CONSIDERATION ABOUT THE USAGE OF THE DUHAMEL INTEGRAL IN VIBRATION MECHANICS

The Duhamel integral is also called convolution integral and usually satisfies the commutative law. It is used to get the general solution of a linear dynamic system subjected to arbitrary loads. Through mathematical and physical analysis, this paper finds that the Duhamel integral no longer satisfies the commutative law when a system is subjected to segmented loads. Even for continuous loads, the commutative law is either not satisfied when calculating in segments. Based on this finding, the correct segment calculation way is clarified. Examples verify the conclusions.