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.

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 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.

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.

scholarly journals Application of Variational Iteration Method with Energy Method for Nonlinear Equation Arisen from Packaging System

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
An-Jun Chen
Keyword(s):  
Energy Method ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Extended Period ◽  
New Method ◽  
Maximum Displacement ◽  
Maximum Acceleration ◽  
Packaging System ◽  
Variational Iteration ◽  
Runge Kutta Method

The variational iteration method (VIM) is widely applied for solving various kinds of nonlinear equations. Despite its simplicity and effectiveness, the accuracy of the method may depend on the iteration steps. However, the more iteration steps one makes, the more complex the results may become. To overcome this shortcoming, a new method combining the VIM with energy method (EM) is proposed and applied to study the nonlinear response of cubic packaging system. The analytical expressions of the important parameters such as the maximum displacement response, the maximum acceleration response of the system, the extended period of the shock, and the conditions for inner resonance of system were obtained. The results show that the maximum of the acceleration and the displacement and the extended period of the shock got by this method are very similar to the ones got by Runge-Kutta method. The result provides the new method for the dropping shock problem of nonlinear packaging system.

scholarly journals Application of He’s Variational Iteration Method to Nonlinear Integro-Differential Equations

2010 ◽  
Vol 65 (5) ◽  
pp. 418-430 ◽  
Author(s):  
Ahmet Yildirim
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Mathematical Tool ◽  
Variational Iteration ◽  
He’S Variational Iteration Method ◽  
Powerful Mathematical Tool

In this paper, an application of He’s variational iteration method is applied to solve nonlinear integro-differential equations. Some examples are given to illustrate the effectiveness of the method. The results show that the method provides a straightforward and powerful mathematical tool for solving various nonlinear integro-differential equations

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