计算模态响应灵敏度的两种方法比较

 从结构强迫振动的有限元方程出发，用Newmark 直接积分法和状态空间法两种不同的方法计算出结构的模态响应。进一步用两种方法推导了模态响应对结构物理参数(如单元杨氏模量)的灵敏度。计算了模态位移、速度和加速度响应对单元杨氏模量的灵敏度，并且对这两种方法的计算效率和精度进行了比较。计算结果表明两者精度相当，但状态空间法所需要的计算计时要少，比Newmark法具有较高的计算效率。因此，状态空间法更适合用于正问题分析中结构动态响应的计算。

Comparison Study on Two Methods to Calculate Modal Response Sensitivities

The sensitivities of modal response with respect to structural physical parameter (i.e. elemental Young’s modulus) are derived. The sensitivities of modal displacement, velocity and acceleration responses with respect to the elemental Young’s modulus are derived from Newmark and State-space methods. A comparison study is carried out on calculation of the response sensitivities from these two methods. The results show that the computational time of state space method is less than that of Newmark method while the preciseness of two methods is almost the same. Thus, state-space method is more suitable for the calculation of dynamic responses in the forward analysis.