振动力学中Duhamel积分应用的思考

CONSIDERATION ABOUT THE USAGE OF THE DUHAMEL INTEGRAL IN VIBRATION MECHANICS

  • 摘要: Duhamel积分也称为卷积积分,通常满足交换律,它给出任意载荷作用下线性动力系统的一般解。本文经过数学和物理分析发现,在分段定义载荷作用时,Duhamel积分不再满足交换律,即使对连续载荷进行分段计算,也不满足交换律。在此基础上,明确了正确的分段计算方法。算例验证了所得结论。

     

    Abstract: The Duhamel integral, also called convolution integral, usually satisfies the commutative law. It is used to derive the general solution of a linear dynamic system subjected to arbitrary loads. Through mathematical and physical analysis, we have uncovered a notable exception: when a system is subjected to segmented loads, the Duhamel integral ceases to uphold the commutative law. Furthermore, even in the context of continuous loads, the commutative property may not hold when computations are performed in segmented manner. In light of this discovery, this paper elucidates the correct methodology for segmented calculations. The validity of these conclusions is further supported by illustrative examples.

     

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