scholarly journals Application of Variational Iteration Method for Dropping Damage Evaluation of the Suspension Spring Packaging System

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Shuang Song ◽  
Ning-ning Duan ◽  
An-jun Chen
Keyword(s):  
Iteration Method ◽  
Duffing Oscillator ◽  
Variational Iteration Method ◽  
Physical Parameters ◽  
Damage Evaluation ◽  
Damage Potential ◽  
Packaging System ◽  
Suspension Spring ◽  
Safe Region ◽  
Boundary Curves

The dropping damage evaluation for packaging system is essential for safe transportation and storage. A dynamic model of nonlinear cubic-quintic Duffing oscillator for the suspension spring packaging system was proposed. Then, a first-order approximate solution was obtained by applying He’s variable iteration method. Based on the results, a damage evaluation equation was derived, which reveals the main controlling physical parameters for damage potential of drop to packaged products concretely. Finally, the dropping damage boundary curves and surfaces for the system were discussed. It was found that decreasing the suspension angle can improve the safe region of the system.

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.

The Damage Boundary Curve of the Suspension Packaging System under Rectangular Pulse

2011 ◽  
Vol 105-107 ◽  
pp. 70-73 ◽  
Author(s):  
Lei Wang ◽  
An Jun Chen
Keyword(s):  
Damping Ratio ◽  
Boundary Curve ◽  
Rectangular Pulse ◽  
Three Dimension ◽  
Dynamical Equations ◽  
Packaging System ◽  
Suspension Spring ◽  
Runge Kutta Method ◽  
Safe Region ◽  
Boundary Curves

The geometric nonlinear dimensionless dynamical equations of suspension spring cushioning packaging system were established and a new concept of damage boundary curves of the system was developed under the action of rectangular pulse. Considering the angle of the suspension spring ,a three-dimension damage boundary curve is obtained.The mathematic results of the equation are calculated by using the four steps Runge-Kutta method. Studies have shown that the dimensionless pulse peak, the angle of suspension spring and the damping ratio of the system can affect the safe region, and that increasing damping can enlarge the safe region of the system. The shock of the packed product can reduce by adjusting the parameters of the system properly. These results have important application value in design of the suspension cushioning system.

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 Study of the Nonlinear Dropping Shock Response of Expanded Foam Packaging System

2013 ◽  
Vol 2013 ◽  
pp. 1-3
Author(s):  
Huan-xin Jiang ◽  
Yong Zhu ◽  
Li-xin Lu
Keyword(s):  
Numerical Simulation ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Equation Of Motion ◽  
High Accuracy ◽  
Packaging System ◽  
First Order ◽  
Approximate Analytical Solutions ◽  
Shock Response

The variational iteration method-2 (VIM-2) is applied to obtain approximate analytical solutions of EPS foam cushioning packaging system. The first-order frequency solution of the equation of motion was obtained and compared with the numerical simulation solution solved by the Runge-Kutta algorithm. The results showed the high accuracy of this VIM with convenient calculation.

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.

Predicting the Temperature Distribution in Longitudinal Fins of Various Profiles with Power Law Thermal Properties Using the Variational Iteration Method

2018 ◽  
Vol 387 ◽  
pp. 403-416 ◽  
Author(s):  
Luyanda Partner Ndlovu ◽  
Raseelo Joel Moitsheki
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Properties ◽  
Temperature Distribution ◽  
Power Law ◽  
Iteration Method ◽  
Group Analysis ◽  
Variational Iteration Method ◽  
Physical Parameters ◽  
Variational Iteration

In this article, the variational iteration method (VIM) is used to analyze heat transfer in longitudinal fins of various profiles with temperature dependent thermal conductivity and heat transfer coefficient. In order to show the efficiency of the VIM, the results obtained using the VIM are compared with the previously obtained results using the differential transform method (DTM) and Lie group analysis of a fin problem with the rectangular profile. After establishing confidence in VIM, heat transfer is analyzed to determine the temperature profiles in longitudinal fins of various profiles with power law thermal properties. The temperature distribution is compared between various profiles. The effects of some physical parameters such as the thermo-geometric fin parameter and thermal conductivity gradient on temperature distribution are illustrated.

Dropping damage evaluation for a hyperbolic tangent cushioning system with a critical component

2011 ◽  
Vol 18 (10) ◽  
pp. 1417-1421 ◽  
Author(s):  
Jun Wang ◽  
Fang Duan ◽  
Jiu-hong Jiang ◽  
Li-xin Lu ◽  
Zhi-wei Wang
Keyword(s):  
Boundary Surface ◽  
Frequency Parameter ◽  
Damage Evaluation ◽  
Critical Component ◽  
Hyperbolic Tangent ◽  
Damage Potential ◽  
Packaging System ◽  
System A ◽  
Parameter Ratio ◽  
Good Agreement

A new concept of dropping damage boundary surface is proposed to evaluate the dropping damage of a critical component for a hyperbolic tangent nonlinear packaging system. A novel dynamic model is established to analyze the effect of three key coordinate parameters, i.e., the non-dimensional dropping shock velocity, the frequency parameter ratio and the defined system parameter, on dropping damage potential. An experiment, which showed good agreement, was conducted to verify the theory proposed.

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 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.

Sign in / Sign up

Export Citation Format

Share Document