For an artery fixed at both ends that has a uniformly distributed mass m, length 1, a constant bending rigidity EI, and

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For An Artery Fixed At Both Ends That Has A Uniformly Distributed Mass M Length 1 A Constant Bending Rigidity Ei And 1 (53.38 KiB) Viewed 53 times

For an artery fixed at both ends that has a uniformly distributed mass m, length 1, a constant bending rigidity EI, and is subjected to axial pulsatile pressure p(t) = pe + p. cos(t), in which po is the mean pressure, pa is the pulse pressure. The time dependent displacement fl) of the artery can be given by d) + (n - En cost)f(t) = 0 (1) dt2 wh no 1- 12 Po Atum - N 772 ΕΙ who ? Pa Atum 12 En = ω2 π2 ΕΙ no مجرا Wno TT? ΕΙ 12 PA + PrAtum Atum = ar? where, r, is the lumen radius of the artery, N is the axial tension, ono is called the nth natural angular frequency of the artery fixed at both ends. For the artery at any given pressure and excitation frequency, fl) can be determined by using Eq. (1). Project description A dynamic system is stable if the displacements under small perturbation are bounded; it is unstable if the displacements of the system are amplified with time. The critical pressure is defined as the minimum pressure at which the displacement is amplified with time. For each given pulse pressure, the mean pressure is gradually increased until the displacement becomes unstable. In this project, solve Eq. (1) numerically to determine the critical pressures (pairs of mean pressure pe and pulse pressure p.) that will cause the artery to lose stability. The simulation step can be taken as below: