利用分段Hermite多项式的线性系统动力响应的求解

A Solution for Dynamic Responses of Linear Systems Using Piecewise Hermite Polynomial

在求解多自由度系统动力响应的Ｄｕｈａｍｅｌ积分中，利用分段Ｈｅｒｍｉｔｅ插值多项式逼近任意动力荷载，推导了相关公式。由于分段Ｈｅｒｍｉｔｅ多项式的Ｄｕｈａｍｅｌ积分有精确解，因而与逐步积分法相比，本文方法不但具有较高的计算精度，而且大大减少了计算工作量。

The piecewise 3 order Hermite interpolating polynomial is employed to approximate arbitrary dynamic loads in the Duhamel integration for the solution of dynamic response of linear systems. The relative formulae are derived. Because the Duhamel integration of piecewise Hermite polynomial is exact, the proposed solution of the paper has higher accuracy and less calculations than traditional step by step integration solution.