分段Hermite插值多项式求解梁的动力反应

A solution to beam dynamic response based on Hermite piecewise polynomial

在求解梁动力反应的Duhamel积分中利用分段三次Hermite插值多项式逼近任意动力荷载，推导了相关公式,当动力荷载为分段三次或三次以下的多项式时，Duhamel积分是有精确解，因而与一般的数值积分法和逐步积分法相比、本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.

In this paper the three-order Hermite piecewise interpolating polynomial is employed to approximate the arbitrary dynamic loads in the Duhamel integration for the solution of dynamic response of beam systems, with relative formulas derived, since the Duhamel integration of piecewise polynomial is exact, the proposed solution is highly accurate and involves less calculations than the traditional step-by-step integration and numerical integration solution,