scholarly journals Resonance Analysis for Tilted Support Spring Coupled Nonlinear Packaging System Applying Variational Iteration Method

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
An-Jun Chen
Keyword(s):  
Approximate Solution ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Dynamical Equations ◽  
Packaging System ◽  
Nonlinear Dynamical ◽  
Packaging Design ◽  
Resonance Analysis ◽  
Variational Iteration ◽  
Critical Components

The coupled nonlinear dynamical equations were developed for a tilted spring packaging system with critical components. The approximate solution and resonance conditions of system were obtained applying a variational iteration method. The resonance conditions, which should be avoided in the packaging design, can be easily obtained by VIM.

Inner-Resonance for a Coupled Oscillator Arising in a Cubic Nonlinear Packaging System with Critical Component

2011 ◽  
Vol 66 (10-11) ◽  
pp. 692-695
Author(s):  
Jun Wang ◽  
Fang Duan ◽  
Rui-Hua Yang ◽  
Zheng-Biao Li ◽  
Li-Xin Lu ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Critical Component ◽  
Coupled Oscillator ◽  
Packaging System ◽  
Packaging Design ◽  
Variational Iteration

In this paper, a dynamic model was proposed for a cushioning packaging system. Conditions for resonance were obtained by applying the variational iteration method (VIM), which should be avoided in the cushioning packaging design.

scholarly journals Inner-Resonance Conditions for Honeycomb Paperboard Cushioning Packaging System with Critical Component

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Jun Wang ◽  
Zhi-geng Fan ◽  
Xiang Hong ◽  
Li-xin Lu
Keyword(s):  
Dynamic Model ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Critical Component ◽  
Packaging System ◽  
Packaging Design ◽  
Coupled Equations ◽  
Variational Iteration

A dynamic model was proposed for a honeycomb paperboard cushioning packaging system with critical component. Then the coupled equations of the system were solved by the variational iteration method, from which the conditions for inner-resonance were obtained, which should be avoided in the cushioning packaging design.

scholarly journals The Approximate Solution of Fractional Fredholm Integrodifferential Equations by Variational Iteration and Homotopy Perturbation Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Abdelouahab Kadem ◽  
Adem Kilicman
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Perturbation Methods ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Constant Coefficients

Variational iteration method and homotopy perturbation method are used to solve the fractional Fredholm integrodifferential equations with constant coefficients. The obtained results indicate that the method is efficient and also accurate.

scholarly journals Variational Iteration Method for Solving the Generalized Degasperis-Procesi Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Qian Lijuan ◽  
Tian Lixin ◽  
Ma Kaiping
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Initial Approximation ◽  
Variational Iteration Method ◽  
Original Equation ◽  
Variational Iteration

We introduce the variational iteration method for solving the generalized Degasperis-Procesi equation. Firstly, according to the variational iteration, the Lagrange multiplier is found after making the correction functional. Furthermore, several approximations ofun+1(x,t)which is converged tou(x,t)are obtained, and the exact solutions of Degasperis-Procesi equation will be obtained by using the traditional variational iteration method with a suitable initial approximationu0(x,t). Finally, after giving the perturbation item, the approximate solution for original equation will be expressed specifically.

scholarly journals Approximate Solution of Linear Fuzzy Initial Value Problems Using Modified Variaional Iteration Method

2021 ◽  
Vol 24 (4) ◽  
pp. 32-39
Author(s):  
Hussein M. Sagban ◽  
◽  
Fadhel S. Fadhel ◽  
Keyword(s):  
Approximate Solution ◽  
Rate Of Convergence ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

The main objective of this paper is to solve fuzzy initial value problems, in which the fuzziness occurs in the initial conditions. The proposed approach, namely the modified variational iteration method, will be used to find the solution of fuzzy initial value problem approximately and to increase the rate of convergence of the variational iteration method. From the obtained results, as it is expected, the approximate results of the proposed method are more accurate than those results obtained without using the modified variational iteration method.

scholarly journals Application of the Variational Iteration Method to Strongly Nonlinear -Difference Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Hsuan-Ku Liu
Keyword(s):  
Approximate Solution ◽  
Time Scales ◽  
Difference Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Numerical Results ◽  
Series Solutions ◽  
Nonlinear Difference Equations ◽  
Strongly Nonlinear ◽  
Variational Iteration

The theory of approximate solution lacks development in the area of nonlinear -difference equations. One of the difficulties in developing a theory of series solutions for the homogeneous equations on time scales is that formulas for multiplication of two -polynomials are not easily found. In this paper, the formula for the multiplication of two -polynomials is presented. By applying the obtained results, we extend the use of the variational iteration method to nonlinear -difference equations. The numerical results reveal that the proposed method is very effective and can be applied to other nonlinear -difference equations.

scholarly journals Variational Iteration Method of Dropping Shock Response for the Suspension Spring Packaging System

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Shuang Song ◽  
An-Jun Chen
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Extended Period ◽  
Packaging System ◽  
Suspension Spring ◽  
Variational Iteration ◽  
Nonlinear Dynamic Equation ◽  
Runge Kutta Method ◽  
Spring System ◽  
Relative Errors

In accordance with dropping shock dimensionless cubic nonlinear dynamic equation of suspension spring system, by variational iteration method, a first-order approximate solution of the system was obtained. The nondimensional peak of displacement, the nondimensional peak of acceleration, and the dropping shock extended period were compared with the results of the Runge-Kutta method, at which relative errors were less than 4%. The influence of suspension angle on peaks of response were discussed. It shows that the maximum response nondimensional acceleration decreases with decrease of the suspension angle under condition of the same nondimensional dropping shock velocity. Conditions for resonance were obtained by applying the variational iteration method, which should be avoided in the packaging design. The results provide reference for suspension spring system design.

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