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. |
| 双曲正切型包装系统跌落冲击的MSLP解 |
| MSLP Analytical Solution for Dropping Shock of Damped Hyperbolic Tangent Nonlinearity Packaging System |
| 投稿时间：2021-01-23 |
| DOI：10.19554/j.cnki.1001-3563.2021.17.022 |
| 中文关键词: 正切非线性 阻尼系统 MSLP法 跌落冲击响应 |
| 英文关键词: tangent nonlinear damped system MSLP method dropping shock response |
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| 中文摘要: |
| 目的 针对双曲正切型非线性有阻尼包装系统在发生跌落冲击时的响应问题，讨论有效的解析求解方法。方法 基于多尺度L-P摄动法(MSLP)讨论系统跌落冲击响应的近似解，并与龙哥库塔法(R-K)的数值结果进行对比。结果 对比结果表明，在无需额外的幅值及频率修正情况下，双曲正切型非线性小阻尼系统(ζ<0.5)跌落冲击的最大位移、加速度响应的一次MSLP近似解的误差均小于5%，且随着阻尼比ζ的减小迅速减小。结论 所求一次MSLP近似解析对于双曲正切型非线性小阻尼包装系统具有较好的计算精度，为此类问题的求解提供了新的方法参考。 |
| 英文摘要: |
| In terms of dropping shock response of damped hyperbolic tangent nonlinearity packaging system, this paper discusses effective method for analytic solution. Based on the multi-scale method and Lindstedt-Poincare perturbation method (MSLP), the approximate solution of dropping shock of damped hyperbolic tangent nonlinear packaging system is discussed. Through comparison with the R-K solutions, the results show that the error of linear MSLP approximate solution for acceleration and maximum displacement of small damping hyperbolic tangent nonlinearity system (ζ<0.5) dropping shock is less than 5%. and the calculation error decreases rapidly with the decrease of the system damping ratio ζ, without additional correction for the amplitude and frequency. The linear MSLP approximate solution has good calculation precision, especially for small damping hyperbolic tangent nonlinearity system. This research provides a new and effective method reference for the analysis of such problems. |
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