Guided waves in immersed incompressible pre-stressed plates and tubes: critical frequency determination

Changes in arterial stiffness are interpreted as a sign of cardiovascular diseases. Despite the fact that the arterial walls are tubes, their elastic properties are mostly assessed by using dispersion curves of guided waves propagating in immersed elastic or hyperelastic plate models (Lamb wave (LW) model). In this study, the critical frequency (fc) for hyperelastic tubes has been investigated beyond which the dispersion curve of guided axial wave (GAW) fits well with that of LW model. To this end, finite element (FE) simulations of GAW and LW models in, respectively, incompressible hyperelastic tubes and plates surrounded by non-viscous fluid are carried out. In addition, a theoretical analysis of LW propagation in hyperelastic immersed plates is presented based on the theory of “superposing small deformations on large initial static deformations”, which can serve as a validation for the FE simulation results. By comparing the dispersion curves in immersed hyperelastic tubes and plates, fc is found. Results show that using a LW model instead of GAW in tubes has enough accuracy at high frequencies and for certain values of radius to thickness ratio. Furthermore, the effects of various parameters including the ratio of the arterial radius to its thickness (𝑅𝑅/ℎ), shear modulus (μ۰) and different values of pre-stretch (λ) on the dispersion curves of GAW are studied.

کلیدواژه ها:

Dispersion curve ، Arterial stiffness ، Guided axial wave ، Incremental theory