关于分数阶Maxwell淤泥模型及其在水波衰减问题中的应用  

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

作　　者：夏乐章[1] 朱克勤[1] 

机构地区：[1]清华大学工程力学系,北京100084

出　　处：《应用数学和力学》2011年第11期1265-1273,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10972117)

摘　　要：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.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 investi- gate 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, which indicated the wave damping induced by mud motions of particular modes. Analysis shows that near resonance, the total damping rate is dominated by the damping rate of the corresponding mode.

关 键 词：海床淤泥 波-泥相互作用 波衰减 分数阶Maxwell模型 

分 类 号：O353.2[理学—流体力学]