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

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。

In terms of dropping shock response of damped hyperbolic tangent nonlinearity packaging system,this pa-per 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 solu-tion for acceleration and maximum displacement of small damping hyperbolic tangent nonlinearity system(ζ<0.5)drop-ping shock is less than 5%.and the calculation error decreases rapidly with the decrease of the system damping ratioζ,without additional correction for the amplitude and frequency.The linear MSLP approximate solution has good calcula-tion precision,especially for small damping hyperbolic tangent nonlinearity system.This research provides a new and ef-fective method reference for the analysis of such problems.