正切非线性包装系统跌落冲击的MSLP解

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (11) : 266-270.

论文

正切非线性包装系统跌落冲击的MSLP解

霍银磊，刘彦亨，陈无忌

作者信息 +

MSLP solution to dropping shock of tangent nonlinear packaging system

HUO Yinlei, LIU Yanheng, CHEN Wuji

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摘要

针对有阻尼正切型非线性包装系统在发生跌落冲击时的响应问题，基于Multi-Scale Lindstedt-Poincare摄动法(MSLP)讨论了系统跌落冲击响应的一、二次近似解。并与龙哥库塔法(R-K)的数值结果及相关文献进行了对比，对比结果显示：对于本文的正切型强非线性包装系统，MSLP计算的最大位移和加速度响应的一阶近似解与R-K数值结果对比的相对误差分别为1.35%和3.28%，二次近似阶的相对误差分别为0.62%和1.84%，在不进行能量修正的情况下，比同伦摄动法[13-14]、牛顿谐波平衡法[17]的精度更高。考虑阻尼系统能量修正的复杂性，所求有阻尼正切型非线性系统跌落冲击一次近似解析具有较好的精度和简洁的形式，为此类问题的求解及工程应用提供了参考。

Abstract

Based on the multi-scale method and Lindstedt-Poincare perturbation method (MSLP)，the approximate solution of dropping shock of damped tangent nonlinear packaging system are discussed. By compared with the R-K solutions and related references, the results show that the analytical expression has good precision, especially for small damping shock response analysis of strong nonlinear packaging system, even without additional correction for the amplitude and frequency. Considering the complexity of energy correction for damped system, the first approximate analysis of dropping shock of damped tangent nonlinear system is more useful, which provides a reference for solving such problems and engineering application benefit from its good precision and simple form.

关键词

正切非线性 / 阻尼系统 / MSLP法 / 跌落冲击响应

Key words

tangent nonlinear

/ damped system / MSLP method / dropping shock

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霍银磊，刘彦亨，陈无忌. 正切非线性包装系统跌落冲击的MSLP解[J]. 振动与冲击, 2022, 41(11): 266-270

HUO Yinlei, LIU Yanheng, CHEN Wuji. MSLP solution to dropping shock of tangent nonlinear packaging system[J]. Journal of Vibration and Shock, 2022, 41(11): 266-270

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