关于Duhamel积分的进一步讨论  

SOME FURTHER DISCUSSION ON DUHAMEL INTEGRAL

作　　者：王怀磊[1,2] WANG Huailei(Institute of Vibration Engineering Research,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)

机构地区：[1]南京航空航天大学振动工程研究所,南京210016 [2]南京航空航天大学机械结构力学及控制国家重点实验室,南京210016

出　　处：《力学与实践》2022年第1期155-158,共4页Mechanics in Engineering

基　　金：国家自然科学基金资助项目(11172126)。

摘　　要：本文对求解线性振动系统任意激励响应的Duhamel积分法作进一步讨论。基于将任意外激励分解成无穷多个脉冲激励的基本思想,以串行累计与并行叠加两种方式对各脉冲激励的作用过程作进一步地分析和阐释,给出了各自的理论依据,揭示出Duhamel积分的并行叠加计算本质。另外,基于微积分运算给出了Duhamel积分的严格数学验证,加深了对Duhamel积分的理论认知。This paper presents a further discussion on Duhamel integral,which is a classical method in solving the dynamic response of a linear system subject to an arbitrary excitation.Based on the basic idea of resolving an arbitrary excitation into infinite number of impulsive excitations,the implementation procedure of the pulse excitations for Duhamel integral is thoroughly discussed from both the way of accumulation in series and the way of superposition in parallel.A new mathematical proof by approach of calculus is provided for verification of Duhamel integral.

关 键 词：Duhamel积分 单位脉冲响应 零初值响应 串行累计 并行叠加 数学验证 

分 类 号：O321[理学—一般力学与力学基础]