Gap Properties of 1D Plasma Annular Periodic Multilayer Structure Based on an Improved Fibonacci Topological Structure

2021 ◽  
Author(s):  
Hong-Mei Peng ◽  
Bao-Fei Wan ◽  
Peng-Xiang Wang ◽  
Dan Zhang ◽  
Hai-Feng Zhang
Keyword(s):  
Band Gap ◽  
Plasma Frequency ◽  
Incident Angle ◽  
Low Frequency ◽  
Interesting Phenomenon ◽  
Azimuthal Mode ◽  
One Dimensional ◽  
Theoretical Support ◽  
Omnidirectional Band Gap ◽  
High Reflection

Abstract In this paper, the characteristics of the omnidirectional band gap (OBG) for one-dimensional (1D) plasma cylindrical photonic crystals (PCPCs) are based on an improved Fibonacci topological (IFT) structure are studied. The influences of the azimuthal mode number, incident angle, plasma thickness, and plasma frequency on the OBG are discussed. It is concluded that increasing the azimuth modulus can significantly expand the bandwidth of the OBG, and the OBG can be moved to the low-frequency direction by increasing the plasma frequency. In addition, an interesting phenomenon can be found that when the number of azimuthal modes is equal to 2, the TM wave can produce an extra high reflection zone. It provides a theoretical support for designing the narrowband filters without introducing any physical defect layers in the structure.

Oscillatory instabilities and dynamics of multi-spike patterns for the one-dimensional Gray-Scott model

2009 ◽  
Vol 20 (2) ◽  
pp. 187-214 ◽  
Author(s):  
WAN CHEN ◽  
MICHAEL J. WARD
Keyword(s):  
Hopf Bifurcation ◽  
Stefan Problem ◽  
Differential Algebraic Equations ◽  
Finite Domain ◽  
Quasi Equilibrium ◽  
Algebraic Equations ◽  
Source Terms ◽  
One Dimensional ◽  
The One ◽  
Oscillatory Instabilities

The dynamics and oscillatory instabilities of multi-spike solutions to the one-dimensional Gray-Scott reaction–diffusion system on a finite domain are studied in a particular parameter regime. In this parameter regime, a formal singular perturbation method is used to derive a novel ODE–PDE Stefan problem, which determines the dynamics of a collection of spikes for a multi-spike pattern. This Stefan problem has moving Dirac source terms concentrated at the spike locations. For a certain subrange of the parameters, this Stefan problem is quasi-steady and an explicit set of differential-algebraic equations characterizing the spike dynamics is derived. By analysing a nonlocal eigenvalue problem, it is found that this multi-spike quasi-equilibrium solution can undergo a Hopf bifurcation leading to oscillations in the spike amplitudes on an O(1) time scale. In another subrange of the parameters, the spike motion is not quasi-steady and the full Stefan problem is solved numerically by using an appropriate discretization of the Dirac source terms. These numerical computations, together with a linearization of the Stefan problem, show that the spike layers can undergo a drift instability arising from a Hopf bifurcation. This instability leads to a time-dependent oscillatory behaviour in the spike locations.

Dimensional tailoring of nitrogen-doped graphene for high performance supercapacitors

RSC Advances ◽  
2016 ◽  
Vol 6 (60) ◽  
pp. 55577-55583 ◽  
Author(s):  
Seung Yong Lee ◽  
Chang Hyuck Choi ◽  
Min Wook Chung ◽  
Jae Hoon Chung ◽  
Seong Ihl Woo
Keyword(s):  
High Performance ◽  
Low Frequency ◽  
Frequency Region ◽  
Transfer Resistance ◽  
One Dimensional ◽  
Nitrogen Doped ◽  
Efficient Charge ◽  
Nitrogen Doped Graphene ◽  
Doped Graphene ◽  
Low Mass

In supercapacitors, one dimensional graphene ribbons which form net-like porous structure demonstrate low mass transfer resistance at low frequency region and a consequent efficient charge transferability.

scholarly journals Unique features of the generation–recombination noise in quasi-one-dimensional van der Waals nanoribbons

Nanoscale ◽  
2018 ◽  
Vol 10 (42) ◽  
pp. 19749-19756 ◽  
Author(s):  
Adane K. Geremew ◽  
Sergey Rumyantsev ◽  
Matthew A. Bloodgood ◽  
Tina T. Salguero ◽  
Alexander A. Balandin
Keyword(s):  
Carrying Capacity ◽  
Van Der Waals ◽  
Low Frequency ◽  
Current Fluctuations ◽  
Electronic Noise ◽  
High Current ◽  
One Dimensional ◽  
Frequency Current

We describe the low-frequency current fluctuations, i.e. electronic noise, in quasi-one-dimensional ZrTe3 van der Waals nanoribbons, which have recently attracted attention owing to their extraordinary high current carrying capacity.

Topological Interface States in the Low-Frequency Band Gap of One-Dimensional Phononic Crystals

2020 ◽  
Vol 14 (5) ◽  
Author(s):  
Zheng-wei Li ◽  
Xin-sheng Fang ◽  
Bin Liang ◽  
Yong Li ◽  
Jian-chun Cheng
Keyword(s):  
Band Gap ◽  
Frequency Band ◽  
Low Frequency ◽  
Interface States ◽  
Phononic Crystals ◽  
One Dimensional

scholarly journals Longitudinal wave propagation in a one-dimensional quasi-periodic waveguide

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190392
Author(s):  
Vladislav S. Sorokin
Keyword(s):  
Wave Propagation ◽  
Wave Attenuation ◽  
Periodic Structures ◽  
Low Frequency ◽  
Periodic Waveguide ◽  
One Dimensional ◽  
Vibration Attenuation ◽  
Direct Separation ◽  
Longitudinal Wave Propagation ◽  
Spatial Modulations

The paper deals with the analysis of wave propagation in a general one-dimensional (1D) non-uniform waveguide featuring multiple modulations of parameters with different, arbitrarily related, spatial periods. The considered quasi-periodic waveguide, in particular, can be viewed as a model of pure periodic structures with imperfections. Effects of such imperfections on the waveguide frequency bandgaps are revealed and described by means of the method of varying amplitudes and the method of direct separation of motions. It is shown that imperfections cannot considerably degrade wave attenuation properties of 1D periodic structures, e.g. reduce widths of their frequency bandgaps. Attenuation levels and frequency bandgaps featured by the quasi-periodic waveguide are studied without imposing any restrictions on the periods of the modulations, e.g. for their ratio to be rational. For the waveguide featuring relatively small modulations with periods that are not close to each other, each of the frequency bandgaps, to the leading order of smallness, is controlled only by one of the modulations. It is shown that introducing additional spatial modulations to a pure periodic structure can enhance its wave attenuation properties, e.g. a relatively low-frequency bandgap can be induced providing vibration attenuation in frequency ranges where damping is less effective.

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