scholarly journals Campbell diagrams of weakly anisotropic flexible rotors

2009 ◽  
Vol 465 (2109) ◽  
pp. 2703-2723 ◽  
Author(s):  
O. N. Kirillov
Keyword(s):  
Wave Propagation ◽  
Degrees Of Freedom ◽  
Travelling Waves ◽  
Continuous Model ◽  
Unperturbed System ◽  
Rotating Shaft ◽  
Campbell Diagram ◽  
Flexible Rotors ◽  
Complex Eigenvalues ◽  
Subcritical Speed

We consider an axi-symmetric flexible rotor perturbed by dissipative, conservative and non-conservative positional forces originated at the contact with the anisotropic stator. The Campbell diagram of the unperturbed system is a mesh-like structure in the frequency–speed plane with double eigenfrequencies at the nodes. The diagram is convenient for the analysis of the travelling waves in the rotating elastic continuum. Computing sensitivities of the doublets, we find that at every particular node the unfolding of the mesh into the branches of complex eigenvalues in the first approximation is generically determined by only four 2×2 sub-blocks of the perturbing matrix. Selection of the unstable modes that cause self-excited vibrations in the subcritical speed range is governed by the exceptional points at the corners of the singular eigenvalue surfaces—‘double coffee filter’ and ‘viaduct’—which are sharply associated with the crossings of the unperturbed Campbell diagram with the definite symplectic (Krein) signature. The singularities connect the problems of wave propagation in the rotating continua with that of electromagnetic and acoustic wave propagation in non-rotating anisotropic chiral media. As mechanical examples a model of a rotating shaft with two degrees of freedom and a continuous model of a rotating circular string passing through the eyelet are studied in detail.

scholarly journals Qualitative Properties of Autocatalytic Reactions Occurring in a Flow System

1985 ◽  
Vol 40 (7) ◽  
pp. 736-747
Author(s):  
Sang H. Kim ◽  
Vladimir Hlavacek
Keyword(s):  
Chaotic Behavior ◽  
Flow System ◽  
Cell Model ◽  
Dispersion Model ◽  
Travelling Waves ◽  
Continuous Model ◽  
Product Inhibition ◽  
Stable Node ◽  
Qualitative Properties ◽  
Intermediate Value

The dynamic behavior of an autocatalytic reaction with a product inhibition term is studied in a flow system. A unique steady state exists in the continuous tank reactor. Linear stability analysis predicts either a stable node, a focus or an unstable saddle-focus. Sustained oscillations around the unstable focus can occur for high values of the Damköhler number (Da). In the distributed system, travelling, standing or complex oscillatory waves are detected. For a low value of Da, travelling waves with a pseudo-constant pattern are observed. With an intermediate value of Da, single or multiple standing waves are obtained. The temporal behavior indicates also the appearance of retriggering or echo waves. For a high value of Da, both single peak and complex multipeak oscillations are found. In the cell model, both regular oscillations near the inlet and chaotic behavior downstream are observed. In the dispersion model, higher Peclet numbers (Pe) eliminate the oscillations. The spatial profile shows a train of pulsating waves for the discrete model and a single pulsating or solitary wave for the continuous model.

scholarly journals From Loschmidt daemons to time-reversed waves

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150156 ◽  
Author(s):  
Mathias Fink
Keyword(s):  
Wave Propagation ◽  
Time Reversal ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Propagation Time ◽  
Reversal Invariance ◽  
Spatial Boundary ◽  
Dual Approaches ◽  
Spatio Temporal

Time-reversal invariance can be exploited in wave physics to control wave propagation in complex media. Because time and space play a similar role in wave propagation, time-reversed waves can be obtained by manipulating spatial boundaries or by manipulating time boundaries. The two dual approaches will be discussed in this paper. The first approach uses ‘time-reversal mirrors’ with a wave manipulation along a spatial boundary sampled by a finite number of antennas. Related to this method, the role of the spatio-temporal degrees of freedom of the wavefield will be emphasized. In a second approach, waves are manipulated from a time boundary and we show that ‘instantaneous time mirrors’, mimicking the Loschmidt point of view, simultaneously acting in the entire space at once can also radiate time-reversed waves.

Optimization of Nonlinear Unbalanced Flexible Rotating Shaft Passing Through Critical Speeds

2021 ◽  
Author(s):  
Sadegh Amirzadegan ◽  
Mohammad Rokn-Abadi ◽  
R. D. Firouz-Abadi
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Oscillations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Angular Acceleration ◽  
Beam Theory ◽  
Rotor System ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Applied Torque

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for this work. The shaft is modeled as a beam and the Euler–Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6 degrees of freedom. In order to solve these equations numerically, the finite element method (FEM) is used. Furthermore, for different bearing properties, rotor responses are examined and curves of passing through critical speeds with angular acceleration due to applied torque are plotted. Then the optimal values of bearing stiffness and damping are calculated to achieve the minimum vibration amplitude, which causes to pass easier through critical speeds. It is concluded that the value of damping and stiffness of bearing change the rotor critical speeds and also significantly affect the dynamic behavior of the rotor system. These effects are also presented graphically and discussed.

Wave Propagation in Sandwich Structures With Multiresonators

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
J. S. Chen ◽  
Y. J. Huang
Keyword(s):  
Wave Propagation ◽  
Timoshenko Beam ◽  
Degrees Of Freedom ◽  
Wave Attenuation ◽  
Sandwich Beam ◽  
Sandwich Beams ◽  
Central Frequency ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
In Series

A new sandwich beam with embedded multiresonators is presented. Two continuum Timoshenko beam models are adopted for modeling sandwich beams. Numerical results show that multiple resonators can lead to multiple resonant-type bandgaps with remarkable wave attenuation. The effective mass is found to become negative for frequencies in the bandgaps where the wave is greatly attenuated. With two identical resonators connected in parallel, only one single bandgap can be found. If two resonators with equal masses and springs are connected in series, the central frequency of the second bandgap is approximated twice of the central frequency of the first gap. For the beam with series-connected resonators, a simple two degrees-of-freedom system is proposed and used for predicting the initial frequencies of the bandgaps while for the beam with resonators in parallel, two separate single degree-of-freedom systems are introduced.

scholarly journals Stochastic Analysis of the Eigenvalue Problem for Mechanical Systems Using Polynomial Chaos Expansion— Application to a Finite Element Rotor

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
E. Sarrouy ◽  
O. Dessombz ◽  
J.-J. Sinou
Keyword(s):  
Finite Element ◽  
Stochastic Analysis ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Eigenvalues And Eigenvectors ◽  
Campbell Diagram ◽  
Complex Eigenvalues ◽  
Gyroscopic Effects ◽  
Rotor Model

This paper proposes to use a polynomial chaos expansion approach to compute stochastic complex eigenvalues and eigenvectors of structures including damping or gyroscopic effects. Its application to a finite element rotor model is compared to Monte Carlo simulations. This lets us validate the method and emphasize its advantages. Three different uncertain configurations are studied. For each, a stochastic Campbell diagram is proposed and interpreted and critical speeds dispersion is evaluated. Furthermore, an adaptation of the Modal Accordance Criterion (MAC) is proposed in order to monitor the eigenvectors dispersion.

Terahertz interface physics: from terahertz wave propagation to terahertz wave generation

2021 ◽  
Author(s):  
Wanyi Du ◽  
Yuanyuan Huang ◽  
Yixuan Zhou ◽  
Xinlong Xu
Keyword(s):  
Wave Propagation ◽  
Degrees Of Freedom ◽  
Impedance Matching ◽  
Wave Impedance ◽  
Terahertz Wave ◽  
Wave Generation ◽  
Band Alignment ◽  
Advanced Materials ◽  
Thz Wave ◽  
Metal Dichalcogenides

Abstract Terahertz (THz) interface physics as a new interdiscipline between THz technique and condensed matter physics has undergone rapid developments in recent years. Especially, the developments of advanced materials, such as graphene, transitional metal dichalcogenides, topological insulators, ferromagnetic metals, and metamaterials, have revolutionized the interface field and further promotes the development of THz functional devices based on interface physics. Moreover, playing at the interface with these advanced materials could unveil a wealth of fascinating physical effects such as charge transfer, proximity effect, inverse spin-Hall effect, and Rashba effect with THz technology by engineering the charge, spin, orbit, valley, and lattice degrees of freedom. In this review, we start from the discussion of the basic theory of THz interface physics, including interface formation with advanced materials, THz wave reflection and transmission at the interface, and band alignment and charge dynamics at the interface. Then we move to recent progresses in advanced materials from THz wave propagation to THz wave generation at the interface. In the THz wave propagation, we focus on the THz wave impedance-matching, Goos–Hänchen and Imbert–Fedorov shifts in THz region, interfacial modulation and interfacial sensing based on THz wave. In the THz wave generation, we summarize the ongoing coherent THz wave generation from van der Waals interfaces, multiferroic interfaces, and magnetic interfaces. The fascinating THz interface physics in advanced materials is promising and promoting novel THz functional devices for manipulating the propagation and generation of THz wave at the interfaces.

A Hybrid Track Model for Studying Dynamic Track/Sprocket Contact

1999 ◽  
Author(s):  
Zheng-Dong Ma ◽  
Noel C. Perkins
Keyword(s):  
Hybrid Model ◽  
Degrees Of Freedom ◽  
Contact Region ◽  
Continuous Model ◽  
Contact Forces ◽  
Tracked Vehicles ◽  
Multibody Model ◽  
Nonlinear Contact ◽  
Track Circuit ◽  
Mining Vehicles

Abstract Tracked vehicles are propelled by the engagement of track pitches and a drive sprocket. This sprocket, referred to as a tumbler for the large tracked mining vehicles considered herein, may wear quickly under the action of the considerable contact forces that develop with the track. This paper summarizes a model of the track/tumbler seating process and the contact forces that control abrasive wear. A vehicle model is developed that employs a hybrid model for the track. This hybrid model combines a multibody model of the track within the seating region of the tumbler with a continuous model of the track elsewhere in the track circuit. The hybrid model is then employed to simulate the track/tumbler interactions and the associated nonlinear contact phenomena. This new modeling approach promotes accuracy within the track/tumbler contact region with few degrees of freedom outside this region where spatial resolution is less important.

652 Stability Analysis of an Unsymmetrical Rotating Shaft with Large Degrees of Freedom : Rational Construction of Reduction Mode

2003 ◽  
Vol 2003 (0) ◽  
pp. _652-1_-_652-6_
Author(s):  
Rinpei KAWASHITA ◽  
Hiroaki TASHIRO ◽  
Takahiro KONDOU ◽  
Takumi SASAKI ◽  
Nobuyuki SOWA
Keyword(s):  
Stability Analysis ◽  
Degrees Of Freedom ◽  
Rotating Shaft ◽  
Rational Construction

Radio Wave Propagation in Stratified Media with Nonuniform Boundaries and Varying Electromagnetic Parameters: Full Wave Analysis

1972 ◽  
Vol 50 (24) ◽  
pp. 3132-3142 ◽  
Author(s):  
E. Bahar
Keyword(s):  
Wave Propagation ◽  
Radio Wave ◽  
Travelling Waves ◽  
Radio Wave Propagation ◽  
Stratified Media ◽  
Electromagnetic Parameters ◽  
Full Wave ◽  
Exact Boundary ◽  
Full Wave Analysis ◽  
Discrete Part

Full wave solutions are derived to the problem of radio wave propagation in stratified media with non-uniform boundaries and varying electromagnetic parameters. The analysis employs a complete set of forward and backward travelling waves. The continuous parts of the wavenumber spectrum constitute the radiation field and the lateral waves, and the discrete part of the spectrum is identified as the surface wave term. The solutions are not restricted by the approximate surface impedance concept and the source and receiver can be situated on opposite sides of the interface. Exact boundary conditions are imposed and the solutions are shown to be consistent with the reciprocity relationships.

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