High-resolution analysis of the complex wave spectrum in a cylindrical shell containing a viscoelastic medium. Part I. Theory and numerical results
High-resolution analysis of the complex wave spectrum in a cylindrical shell containing a viscoelastic medium. Part I. Theory and numerical results
复制标题
对含有粘弹性介质的圆柱壳中的复杂波谱进行高分辨率分析。
DOI：
10.1121/1.419956
复制
发表时间：
1997
影响因子：
2.4
通讯作者：
J. Dual
中科院分区：
文献类型：
--
作者：
J. Vollmann;J. Dual
本文导出了含有线性粘弹性介质的各向同性薄壁圆柱壳中轴对称波模的频率与复波数之间的关系。在空圆柱壳中，壳壁弯曲和纵向运动耦合。当粘弹性介质被封闭时，壳体的运动受到复体积模量和剪切模量以及封闭介质的密度的影响。用麦克斯韦模型描述复拉梅常数λ和μ的本构方程。通过改变复模量，介质可以被建模为无粘流体、弹性材料或这两个极端之间的任何东西。通过计算复频散关系，数值讨论了线弹性薄壁壳体与粘弹性介质的相互作用。数值结果给出了一个空的壳和壳填充有三种类型的核心材料：无粘流体，剪切耗散流体，剪切弹性流体。在一篇配套论文[J. Vollmann等人，J. Acoust.美国社会102，909-920（1997）]，详细描述了用于执行色散关系的高分辨率测量的实验装置和信号处理。理论和实验结果进行了比较。
In this study the relation between frequency and complex wave number of axisymmetric wave modes in an isotropic, thin-walled, cylindrical shell containing a linear viscoelastic medium is derived. Shell wall bending and longitudinal motion are coupled in an empty cylindrical shell. When a viscoelastic medium is enclosed, the shell motion is affected by the complex bulk and shear modulus, as well as by the density of the medium enclosed. A Maxwell model is used for both complex Lame constants λ and μ to describe the constitutive equations of the medium. By varying the complex moduli, the medium can be modeled as an inviscid fluid, an elastic material, or anything between these two extremes. The interaction of the thin-walled linear elastic shell and the viscoelastic medium is discussed numerically by calculating the complex dispersion relation. Numerical results are presented for an empty shell and a shell filled with three types of core material: an inviscid fluid, a shear dissipative fluid, and a shear elastic fluid. In a companion paper [J. Vollmann et al., J. Acoust. Soc. Am. 102, 909–920 (1997)], the experimental setup and the signal processing used to perform the high-resolution measurement of the dispersion relation are described in detail. Theoretical and experimental results are compared.