Nonlinear Polarisationoscillations in a Biophysical Model-System I: Internal Dynamics

1981 ◽  
Vol 36 (9-10) ◽  
pp. 888-892 ◽  
Author(s):  
F. Kaiser ◽  
Z. Szabo
Keyword(s):  
Nonlinear Model ◽  
Biological System ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Dipole Interaction ◽  
Model Potential ◽  
Model System ◽  
Biophysical Model ◽  
Internal Dynamics ◽  
Dipole State

Abstract To describe a metastable electrical dipole state in a biological system. Fröhlich suggested a nonlinear model potential. In this paper we investigate a system of two such dipoles coupled by a dipole-dipole interaction. M athem atically this model is described by two coupled nonlinear differential equations. In the investigation of the dynamics of the system we distinguish three solution types of the equations of motion.

Nonlinear Polarisationoscillations in a Biophysical Model System II: External Dynamics

1982 ◽  
Vol 37 (9) ◽  
pp. 733-738 ◽  
Author(s):  
Z. Szabo ◽  
F. Kaiser
Keyword(s):  
External Field ◽  
Coupled Oscillators ◽  
Anharmonic Oscillator ◽  
Phase Locking ◽  
Dipole Interaction ◽  
Model Potential ◽  
Model System ◽  
Biophysical Model ◽  
Dipole State ◽  
Linear Damping

Abstract Nonlinear Polarisationoscillations To describe a metastable electric dipole state in a biological system, Fröhlich suggested a nonlinear model potential. In this paper we investigate a system of two nonlinear dipoles, which are coupled by a dipole-dipole interaction. We apply an external field and add linear damping terms. The external drive leads to a phase-locking of the dipoles. Mathematically, the system corresponds to an externally driven anharmonic oscillator with damping. We investigate the system of coupled oscillators and look for the stable and metastable solutions as a function of the internal and external parameters.

The Effects of Flare and Overhangs on the Motions of a Yacht in Head Seas

1993 ◽  
Author(s):  
John C. Kuhn ◽  
Eric C. Schlageter
Keyword(s):  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Order Effects ◽  
Third Order ◽  
Numerical Work ◽  
Strip Theory ◽  
Hull Forms ◽  
The Time Domain ◽  
The Impact

The coupled heave and pitch motions of hull forms with flare and overhangs are examined numerically. The presence of flare and overhangs is numerically modelled with nonlinear hydrostatic and Froude-Krylov forces based on integrals over the instantaneous wetted surface. Forces due to radiation and diffraction are computed with a linear strip-theory. These forces are combined in two coupled nonlinear differential equations of motion that are solved in the time domain with a fourth-order Runge-Kutta integration method. An assessment of the impact of flare and overhangs on motions is obtained by comparing these nonlinear solutions with solutions of the traditional linear equations of motion, which do not contain forces due to flare and overhangs. For an example based on an International America's Cup Class yacht design, it is found that the nonlinear heave and pitch motions are smaller than the linear motions. This is primarily due to reduced first-order response components, which are coupled with nonlinear response components. Comparisons of these results with towing tank data demonstrate that the nonlinear procedure improves prediction quality relative to linear results. In support of this numerical work, the hydrostatic and Froude­Krylov force integrals are expanded in Taylor series with respect to wave elevation. These results indicate how hydrostatic and Froude-Krylov forces change with changing flare and overhang angles, revealing that sectional slope has second and third-order effects on forces while sectional curvature and overhang angles produce third-order effects.

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.

A New Electrode Regulator System Identification of Arc Furnace Based on Time-Variant Nonlinear-Linear-Nonlinear Model

2016 ◽  
Vol 2 (1) ◽  
pp. 32
Author(s):  
Jinfeng Wang ◽  
Shoulin Yin ◽  
Xueying Wang
Keyword(s):  
Nonlinear Model ◽  
Model System ◽  
Time Varying ◽  
Arc Furnace ◽  
Identification Process ◽  
System Parameters ◽  
Online Identification ◽  
Arc Characteristics ◽  
Controlling System ◽  
The Mind

<p>In this paper, we express arc furnace electrode regulator system as a time-variant nonlinear-linear-nonlinear model. On this basis, we propose an online identification method based on nonlinear-linear-nonlinear model system. This new scheme solves the problem of model variation and prediction precision decline causing by time-varying of arc characteristic. In order to dispose the difficulty of parameters separation in the online identification process, this new method adopts the mind of update the parameters of linear parts and nonlinear parts respectively. It realizes the parameters separation of system effectively. Simulation results show that this method can track the changes of arc characteristics effectively. That it achieves the aim of real-time monitoring and controlling system parameters.</p>

Nonlinear Dynamic Modeling and Simulation of an Insect-Like Flapping Wing

2014 ◽  
Vol 555 ◽  
pp. 3-10 ◽  
Author(s):  
Afshin Banazadeh ◽  
Neda Taymourtash
Keyword(s):  
Modeling And Simulation ◽  
Reference Frames ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Added Mass ◽  
Open Loop ◽  
Flapping Wing ◽  
Loop Dynamics ◽  
Three Degree Of Freedom ◽  
Nonlinear Dynamic Modeling

The main objective of this paper is to present the modeling and simulation of open loop dynamics of a rigid body insect-like flapping wing. The most important aerodynamic mechanisms that explain the nature of the flapping flight, including added mass, rotational lift and delayed stall, are modeled. Wing flapping kinematics is described using appropriate reference frames and three degree of freedom for each wing with respect to the insect body. In order to simulate nonlinear differential equations of motion, 6DOF model of the insect-like flapping wing is developed, followed by an evaluation of the simulation results in hover condition.

Application of a Hilbert Transform-Based Algorithm for Parameter Estimation of a Nonlinear Ocean System Roll Model

1997 ◽  
Vol 119 (4) ◽  
pp. 239-243 ◽  
Author(s):  
O. Gottlieb ◽  
M. Feldman
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Model ◽  
Hilbert Transform ◽  
Random Noise ◽  
Nonlinear Damping ◽  
Model System ◽  
Field Calibration ◽  
Calibration Test ◽  
Fishing Boat ◽  
Backbone Curves

We combine an averaging procedure with a Hilbert transform-based algorithm for parameter estimation of a nonlinear ocean system roll model. System backbone curves obtained from data are compared to those obtained analytically and are found to be accurate. Sensitivity of the results is tested by introducing random noise to a nonlinear model describing roll response of a small fishing boat. An example field calibration test of a small semisubmersible exhibiting nonlinear damping is also considered.

Effects of Tip Mass and Interaction Force on Nonlinear Behavior of Force Modulation FM-AFM Cantilever

2016 ◽  
Vol 33 (2) ◽  
pp. 257-268 ◽  
Author(s):  
K. E. Torkanpouri ◽  
H. Zohoor ◽  
M. H. Korayem
Keyword(s):  
Frequency Shift ◽  
Nonlinear Model ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
Interaction Force ◽  
Beam Model ◽  
Frequency Shifts ◽  
Excitation Mode ◽  
Force Modulation ◽  
Tip Mass

AbstractInfluences of the tip mass, excitation mode of Frequency Modulated Atomic Force Microscope (FM-AFM) on the resonance frequency shift in force modulation (FM) mode are studied. Governing equations of motion are determined based on Timoshenko beam model with concentrated end mass. Approach point and base amplitude are set such that the FM-AFM remains just in FM mode. Either the linearized and nonlinear Derjaguin-Muller-Toporov (DMT) model are investigated. Then frequency shifts are determined for various interaction force regimes. It is showed the effect of tip mass on frequency shift is significant even for small tips. Nonlinear model shows lower frequency shifts in comparison with linearized model. It is showed that the amplitude of response is increased by increasing the tip mass and order of base excitation. Deviation of frequency shift between linearized and nonlinear solution are studied. It is declared that the error between linearized and nonlinear model is complicated. A deviation index is used for explaining behavior of error while tip mass and excitation mode are changed. It is showed, this index predicts the trend of error in all excitation modes and force cases. Behavior of system is linearizing by increasing the order of excitation, generally.

Torquewhirl—A Theory to Explain Nonsynchronous Whirling Failures of Rotors With High-Load Torque

1978 ◽  
Vol 100 (2) ◽  
pp. 235-240
Author(s):  
J. M. Vance
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
High Power ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Rotating Machinery ◽  
High Load ◽  
Driving Mechanism ◽  
Load Torque ◽  
Driving Torque

Numerous unexplained failures of rotating machinery by nonsynchronous shaft whirling point to a possible driving mechanism or source of energy not identified by previously existing theory. A majority of these failures have been in machines characterized by overhung disks (or disks located close to one end of a bearing span) and/or high power and load torque. This paper gives exact solutions to the nonlinear differential equations of motion for a rotor having both of these characteristics and shows that high ratios of driving torque to damping can produce nonsynchronous whirling with destructively large amplitudes. Solutions are given for two cases: (1) viscous load torque and damping, and (2) load torque and damping proportional to the second power of velocity (aerodynamic case). Criteria are given for avoiding the torquewhirl condition.

Stability of the High-Speed Journal Bearing Under Steady Load: 1—The Incompressible Film

1962 ◽  
Vol 84 (3) ◽  
pp. 351-357 ◽  
Author(s):  
M. M. Reddi ◽  
P. R. Trumpler
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Orbital Motion ◽  
Hydrodynamic Force ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Static Equilibrium ◽  
The Stability ◽  
External Loads ◽  
Steady Load

The phenomenon of oil-film whirl in bearings subjected to steady external loads is analyzed. The journal, assumed to be a particle mass, is subjected to the action of two forces; namely, the external load acting on the bearing and the hydrodynamic force developed in the fluid film. The resulting equations of motion for a full-film bearing and a 180-deg partial-film bearing are developed as pairs of second-order nonlinear differential equations. In evaluating the hydrodynamic force, the contribution of the shear stress on the journal surface is found to be negligible for the full-film bearing, whereas for the partial-film bearing it is found to be significant at small attitude values. The equations of motion are linearized and the coefficients of the resulting characteristic equations are studied for the stability of the static-equilibrium positions. The full-film bearing is found to have no stable static-equilibrium position, whereas the 180-deg partial-film bearing is found to have stable static-equilibrium positions under certain parametric conditions. The equations of motion for the full-film bearing are integrated numerically on a digital computer. The results show that the journal center, depending on the parametric conditions, acquired either an orbital motion or a dynamical path of increasing attitude terminating in bearing failure.

Application of GDQ method in nonlinear analysis of a flexible manipulator undergoing large deformation

2013 ◽  
Vol 227 (12) ◽  
pp. 2671-2685 ◽  
Author(s):  
Mohammad R Fazel ◽  
Majid M Moghaddam ◽  
Javad Poshtan
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equation ◽  
Flexible Manipulator ◽  
Runge Kutta Method ◽  
Highly Nonlinear ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Generalized Differential

Analysis of a flexible manipulator as an initial value problem, due to its large deformations, involves nonlinear ordinary differential equations of motion. In the present work, these equations are solved through the general Frechet derivatives and the generalized differential quadrature (GDQ) method directly. The results so obtained are compared with those of the fourth-order Runge–Kutta method. It is seen that both the results match each other well. Further considering the same manipulator as a boundary value problem, its governing equation is a highly nonlinear partial differential equation. Again applying the general Frechet derivatives and the GDQ method, it is seen that the results are in good match with the linear theory. In both cases, the general Frechet derivatives are introduced and successfully used for linearization. The results of the present study indicate that the GDQ method combined with the general Frechet derivatives can be successfully used for the solution of nonlinear differential equations.

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