Reflection, transmission, and dissipation of plane waves in sandwiched functionally graded thermo- electro-elastic nanoplates via nonlocal integral elasticity theory

On account of the Lord-Shulman thermo-electric-elastic (TEE) theory and the nonlocal integral elasticity effect, the propagation of the plane wave in sandwiched functionally graded material (FGM) nanoplates, especially its energy dissipation, is investigated. A mathematical model is established by using the extended Legendre polynomial series approach. After imposing the mechanical, electrical and thermal boundary conditions by using the Legendre series, the reflection and transmission as well as the dissipation energy ratios are obtained. The influences of the nonlocal effect, relaxation time, gradient index, and electric filed are discussed. It is found that the nonlocal effect on the reflection of P waves is consistent with their transmission, but opposite to reflection of SV waves. Meanwhile, the nonlocal effect increases the dissipation. Besides, the dissipation variation in the normal incidence mainly comes from the transmission waves. The study is beneficial for the design of wave characteristics in TEE FGM nanoplates.