变截面压杆稳定问题半解析解

Semi-analytical Approach for Stability of Variable Cross-section Compression Bars

介绍变截面压杆稳定问题的半解析求解方法 ,在这一方法中应用了模态摄动法 .首先以均匀梁的低阶纵向振动模态函数构成求解子空间 ,然后在此子空间中把变截面压杆稳定由变系数偏微分方程描述的求解问题转化为非线性代数方程组的求解 ,从而简化了计算过程 .通过算例比较 ,说明本方法简便实用 ,且有良好的近似性 .

A semi-analytical approach is developed to analyze the stability of the variable cross-section compression bar.In this method,the mode perturbation method is applied.First,the lower analytical modal functions of the uniform bar in longitudinal vibration are used to form an approximate solution subspace.Then the stability solution of the variable cross-section compression bar,that is discribed by a partial differential equation with variable coefficient is transformed into solving a set of algebraic equations established in the subspace.Therefore,the computational procedure is simplified effectively.It is shown by several numerical examples that this method is simple and practicable,and owns good precision.