scholarly journals To the theory of synchronization of interacting pendulums oscillating in the parallel planes

2020 ◽  
Vol 20 (1) ◽  
pp. 15-37
Author(s):  
S.O. Gladkov ◽  
◽  
S.B. Bogdanova ◽  
Keyword(s):  
Numerical Solution ◽  
Complex Plane ◽  
Nonlinear Dynamic ◽  
Functional Equations ◽  
Electromagnetic Interaction ◽  
Theta Functions ◽  
Addition Theorem ◽  
Physical Factors ◽  
Motion Equations ◽  
Dynamic Motion

The problem of interacting metal pendulums oscillating in parallel planes, the distance $b$ between the suspension points of which is fixed and equally, has been solved. The principle possibility of their synchronization is provided by taking into account two physical factors: 1. Effect of electromagnetic interaction between them and 2. Accounting for EM radiation of each pendulum, leading to non-linear attenuation. The system of nonlinear dynamic motion equations obtained by a strict mathematical path is analyzed, and their numerical solution is given. The article offers a new method for constructing the pairs of function which are holomorphic on the whole complex plane and satisfy functional equations such as the addition theorem for theta functions.

FINITE DIFFERENCE METHOD FOR SOLVING THE NONLINEAR DYNAMIC EQUATION OF UNDERWATER TOWED SYSTEM

2014 ◽  
Vol 11 (04) ◽  
pp. 1350060 ◽  
Author(s):  
ZHIJIANG YUAN ◽  
LIANGAN JIN ◽  
WEI CHI ◽  
HENGDOU TIAN
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Computational Time ◽  
Algebraic Equations ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Dynamic Equations

A wide body of work exists that describes numerical solution for the nonlinear system of underwater towed system. Many researchers usually divide the tow cable with less number elements for the consideration of computational time. However, this type of installation affects the accuracy of the numerical solution. In this paper, a newly finite difference method for solving the nonlinear dynamic equations of the towed system is developed. The mathematical model of tow cable and towed body are both discretized to nonlinear algebraic equations by center finite difference method. A newly discipline for formulating the nonlinear equations and Jacobian matrix of towed system are proposed. We can solve the nonlinear dynamic equation of underwater towed system quickly by using this discipline, when the size of number elements is large.

Chaotic Vibration of Fractional Calculus Model Viscoelastic Arch

2014 ◽  
Vol 668-669 ◽  
pp. 151-155
Author(s):  
Fan Huang ◽  
Jun Huang ◽  
Shao Bin Dai
Keyword(s):  
Fractional Calculus ◽  
Forced Vibration ◽  
Periodic Motion ◽  
Nonlinear Dynamic ◽  
Material Parameter ◽  
Load Parameter ◽  
Motion Equations ◽  
Dynamic Behaviors ◽  
Chaotic Vibration ◽  
The Stability

Nonlinear dynamic behaviors of the fractional calculus model viscoelastic arch are discussed in this paper. The motion equations governing dynamic behaviors of the viscoelastic arch is derived and simplified by Galerkin method. The numerical method for solving the motion equations with fractional calculus is presented here. The influences of the load parameter and the material parameter are considered respectively. The results show that the chaotic vibration of the arch appears in forced vibration. And both the load parameter and the material parameter affect the dynamic behavior of the arch. With the increasing of the load parameter, the motion states changed from periodic motion with period 1 to complex motions, such as mult-periodicity, quasi-periodicity or chaos. The increasing of the material parameter benefits the stability of the structures.

scholarly journals PECULIARITIES OF ELECTROMAGNETIC FILTER OPERATION IN PENNING SOURCE WITH METAL HYDRIDE CATHODE

2020 ◽  
pp. 111-114
Author(s):  
I. Sereda ◽  
Ya. Hrechko ◽  
Ie. Babenko ◽  
A. Kashaba
Keyword(s):  
Numerical Solution ◽  
Experimental Verification ◽  
Metal Hydride ◽  
Charged Particles ◽  
Axial Flow ◽  
Axial Direction ◽  
Hydrogen Ions ◽  
Optimal Parameters ◽  
Motion Equations ◽  
Filter Operation

The paper describes a method of negative hydrogen ions separation from axial flow of charged particles extracted from Penning discharge with a metal hydride cathode. For this purpose, an electromagnetic filter has been designed basing on numerical solution of motion equations of charged particles in the filter. The optimal parameters of the filter operation were determined for the effective registration of negative hydrogen ions extracted in axial direction. Performed calculations together with experimental verification shows that there are not more than 10% electrons in the registered H– current. This model could be applied for the interpretation of any experiments with H– ions separation from an axial flow of charged particles extracted from a source with cylindrical geometry.

scholarly journals Finite Element Modelling and Simulating Effects of Hairiness Performance on Hairiness Entanglement During Fabric Pilling

2021 ◽  
Author(s):  
Qi Xiao ◽  
Rui Wang ◽  
Hongyu Sun ◽  
Jingru Wang
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
Strain Energy ◽  
Dissipation Energy ◽  
Motion Equations ◽  
Dynamic Motion ◽  
Element Simulation ◽  
Frictional Dissipation ◽  
Simulation Results ◽  
Good Agreement

Abstract For analyzing behaviors of hairiness entanglement during fabric pilling, nonlinear dynamic motion equations are deduced based on the elastic thin rod element, combined with the moving characteristics of hairiness, which follow the principles of mechanical equilibrium and energy conservation. The finite element simulation model of the effects of hairiness performance on behaviors of hairiness entanglement was established by ABAQUS. The analysis solution values of nonlinear dynamics were compared with the finite element simulation results. The results showed that hairiness elastic modulus, hairiness friction coefficient and hairiness diameter have significant effects on frictional dissipation energy, strain energy and kinetic energy produced by hairiness entanglement during pilling. Compared the finite element simulation results with analysis solution values, they are in good agreement. The fitness is greater than 0.96, which verifies the validity of finite element method.

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