关于分数阶Maxwell淤泥模型及其在水波衰减问题中的应用

分数阶Maxwell模型可用来模拟粘弹性的海床淤泥．与传统的有理分式模型相比，分数阶Maxwell模型可以用更少的自由参数，较好地描述某些真实淤泥的流变特性．将该分数阶Maxwell模型用于研究淤泥与自由表面水波的相互作用，并得到了线形单色波的衰减率．从水波衰减率曲线中可观测到淤泥层的共振现象，共振时衰减率将达到峰值．对于线形单色波，其衰减率还可表示为各模态衰减率之和，从而可研究某一模态的运动对水波衰减的影响．模态分析表明，当某一模态运动引发共振时，总衰减率由该模态的模态衰减率决定．

On a Fractional-Order Maxwell Model of Seabed Mud and Its Effect to Surface-Wave Damping

A fractional-order Maxwell model was used to describe viscoelastic seabed mud.The experimental data of real mud were fitted well by the fractional-order Maxwell model,which had fewer parameters than the traditional one.This model was then applied to investigate the effect of mud on surface-wave damping.The damping rate of a linear monochromatic wave was obtained.The elastic resonance of the mud layer was observed,which led to the peaks of the damping rate.The damping rate was a sum of modal damping rates,wh...