Elastic wave attenuation in a functionally graded viscoelastic couple stress plate, sandwiched between two elastic half-spaces

Taking the viscoelasticity and size-dependent effect into account, the reflection and transmission of elastic waves through functionally graded viscoelastic plate sandwiched in two elastic half-spaces are investigated. The extended analytical integration Legendre polynomial method and Kelvin-Voigt viscoelastic model in the context of the modified couple stress theory are utilized to perform the derivation. The global matrix method is used to confirm the validity of the extended analytical integration Legendre polynomial method. Compared with the global matrix method, the extended analytical integration Legendre polynomial method provides an efficient numerical calculation method without layering and iterative root seeking. The influences of the couple stress, viscoelasticity and inhomogeneity of medium on elastic wave reflection and transmission are discussed. In addition, the attenuation caused by the viscoelasticity is analyzed. It is found that the couple stress effect weakens the influence of the viscoelasticity, while the viscoelasticity strengthens the couple stress effect. The couple stress effect decreases the attenuation, while the inhomogeneity increases the attenuation. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

Taking into consideration the effects of viscoelasticity and size-dependency, this study investigates the reflection and transmission of elastic waves through functionally graded viscoelastic plates sandwiched between two elastic half-spaces. The extended analytical integration Legendre polynomial method and Kelvin-Voigt viscoelastic model under the modified couple stress theory are utilized for the derivation. The global matrix method is employed to validate the extended analytical integration Legendre polynomial method. The study discusses the influences of couple stress, viscoelasticity, and medium inhomogeneity on elastic wave reflection and transmission, as well as the attenuation caused by viscoelasticity.