利用Hermite多项式求解动态响应问题的新方法

A new solution to dynamic response by use of hermite polynomial

结合了解析方法和数值方法优点 ,本文提出了一种求解机械振动和电振荡问题的新方法 .在求解动态响应的 Duhamel积分中 ,利用分段 Hermite插值多项式逼近任意激励 ,并推导了相关公式 .由于分段 Hermite多项式的 Duhamel积分有精确解 ,因而和现在常用的逐步积分法相比 ,本方法不但具有高的多的计算精度 。

By combining the merits of the analytic method and those of the numerical method,this paper proposes a new method for solving the problem of mechanical vibration and electrical oscillation.In this new method,the piecewise Hermite interpolation polynomial is employed to approximate any arbitrary excitation while using Duhamel integral to solve the problem of dynamic response,with relevant formulas derived.Since the Duhamel integral for piecewise Hermite interpolation polynomial is precise,the proposed solution is higher in accuracy and involves less calculation than the traditional step by step integration method.