Vibration Analysis of Vessels Conveying Blood Flow Embedded in Viscous Fluid

Vibration analysis of vessels conveying blood flow embedded in viscous fluid is studied based on the modified strain gradient theory. The viscoelastic vessels are simulated as a non-classical Euler-Bernoulli beam theory. Employing Hamilton’s principle, the governing equations for size-dependent vessels are derived. The Galerkin method is used in order to transform the resulting equations into general eigenvalue equations. The effects of the blood flow profile and its modification factors, red blood cells (RBCs) and hematocrit are considered in the blood flow. Besides, the influences of the constitutional material gradient scale, blood flow, internal pressure, structural damping coefficient, viscous fluid substrate and various boundary conditions on the natural frequencies and critical buckling velocities are studied. It is revealed that as the hematocrit, fluid viscosity of substrate, internal pressure and mass ratio increase, the natural frequencies and critical buckling velocities decrease. Furthermore, the results indicated that the strain gradient theory predicts the highest natural frequencies and critical buckling velocities among others. The results are compared with those available in the literature and good agreement has been observed.