摘要
本文研究数学物理中的Duhamel原理(齐次化原理)与单自由度线性振动系统中的Duhamel积分之间的内在联系。从一般Duhamel原理思想出发,导出了Duhamel原理应用于单自由度线性振动系统时的两种积分形式,称为第一积分形式和第二积分形式。提出了贡献度函数的概念,探讨了两种不同贡献度函数及相应的两种积分形式的物理意义及各自之间的相互关系。通过进一步求解贡献度函数,揭示出单自由度振动系统中与Duhamel原理积分形式所对应的具体数学表达式即为系统的Duhamel积分,最后基于贡献度函数概念总结了Duhamel积分的物理意义。
This paper studies the internal relationship between the Duhamel principle(homogenization principle) in the method of mathematical physics and the Duhamel integral for the solution of linear vibration systems of single degree of freedom. Starting from the general idea of Duhamel principle, two integral forms are derived when Duhamel principle is applied to a single degree of freedom linear vibration system, namely the first integral form and the second integral form. The concept of contribution function is proposed, and the physical significance and mutual relationship of the two different contribution functions are discussed. By solving the expression of contribution function, it is revealed that the specific mathematical expression corresponding to the two integral forms of Duhamel principle in the single degree of freedom vibration system is the Duhamel integral of the system, and the physical significance of Duhamel integral is summarized through the contribution function.
作者
王怀磊
WANG Huailei(State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing,Jiangsu 210016)
出处
《物理与工程》
2022年第6期16-20,共5页
Physics and Engineering
