Modulation of non-linear axial and transverse waves in a fluid-filled thin elastic tube
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CitationAkgün, G., & Demiray, H. (2000). Modulation of non-linear axial and transverse waves in a fluid-filled thin elastic tube. International Journal of Non-Linear Mechanics, 35(4), 597-611. doi:10.1016/S0020-7462(99)00044-X
In the present work, utilizing the non-linear equations of a pre-stressed thin elastic tube filled with an incompressible inviscid fluid the propagation of weakly non-linear waves in such a medium is studied. Considering that the arteries are initially subjected to a large static transmural pressure P-0 and an axial stretch lambda(z) and, in the course of blood flow, a finite time-dependent displacement is added to this initial field, the non-linear equations governing the motion of the tube in the radial and axial directions are obtained. Utilizing the reductive perturbation technique the amplitude modulation of weakly non-linear but strongly dispersive waves is examined. The localized travelling wave solution to the evolution equation is given and the stability condition is discussed.