The Analysis of the Dynamic Behavior of the Nonlinear Oscillations of a Fluttering Plate Based on the Periodicity Ratio Method

2012 ◽  
Author(s):  
Liming Dai ◽  
Xiaojie Wang
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Oscillation ◽  
Nonlinear Oscillations ◽  
Ratio Method ◽  
Kutta Method ◽  
Governing Equations ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Runge Kutta Method ◽  
Runge Kutta

In this paper, an investigation of the dynamic behavior of a fluttering plate is performed. The governing equations of the nonlinear oscillation derived using Galerkin’s method are presented and solved numerically by the Runge-Kutta method. Four modes are used for accurate results. The periodicity ratio method is briefly introduced and applied to generate the region diagram for the motion of the plate. The corresponding motions under different parameters following the region diagram are illustrated. The results demonstrate the efficiency and accuracy of periodicity ratio method.

scholarly journals Dynamic behavior of sail tower SPS based on the symplectic Runge-Kutta method

2016 ◽  
Vol 46 (12) ◽  
pp. 1242-1253
Author(s):  
ZiChen DENG ◽  
ShanShan CAO ◽  
QingJun LI ◽  
XianHong JIANG
Keyword(s):  
Dynamic Behavior ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta

scholarly journals Spectral Fixed Point Method for Nonlinear Oscillation Equation with Periodic Solution

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Ding Xu ◽  
Xian Wang ◽  
Gongnan Xie
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Oscillation ◽  
Fixed Point Method ◽  
Point Method ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Linear Oscillation ◽  
Oscillation Equation

Based on the fixed point concept in functional analysis, an improvement on the traditional spectral method is proposed for nonlinear oscillation equations with periodic solution. The key idea of this new approach (namely, the spectral fixed point method, SFPM) is to construct a contractive map to replace the nonlinear oscillation equation into a series of linear oscillation equations. Usually the series of linear oscillation equations can be solved relatively easily. Different from other existing numerical methods, such as the well-known Runge-Kutta method, SFPM can directly obtain the Fourier series solution of the nonlinear oscillation without resorting to the Fast Fourier Transform (FFT) algorithm. In the meanwhile, the steepest descent seeking algorithm is proposed in the framework of SFPM to improve the computational efficiency. Finally, some typical cases are investigated by SFPM and the comparison with the Runge-Kutta method shows that the present method is of high accuracy and efficiency.

scholarly journals Generalized displacements and momenta formulations of an electromechanical plunger

2020 ◽  
Vol 15 (2) ◽  
pp. 173-184
Author(s):  
Tamás Szabó ◽  
László Rónai
Keyword(s):  
Differential Equations ◽  
Kutta Method ◽  
Governing Equations ◽  
Generalized Coordinates ◽  
Runge Kutta Method ◽  
Systems Of Differential Equations ◽  
Lumped Parameter ◽  
Extended Hamilton’S Principle ◽  
Generalized Displacements ◽  
Runge Kutta

This paper deals with four different derivations of the governing equations of a solenoid plunger with lumped-parameter. Energy-based modeling is employed with extended Hamilton's principle with independent generalized coordinates and generalized momenta in order to be applicable to composite Lagrange's equations. In the electromechanical models, displacements and charges are regarded to be generalized coordinates, mechanical momenta and flux linkages are the generalized momenta. The derived systems of differential equations are solved numerically with the Runge-Kutta method.

scholarly journals ANFIS based Machine Repair Model with Control Policies and Working Vacation

2019 ◽  
Vol 4 (6) ◽  
pp. 1522-1533
Author(s):  
Rachita Sethi ◽  
Amita Bhagat ◽  
Deepika Garg
Keyword(s):  
Fuzzy Inference ◽  
Minimum Cost ◽  
Transient State ◽  
Kutta Method ◽  
Governing Equations ◽  
Working Vacation ◽  
Inference System ◽  
Runge Kutta Method ◽  
Neuro Fuzzy ◽  
Runge Kutta

This study is concerned with the transient state analysis of M/M/1 machine repairable system consisting of M operating units. F-policy is quite useful to avoid the overloading of failed machines that arrive for repair in the system. The failed machines are repaired by a server that is susceptible to failure and follows the threshold recovery while being repaired. The server leaves for a vacation if there are no machines waiting in the system for the repair. Runge-Kutta method is implemented to solve the governing equations and evaluate the system's state probabilities. Cost function is also designed to determine the system’s minimum cost. In addition, the numerical outcomes acquired by the Runge-Kutta method are compared with the results generated by adaptive neuro-fuzzy inference system (ANFIS).

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.

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