Non-linear wave modulation in a prestressed viscoelastic thin tube filled with an inviscid fluid |
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| Affiliation: | 1. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China;2. State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;1. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan;2. Nonlinear and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. Department of Mathematics, Faculty of Sciences, HITEC University, Taxila, 44400, Pakistan;2. Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan |
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| Abstract: | ![]()
In the present work, the propagation of weakly non-linear waves in a prestressed thin viscoelastic tube filled with an incompressible inviscid fluid is studied. Considering that the arteries are initially subjected to a large static transmural pressure P0 and an axial stretch λz and, in the course of blood flow, a finite time-dependent displacement is added to this initial field, the governing non-linear equation of motion in the radial direction is obtained. Using the reductive perturbation technique, the propagation of weakly non-linear, dispersive and dissipative waves is examined and the evolution equations are obtained. Utilizing the same set of governing equations the amplitude modulation of weakly non-linear and dissipative but strongly dispersive waves is examined. The localized travelling wave solution to these field equations are also given. |
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