狭缝空腔间粘弹性体中弹性波传播特性的研究

The propagation of elastic wave in viscoelastic structure with slot cavum

利用笛卡尔坐标下的Kelvin-Voigt线性粘弹性模型,研究了无限长粘弹性狭缝通道中波的传播和衰减。利用自适应绕数求根方法,针对具有狭缝形空腔周期性分布覆盖层的吸声问题,求得频散方程的根,并且得到无限长狭缝空腔中相速度频散曲线和衰减曲线。分析了各阶模式对无限长粘弹性狭缝结构中波传播的相速度和衰减的影响。通过引入复粘弹性模量,粘弹性波动方程具有弹性波动方程相对应的形式,计算中可用复值粘弹性模量代替相应的弹性模量。粘弹性狭缝结构中所有波传播模式均存在衰减,高阶波在某个频率以下衰减非常大,而在该频率以上逐渐减小;最低阶模式的相速度与材料无损耗的情况非常接近。粘弹性狭缝结构中波传播的衰减特性不仅与狭缝的结构参数有关,还与粘弹性材料本身的复弹性模量有关。

With the linear viscoelatic model of Kelvin-Voigt in Descartes Coordinate,the propagation and attenuation of elastic wave in infinite slot cavum are studied.An adaptive winding number intergral algorithm is proposed for the determination of roots of dispersion equation,and the phase velocity and attenuation in infinite slot cavum are obtained.The influence of different order pattern on phase velocity and attenuation is analyzed.By importing complex viscoelatic quantity,the viscoelastic wave equation has the same form as elastic wave equation,and the elastic quantity can be replaced with complex viscoelatic quantity in calculation.There is attenuation in all propagation patterns in slot cavum.The attenuation of high order waves is very high below a certain special frequency,and will decline above the special frequency.Phase velocity of the lowest pattern is similar to that in elastic material.The attenuation characteristic of wave propagation in viscoelstic slot cavum not only relate to the structure parameter,but also to the complex viscoelastic quantity.