Propagation and attenuation of Lamb waves in functionally graded fractional viscoelastic soft plates with a pre-deformation

An improved understanding of the wave propagation in incompressible soft structures with a pre-deformation, especially the grasp of viscoelastic effect, could fundamentally catalyze technical developments in many areas including medicine, and rubber. Based on the nonlinear elasticity and linear incremental theories, a fractional order hyper-viscoelastic model is established to derive dynamic equations of Lamb waves in functionally graded pre-deformed viscoelastic soft plates. The fractional-order Kelvin-Voigt model is applied to concern the viscoelasticity. An improved Legendre polynomial method is employed to analytically solve wave equations. The complex wave solutions are obtained without the iterative. The correctness of the present method is validated by a comparison with the finite element method. The influence of viscoelasticity and pre-formation on dispersion and attenuation curves is investigated. Some new wave phenomena are revealed: Phase velocity and attenuation of Lamb waves can be controlled by altering stretch ratios lambda i, and the pre-stretching restrains the viscoelastic effect; The minimum attenuation frequency can be adjusted by altering the material component distributions. Results provide the foundation for the design of biomaterials with the controllable viscoelasticity to greatly promote their applications in the regenerative medicine.