Research on Nonlinear Dynamics of Liquid Sloshing in Rrectangular Ttank

2011 ◽  
Vol 66-68 ◽  
pp. 1695-1702
Author(s):  
Yi Tang ◽  
Xiao Ping Zhu ◽  
Min Chang ◽  
Zhou Zhou
Keyword(s):  
Nonlinear Dynamics ◽  
Variational Principle ◽  
Free Boundary ◽  
Liquid Sloshing ◽  
Free Boundary Value Problem ◽  
Kutta Method ◽  
Modal System ◽  
Nonlinear Characteristics ◽  
Infinite Dimensional ◽  
Runge Kutta Method

Based on the assumption of ideal fluid, this paper both employed modes method and pressure variational principle to transfer free boundary value problem describing liquid nonlinear sloshing into infinite dimensional modal system integrated by Runge-Kutta method. The results shows that nonlinear characteristics of liquid sloshing in rectangular tank.

Application of the piecewise constant method in nonlinear dynamics of drill string

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jialin Tian ◽  
Jie Wang ◽  
Yi Zhou ◽  
Lin Yang ◽  
Changyue Fan ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Drill String ◽  
Vibration Velocity ◽  
Kutta Method ◽  
Time Step ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Abstract Aiming at the current development of drilling technology and the deepening of oil and gas exploration, we focus on better studying the nonlinear dynamic characteristics of the drill string under complex working conditions and knowing the real movement of the drill string during drilling. This paper firstly combines the actual situation of the well to establish the dynamic model of the horizontal drill string, and analyzes the dynamic characteristics, giving the expression of the force of each part of the model. Secondly, it introduces the piecewise constant method (simply known as PT method), and gives the solution equation. Then according to the basic parameters, the axial vibration displacement and vibration velocity at the test points are solved by the PT method and the Runge–Kutta method, respectively, and the phase diagram, the Poincare map, and the spectrogram are obtained. The results obtained by the two methods are compared and analyzed. Finally, the relevant experimental tests are carried out. It shows that the results of the dynamic model of the horizontal drill string are basically consistent with the results obtained by the actual test, which verifies the validity of the dynamic model and the correctness of the calculated results. When solving the drill string nonlinear dynamics, the results of the PT method is closer to the theoretical solution than that of the Runge–Kutta method with the same order and time step. And the PT method is better than the Runge–Kutta method with the same order in smoothness and continuity in solving the drill string nonlinear dynamics.

scholarly journals Investigation of the Effect of Additive White Noise on the Dynamics of Contact Interaction of the Beam Structure

2019 ◽  
Author(s):  
Ольга Салтыкова ◽  
Olga Saltykova ◽  
Александр Кречин ◽  
Alexander Krechin
Keyword(s):  
Nonlinear Dynamics ◽  
White Noise ◽  
Contact Interaction ◽  
Geometric Nonlinearity ◽  
Chaotic Dynamics ◽  
Kutta Method ◽  
Beam Structure ◽  
Runge Kutta Method ◽  
Additive White Noise ◽  
The Finite Difference Method

The purpose of this work is to study and scientific visualization the effect of additive white noise on the nonlinear dynamics of beam structure contact interaction, where beams obey the kinematic hypotheses of the first and second approximation. When constructing a mathematical model, geometric nonlinearity according to the T. von Karman model and constructive nonlinearity are taken into account. The beam structure is under the influence of an external alternating load, as well as in the field of additive white noise. The chaotic dynamics and synchronization of the contact interaction of two beams is investigated. The resulting system of partial differential equations is reduced to a Cauchy problem by the finite difference method and then solved by the fourth order Runge-Kutta method.

On the Harmonic Oscillations for the Motion of a Dynamical System

2017 ◽  
Vol 13 (2) ◽  
pp. 4657-4670
Author(s):  
W. S. Amer
Keyword(s):  
Dynamical System ◽  
Numerical Solutions ◽  
Equation Of Motion ◽  
Parameter Method ◽  
Kutta Method ◽  
Small Parameter Method ◽  
Harmonic Oscillations ◽  
Pivot Point ◽  
Runge Kutta Method ◽  
High Consistency

This work touches two important cases for the motion of a pendulum called Sub and Ultra-harmonic cases. The small parameter method is used to obtain the approximate analytic periodic solutions of the equation of motion when the pivot point of the pendulum moves in an elliptic path. Moreover, the fourth order Runge-Kutta method is used to investigate the numerical solutions of the considered model. The comparison between both the analytical solution and the numerical ones shows high consistency between them.

Numerical Approximations to Solution of Biochemical Reaction Model

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Ahmet Gökdogan ◽  
Mehmet Merdan
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Transformation Method ◽  
Reaction Model ◽  
Biochemical Reaction ◽  
Graphical Form ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.

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