The transient rotation responses of simple, axisymmetric, viscoelastic structures are of interest for interpretation of experiments designed to characterize materials and closed structures such as the brain using magnetic resonance techniques. Here, we studied the response of a Maxwell viscoelastic cylinder to small, sinusoidal displacement of its outer boundary. The transient strain field can be calculated in closed form using any of several conventional approaches. The solution is surprising: the strain field develops a singularity that appears when the wavefront leaves the center of the cylinder, and persists as the wavefront reflects to the outer boundary and back to the center of the cylinder. The singularity is alternately annihilated and reinitiated upon subsequent departures of the wavefront from the center of the cylinder until it disappears in the limit of steady state oscillations. We present the solution for this strain field, characterize the nature of this singularity, and discuss its potential role in the mechanical response and evolved morphology of the brain.

中文翻译：

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振荡麦克斯韦粘弹性圆柱体中的应变局部化


简单、轴对称、粘弹性结构的瞬态旋转响应对于解释旨在使用磁共振技术表征材料和闭合结构（例如大脑）的实验很有意义。在这里，我们研究了麦克斯韦粘弹性圆柱体对其外边界的小正弦位移的响应。瞬态应变场可以使用几种传统方法中的任何一种以封闭形式计算。该解决方案令人惊讶：应变场形成了一个奇点，该奇点在波前离开圆柱体中心时出现，并且在波前反射到圆柱体外边界并返回圆柱体中心时持续存在。当波前离开圆柱体中心时，奇点交替地消失和重新启动，直到它在稳态振荡的极限中消失。我们提出了该应变场的解决方案，描述了该奇点的性质，并讨论了其在大脑的机械响应和进化形态中的潜在作用。