Acoustoelastic and viscoelastic effects on guided wave characteristics in an incompressible plate

Owing to the high fluid content, most incompressible soft structures typically exhibit viscosity, which has a significant influence on wave characteristics, especially attenuation. Meanwhile, they are inevitably prestressed owing to the volume-preserving deformations. Therefore, it is essential to investigate acoustoelastic and viscoelastic effects to better understand guided wave characteristics in a pre-stressed soft plate. To this end, a hyperviscoelastic model concerning viscoelasticity, acoustoelasticity, and nonlinearity is established to deduce the governed equations. An analytical integration orthogonal polynomial method is employed to solve complex solutions of wave equations. The dispersion, attenuation, and wave shapes are illustrated. The acoustoelastic and viscoelastic effects are analyzed. Some new wave phenomena are revealed: The pre-stretching inhibits wave attenuation, and the pre-compression promotes attenuation; As the pre-stress increases, high-frequency phase velocity and incremental displacement amplitudes increase. The results lay a theoretical foundation for guided wave elastography, quantitative characterization, and disease diagnosis of biological soft tissue.