关于Duhamel积分的进一步讨论1)

SOME FURTHER DISCUSSION ON DUHAMEL INTEGRAL1)

  • 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。

     

    Abstract: 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.

     

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