Reflection, transmission and energy ratio characteristics of elastic waves in fractional-order viscoelastic nanoplates

Abstract

Based on nonlocal elasticity theory, the Weyl definition of fractional-order derivatives and the extended Legendre orthogonal polynomial method are employed to solve the elastic wave reflection and transmission characteristics in two fractional viscoelastic nanoplates sandwiched in two elastic half-spaces in the context of the Kelvin–Voigt viscoelastic theory. The extended Legendre polynomial method is verified by the existing literature and global matrix method. The influences of nonlocal effects and fractional order on the reflection, transmission and energy ratio of elastic waves are analyzed. The result of research shows that the nonlocal effect increases the energy dissipation caused by viscoelasticity. The nonlocal effect and viscoelasticity is related to fractional order (ɑ): When ɑ < 0.3, the mutual strength between viscoelastic and nonlocal effects becomes stronger with the decrease of the fractional order; when ɑ ˃ 0.3, the mutual inhibition of viscoelasticity and nonlocal effects becomes stronger with the increase in fractional order; and when ɑ  =  0.3, the viscoelasticity and nonlocal effects show changes from strength to inhibition with the increase in nonlocal effects. With the increase in incident frequency, the critical angles of pure elastic structure and viscoelastic structure become smaller and larger, respectively. The results can be used in the fabrication and design of SAW devices, transducers and sensors, and to improve the stability and performance of micro/nano-electronic components.