Research on freestanding package nonlinear rocking response under vehicle braking condition

ZHU Dapeng1,QI Zhenmin1,2,CAO Xingxiao3

Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (16) : 152-158.

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PDF(1390 KB)
Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (16) : 152-158.

Research on freestanding package nonlinear rocking response under vehicle braking condition

  • ZHU Dapeng1,QI Zhenmin1,2,CAO Xingxiao3
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Abstract

The freestanding package, excited by the half-sine pulse under the vehicle braking condition, sometimes easily overturns during the rocking motion. Therefore, the research on package rocking properties and overturning risks is important for cargo transportation safety. In this paper, nonlinear rocking response of freestanding package is analyzed(α>15°). A recurrent neural network is formulated and trained to simulate forced rocking response of freestanding package with accuracy. Given the initial response angle and angular velocity, in free rocking phase, the Jacobi elliptic functions are used to formulate analytical response expression, the energy conservation principle is applied, the package nonlinear rocking overturning condition is formulated in package free rocking phase. The package nonlinear forced and free response analysis methods are applied to obtain package overturning boundary condition, the simulation results indicate, in both forced and free response phase, the package make anticlockwise rotation about point O and may overturn. The altitude of pulse which can lead to package overturn in forced response phase is greater than that in free response phase, we can conclude the package rocking overturning is more inclined to occurs in free response phase.

Key words

transport packaging / nonlinear rocking response / overturn condition / overturning parameter boundary

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ZHU Dapeng1,QI Zhenmin1,2,CAO Xingxiao3 . Research on freestanding package nonlinear rocking response under vehicle braking condition[J]. Journal of Vibration and Shock, 2024, 43(16): 152-158

References

[1] 霍银磊,姬喜龙,刘彦亨.双曲正切型包装系统跌落冲击的MSLP解[J].包装工程, 2021, 42(17):168-173. HUO Yin-lei, JI Xi-long, LIU Yan-heng. MSLP Analytical Solution for Dropping Shock of Damped Hyperbolic Tangent Nonlinearity Packaging System[J]. Packaging Engineering, 2021, 42(17):168-173. [2]李志强,田洋洋,刘随强.锂电池运输包装设计与跌落仿真分析[J].包装工程, 2022, 43(21):137-143. Li Zhi-qiang, TIAN Yang-yang, LIU Sui-qiang. Transport Packaging Design and Drop Simulation Analysis of Lithium Battery[J]. Packaging Engineering, 2022, 43(21):137-143. [3] 陈俊菲,张元标,林聪.随机振动下产品包装系统传递路径分析[J].振动工程学报, 2023, 36(2):507-516. CHEN Jun-fei, ZHANG Yuan-biao, LIN Cong. Transfer path analysis of product packaging system under random vibration[J]. Journal of Vibration Engineering, 36(2):507-516. [4] Yang S P, Liu Z C. Reliability analysis for product package via probability density function of acceleration random response[J]. Journal of Vibration and Control, 2023: 10775463231171961. [5] Yang S P, Wang Z W. Acceleration spectrum analysis of hyperbolic tangent package under random excitation[J]. Packaging Technology and Science, 2021, 34(9): 579-587. [6] 高德,卢富德.考虑转动的双曲正切与正切组合模型缓冲系统冲击响应研究[J].振动工程学报,2012,25(1):6-11. GAO De, LU Fu-de. The shock response of hyperbolic tangent and tangent comprehensive model on cushion system considering rotary motion[J].Journal of Vibration Engineering, 2012,25(1):6-11.. [7] Housner G W. The behavior of inverted pendulum structures during earthquakes[J]. Bulletin of the seismological society of America, 1963, 53(2): 403-417. [8] Voyagaki E, Psycharis I N, Mylonakis G. Complex response of a rocking block to a full-cycle pulse[J]. Journal of Engineering Mechanics, 2014, 140(6): 04014024. [9] Dimitrakopoulos E G, DeJong M J. Revisiting the rocking block: closed-form solutions and similarity laws[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012, 468(2144): 2294-2318. [10] Makris N. A half-century of rocking isolation[J]. Earthquakes and Structures, 2014,7(6):1187-1221. [11] Lachanas C G, Vamvatsikos D. Rocking incremental dynamic analysis[J]. Earthquake engineering & structural dynamics, 2022, 51(3): 688-703. [12] Sieber M, Vassiliou M F, Anastasopoulos I. Intensity measures, fragility analysis and dimensionality reduction of rocking under far‐field ground motions[J]. Earthquake Engineering & Structural Dynamics, 2022, 51(15): 3639-3657. [13] Giouvanidis A I, Dimitrakopoulos E G. Rocking amplification and strong‐motion duration[J]. Earthquake Engineering & Structural Dynamics, 2018, 47(10): 2094-2116. [14] Kazantzi A K, Lachanas C G, Vamvatsikos D. Seismic response distribution expressions for rocking building contents under ordinary ground motions[J]. Bulletin of Earthquake Engineering, 2022, 20(12): 6659-6682. [15] Frost P, Cacciola P. Rocking of rigid blocks standing on a horizontally-moving compliant base[J]. International Journal of Non-Linear Mechanics, 2023, 153: 104416. [16] Hogan S J. On the dynamics of rigid-block motion under harmonic forcing[J]. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1989, 425(1869): 441-476. [17] Liu Y, Páez Chávez J, Brzeski P, et al. Dynamical response of a rocking rigid block[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2021, 31(7): 073136. [18] Di Egidio A, Alaggio R, Aloisio A, et al. Analytical and experimental investigation into the effectiveness of a pendulum dynamic absorber to protect rigid blocks from overturning[J]. International Journal of Non-Linear Mechanics, 2019, 115: 1-10. [19] Brzeski P, Kapitaniak T, Perlikowski P. The use of tuned mass absorber to prevent overturning of the rigid block during earthquake[J]. International Journal of Structural Stability and Dynamics, 2016, 16(10): 1550075. [20] Vassiliou M F, Makris N. Analysis of the rocking response of rigid blocks standing free on a seismically isolated base[J]. Earthquake Engineering & Structural Dynamics, 2012, 41(2): 177-196. [21] Salas A H, Abu Hammad M, Alotaibi B M, et al. Closed-form solutions to a forced damped rotational pendulum oscillator[J]. Mathematics, 2022, 10(21): 4000. [22] Alyousef H A, Salas A H, Alharthi M R, et al. Galerkin method, ansatz method, and He’s frequency formulation for modeling the forced damped parametric driven pendulum oscillators[J]. Journal of Low Frequency Noise, Vibration and Active Control, 2022, 41(4): 1426-1445. [23] Alhejaili W, Salas A H, El-Tantawy S A. Novel Approximations to the (Un) forced Pendulum–Cart System: Ansatz and KBM Methods[J]. Mathematics, 2022, 10(16): 2908. [24] Pan S, Duraisamy K. Long-time predictive modeling of nonlinear dynamical systems using neural networks[J]. Complexity, 2018, 2018: 1-26. [25] Hesthaven J S, Ubbiali S. Non-intrusive reduced order modeling of nonlinear problems using neural networks[J]. Journal of Computational Physics, 2018, 363: 55-78. [26] Geneva N, Zabaras N. Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks[J]. Journal of Computational Physics, 2020, 403: 109056. [27] Lagaris I E, Likas A, Fotiadis D I. Artificial neural networks for solving ordinary and partial differential equations[J]. IEEE transactions on neural networks, 1998, 9(5): 987-1000. [28] Hornik K, Stinchcombe M, White H. Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks[J]. Neural networks, 1990, 3(5): 551-560.
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