In this paper, a dynamic model was proposed for a corrugated paperboard cushioning packaging system. The variational iteration method was applied and the multiplier was identified. The approximate solution for the nonlinear equations was obtained and compared with the numerical simulation results with ordinary differential equation solver in MATLAB, showing good agreement. Then resonance conditions were obtained, which should be avoided in the cushioning packaging design.
BurgessGJ (1988) Products fragility and damage boundary theory. Packaging Technology and Science15(10): 5–10.
2.
FarazNKhanYAustinF (2010) An alternative approach to differential-difference equations using the variational iteration method. Zeitschrift fur Naturforschung Section A65(12): 1055–1059.
3.
GanjiSSGanjiDDSfahaniMG (2010) Application of AFF and HPM to the systems of strongly nonlinear oscillation. Current Applied Physics10(5): 1317–1325.
4.
Gao D (1992) Theoretical study on cushioning performance and model of corrugated fiberboard. Master Thesis, Zhejiang University, Hangzhou, People’s Republic of China.
5.
GaoDXiDC (1995) The dynamic compressive property and the model of corrugated fiberboard. Packaging Engineering16(3): 5–10.
GeCF (2009) Application of finite element analysis to predict the critical top-load of a corrugated box. Journal of Applied Packaging Research3(3): 137–147.
8.
HeJH (1999) Variational iteration method - a kind of non-linear analytical technique: some examples. International Journal of Non-Linear Mechanics34699–708.
9.
HeJHWuGCAustinF (2010) The variational iteration method which should be followed. Nonlinear Science Letters A11–30.
10.
KimiaeifarASaidiARSohouliAR (2010) Analysis of modified Van der Pol's oscillator using He's parameter-expanding methods. Current Applied Physics10(1): 279–283.
11.
MalekiSAhmadiF (2010) Using expanded polystyrene as a seismic energy dissipation device. Journal of Vibration and Control17(10): 1481–1497.
12.
MehdipourIGanjiDDMozaffariM (2010) Application of the energy balance method to nonlinear vibrating equations. Current Applied Physics10(1): 104–112.
13.
NewtonRE (1968) Fragility Assessment Theory and Practice, Monterey CA: Monterey Research Laboratory, Inc.
14.
WangJWangDM (2011) Cushioning dynamic model for double-layer medium corrugated paperboard packaging system and damage evaluation. Journal of Functional Materials42173–174, 192.
15.
WangJWangZW (2008) Damage boundary surface of a tangent nonlinear packaging system with critical components. Journal of Vibration and Shock27166–167. in Chinese.
16.
WangJYangRHLiZB (2010) Inner-resonance in a cushioning packaging system. International Journal of Nonlinear Sciences & Numerical Simulation11351–352.
17.
Wang J, Duan F, Jiang JH et al. (2011a) Dropping damage evaluation for a hyperbolic tangent cushioning system with a critical component. Journal of Vibration and Control (in press).
18.
WangJWangZWLuLX (2011b) Three-dimensional shock spectrum of critical component for nonlinear packaging system. Shock and Vibration18437–445.
19.
WangZLWuCFXiDC (1998) Damage boundary of a packaging system under rectangular pulse excitation. Packaging Technology and Science11189–202.
20.
WazwazAM (2009) The variational iteration method for analytic treatment for linear and nonlinear ODEs. Applied Mathematics and Computation212(1): 120–134.
21.
WhiteSWKimSKBajajAK (2010) Experimental techniques and identification of nonlinear and viscoelastic properties of flexible polyurethane foam. Nonlinear Dynamics22281–313.
22.
ZhangLZDupuisR (2011) Measurement and identification of dynamic properties of flexible polyurethane foam. Journal of Vibration and Control17517–526.