scholarly journals Entropy and irreversibility for a single isolated two level system: New individual quantum states and new nonlinear equation of motion

1985 ◽  
Vol 24 (2) ◽  
pp. 119-134 ◽  
Author(s):  
Gian Paolo Beretta
Keyword(s):  
Nonlinear Equation ◽  
Equation Of Motion ◽  
Quantum States ◽  
Level System

Nonlinear Vibrations of a Hinged Beam Including Nonlinear Inertia Effects

1973 ◽  
Vol 40 (1) ◽  
pp. 121-126 ◽  
Author(s):  
S. Atluri
Keyword(s):  
Nonlinear Equation ◽  
Nonlinear Vibrations ◽  
Initial Conditions ◽  
Equation Of Motion ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Nonlinear Ordinary Differential Equations ◽  
Inertia Effects ◽  
Modal Expansion ◽  
General Response

This investigation treats the large amplitude transverse vibration of a hinged beam with no axial restraints and which has arbitrary initial conditions of motion. Nonlinear elasticity terms arising from moderately large curvatures, and nonlinear inertia terms arising from longitudinal and rotary inertia of the beam are included in the nonlinear equation of motion. Using a Galerkin variational method and a modal expansion, the problem is reduced to a system of coupled nonlinear ordinary differential equations which are solved for arbitrary initial conditions, using the perturbation procedure of multiple-time scales. The general response and frequency-amplitude relations are derived theoretically. Comparison with previously published results is made.

ASYMPTOTIC NUMERICAL METHOD FOR THE DYNAMIC STUDY OF NONLINEAR VIBRATION ABSORBERS

2014 ◽  
Vol 06 (05) ◽  
pp. 1450053 ◽  
Author(s):  
FATHI DJEMAL ◽  
FAKHER CHAARI ◽  
JEAN LUC DION ◽  
FRANCK RENAUD ◽  
IMAD TAWFIQ ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Vibration Control ◽  
Numerical Method ◽  
Nonlinear Vibration ◽  
Degrees Of Freedom ◽  
Equation Of Motion ◽  
Vibration Absorbers ◽  
Asymptotic Numerical Method ◽  
Dynamic Absorber ◽  
Newton Raphson

Vibrations are usually undesired phenomena as they may cause discomfort, disturbance, damage, and sometimes destruction of machines and structures. It must be reduced or controlled or eliminated. One of the most common methods of vibration control is the use of the dynamic absorber. The paper is interested in the study of a nonlinear two degrees of freedom (DOF) model. To solve nonlinear equation of motion a high order implicit algorithm is proposed. It is based on the introduction of a homotopy, an implicit scheme of Newmark and the use of techniques of Asymptotic Numerical method (ANM). We propose also a regularization of the contact force to overcome the difficulty of the singularity in this model. A comparison will be presented between the results obtained by the proposed algorithm and those using the classical Newton–Raphson and Newmark time scheme.

Self-Excited Vibration Model of Dragonfly’s Wing Based on the Concept of Bionic Design for Small- or Micro-Sized Actuators

1997 ◽  
Author(s):  
Sagiri Ishimoto ◽  
Hiromu Hashimoto
Keyword(s):  
Nonlinear Equation ◽  
Driving Forces ◽  
Stable Limit Cycle ◽  
Equation Of Motion ◽  
Stable Limit ◽  
Bionic Design ◽  
Wing Vibration ◽  
Vibration Model ◽  
Excited Vibration ◽  
Sympetrum Frequens

Abstract This paper describes a self-excited vibration model of dragonfly’s wing based on the concept of bionic design, which is expected as a technological hint to solve the scale effect problems in developing the small- or micro-sized actuators. From a morphological consideration of flight muscle of dragonfly, the nonlinear equation of motion for the wing considering the air drag force due to flapping of wing is formulated. In the model, the dry friction-type and Van der Pol-type driving forces are employed to power the flight muscles and to generate the stable self-excited wing vibration. Two typical Japanese dragonflies, “Anotogaster sieboldii Selys” and “Sympetrum frequens Selys”, are selected as examples, and the self-excited vibration analyses for these dragonfly’s wings are demonstrated. The linearized solutions for the nonlinear equation of motion are compared with the nonlinear solutions, and the vibration system parameters to generate the stable limit cycle of self-excited wing vibration are determined.

Nonlinear Response of Marine Riser with Large Displacement Excited by Top-End Vessel Motion using Penalty Method

2020 ◽  
Vol 20 (04) ◽  
pp. 2050052 ◽  
Author(s):  
Karun Klaycham ◽  
Chainarong Athisakul ◽  
Somchai Chucheepsakul
Keyword(s):  
Nonlinear Equation ◽  
Nonlinear Dynamic ◽  
Oscillation Frequency ◽  
Penalty Method ◽  
Equation Of Motion ◽  
Ocean Current ◽  
Computational Time ◽  
Response Analysis ◽  
Marine Riser ◽  
Vessel Motion

A marine riser operated in a deep-water field could be substantially affected by large amounts of movement of the floating platform, which is more complicated and very challenging to analyze. This paper presents a mathematical model involving nonlinear dynamic response analysis of a marine riser caused by sways and heave motions at the top end, which are treated as the constraint conditions. The nonlinear equation of motion, arising from the nonlinearity of the ocean current and wave loadings, is derived and written in general matrix form using the finite element method. The excitation caused by platform movement is imposed on the riser system through the time-dependent constrained condition using the penalty method. The advantages of this method are that it is easily implemented on the nonlinear equation of motion and it requires no additional unknown variable, and thus consumes less computational time. By this method, the stiffness matrix and the force vector of the system are then modified, enforcing top-end vessel motion. The dynamic responses are evaluated by using numerical time integration based on Newmark’s method with direct iteration. The effects of the oscillation frequency of top-end vessel sway and heave motions on the nonlinear dynamic characteristics of the riser are investigated. The numerical results reveal that the riser responses to the top-end vessel excitation behave like a periodic motion, which is conformable to the characteristics of vessel movements. The increase in the oscillation frequency of the top-end vessel increases the maximum displacement amplitude for both the horizontal and vertical directions. The directional motion of the vessel also significantly influences the response amplitude of the riser.

scholarly journals NONSTATIC AdS2 BRANES AND THE ISOMETRY GROUP OF AdS3 SPACE–TIME

2002 ◽  
Vol 17 (06) ◽  
pp. 309-318 ◽  
Author(s):  
SHIJONG RYANG
Keyword(s):  
Nonlinear Equation ◽  
Isometry Group ◽  
Outer Automorphism ◽  
Static Solution ◽  
Equation Of Motion ◽  
Space Time ◽  
Cylindrical Coordinates

For the D-branes on the SL (2,R) WZW model we present a particular choice of outer automorphism for the gluing condition of currents that leads to a special AdS2 brane configuration. This configuration is shown to be a static solution in the cylindrical coordinates, and a nonstatic solution in the Poincaré coordinates to the nonlinear equation of motion for the Dirac–Born–Infeld action of a D-string. The generalization of it gives a family of nonstatic AdS2 brane solutions. They are demonstrated to transform to each other under the isometry group of AdS3 space–time.

scholarly journals Boussinesq Solitons as Propagators of Neural Signals

2018 ◽  
Vol 3 (1) ◽  
pp. 120 ◽  
Author(s):  
Edgar Villagran Vargas ◽  
Juan Ramón Collantes C. ◽  
Máximo A. Agüero Granados
Keyword(s):  
Nonlinear Equation ◽  
Linear Equation ◽  
Boussinesq Equation ◽  
Equation Of Motion ◽  
Simplified Model ◽  
Melting Transition ◽  
Single Neurons ◽  
Neural Signals ◽  
Non Linear Equation ◽  
Lipid Melting

We  consider  certain  approximation for determining the  equation  of motion  for nerve  signals by  using  the  model  of the  lipid  melting  of membranes.   The  nerve  pulses  are  found  to  display nonlinearity and  dispersion  during  the  melting  transition.  In this  simplified model the  nonlinear equation  early  proposed  by  Heimburg  and  coworkers  transformed to  the  well known  integrable Boussinesq  non linear  equation.   Under  specific values of the  parametric space this  system  shows the  existence  of singular  and  regular  soliton  like structures.   After  their  collisions  the  mutual creation  and annihilation (each other)  of nerve signals along the  nerve,  during  their  propagation, has been observed.Keywords: Boussinesq equation,  singular  solitons,  single neurons,  neural  code.

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