Semi-Analytic Solution and Stability of a Space Truss Using a High-Order Taylor Series Method
Semi-Analytic Solution and Stability of a Space Truss Using a High-Order Taylor Series Method
复制标题
使用高阶泰勒级数方法的空间桁架的半解析解和稳定性
作者：
Sudeok Shon;Seungjae Lee;J. Ha;C. Cho
本文利用高阶泰勒级数法得到的精确解分析了钢网架的动力失稳（或屈曲）。一个是用于获得分析不稳定性的数值解，因为它是很难找到的几何非线性系统的解析解。然而，数值解可能会产生不正确的分析的情况下，空间桁架模型具有高度的非线性。因此，我们利用高阶泰勒级数的半解析解来分析非线性桁架系统的失稳问题。基于半解析解，研究了桁架系统在阶跃、正弦和拍频激励下的动力失稳问题。分析结果表明，即使在各种力的作用下，相空间中仍能观察到可靠的吸引子。此外，与周期正弦和拍频激励的动力屈曲水平是较低的，和响应的反应敏感，根据拍频和正弦激励。
This study is to analyse the dynamical instability (or the buckling) of a steel space truss using the accurate solutions obtained by the high-order Taylor series method. One is used to obtain numerical solutions for analysing instability, because it is difficult to find the analytic solution for a geometrical nonlinearity system. However, numerical solutions can yield incorrect analyses in the case of a space truss model with high nonlinearity. So, we use the semi-analytic solutions obtained by the high-order Taylor series to analyse the instability of the nonlinear truss system. Based on the semi-analytic solutions, we investigate the dynamical instability of the truss systems under step, sinusoidal and beating excitations. The analysis results show that the reliable attractors in the phase space can be observed even though various forces are excited. Furthermore, the dynamic buckling levels with periodic sinusoidal and beating excitations are lower, and the responses react sensitively according to the beating and the sinusoidal excitation.