Vibration characteristics of elastic nanostructures embedded in fluid medium have been used for biological and mechanical sensing and also to investigate the materials mechanical properties. The fluid medium surrounding the nanostructure is typically modeled as a Newtonian fluid. A novel approach based on the exact theory has been developed in this paper, to accurately predict the various vibration scenarios of an elastic sphere, in a compressible viscous fluid. Then, the analysis is extended to a viscoelastic medium using the Maxwell fluid model. To demonstrate the accuracy of the present approach, a comparison is made with the published theoretical results in the literature in some particular cases, which shows a very good agreement. The effects of fluid compressibility and viscoelasticity are discussed in details, and we demonstrate that the fluid compressibility plays a significant role in the vibration modes of an elastic sphere. Results also show that the different vibration modes of a sphere trigger a viscoelastic response in water–glycerol mixtures similar to that of literature. In addition, the obtained results can serve as benchmark solution in design of liquid sensors.

中文翻译：

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预测复杂流体中嵌入弹性球体振动特性的解析方法

嵌入流体介质中的弹性纳米结构的振动特性已用于生物和机械感测，还用于研究材料的机械性能。围绕纳米结构的流体介质通常被建模为牛顿流体。本文开发了一种基于精确理论的新颖方法，可准确预测可压缩粘性流体中弹性球体的各种振动情况。然后，使用麦克斯韦流体模型将分析扩展到粘弹性介质。为了证明本方法的准确性，在某些特定情况下，将其与文献中已发表的理论结果进行了比较，这显示出很好的一致性。详细讨论了流体可压缩性和粘弹性的影响，并且我们证明了流体的可压缩性在弹性球体的振动模式中起着重要的作用。结果还表明，与文献相似，球体的不同振动模式在水-甘油混合物中引发粘弹性响应。此外，所得结果可作为液体传感器设计的基准解决方案。