### Analysis of spatial resonance in a small vessel to study vibration-induced digital vascular disorder

#### Abstract

The vibration response of small arteries is studied by modeling the system as an elastic tube filled with incompressible fluid embedded in an elastic foundation. The entire artery system is represented by a series of circuits and the segments of the artery system is considered to be small oscillatory dynamic systems connected serially by the fluid impedance. The resonance frequency of the digital artery is calculated with 0.1mm thickness, 0.49 Poisson's ratio, 15 MPa Young's modulus and 50mm length of the vessel. When the cochlea are subjected to sound of a given frequency. the basilar membrane vibrates with large amplitude at a particular position, and the position depends on the frequency of the sound. A very interesting observation is that when the input is from the large diameter side, the same artery system does not show any spatial resonance.

#### Keywords

Poisson ratio; Resonance; Basilar membranes; Digital artery; Elastic foundation; Elastic tubes; Incompressible fluid; Large amplitude; Large diameter; Oscillatory dynamics; Poisson's ratio; Resonance frequencies; Spatial resonance; Vibration response; Young's Modulus

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