Validity of the linear viscoelastic model for a polymer cylinder with ultrasonic hysteresis-type absorption in a nonviscous fluid

摘要

A necessary condition for the validity of the linear viscoelastic model for a(passive) polymeric cylinder with an ultrasonic hysteresis-type absorptionsubmerged in a non-viscous fluid requires that the absorption efficiency ispositive (Qabs > 0) satisfying the law of the conservation of energy. Thiscondition imposes restrictions on the values attributed to the normalizedabsorption coefficients for the compressional and shear-wave wavenumbers foreach partial-wave mode n. The forbidden values produce negative axial radiationforce, absorption and extinction efficiencies, as well as an enhancement of thescattering efficiency, not in agreement with the conservation of energy law.Numerical results for the radiation force, extinction, absorption andscattering efficiencies are performed for three viscoelastic (VE) polymercylinders immersed in a non-viscous host liquid (i.e. water) with particularemphasis on the shear-wave absorption coefficient of the cylinder, thedimensionless size parameter and the partial-wave mode number n. Mathematicalconstraints are established for the non-dimensional absorption coefficients ofthe longitudinal and shear waves for a cylinder (i.e. 2D case) and a sphere(i.e. 3D case) in terms of the sound velocities in the VE material. Theanalysis suggests that the domain of validity for any viscoelastic modeldescribing acoustic attenuation inside a lossy cylinder (or sphere) in anon-viscous fluid must be verified based upon the optical theorem.