In this article, wave propagation responses of a double-layer magneto-electro-viscoelastic (DLMEVE) nanoplate as an intelligent material is studied via modified couple stress and nonlocal strain gradient hypotheses to investigate magnitude of surface layers changes. Both, real and imaginary parts of wave propagation responses are considered and investigated based on the Kelvin–Voigt model of viscoelastic nanoplate model. A refined plate model is applied to extent the governing equations through the modified couple stress and Kelvin–Voigt models. Hamilton’s principle will be employed to determine equilibrium equations to be solved analytically. The motivation of the present research is investigating small-scale coefficients, visco-Pasternak foundation, orthotropic angle effects, and also other effective parameters on the increasing and diminishing of surface layers of the DLMEVE nanoplate in a wave propagation analysis for both real and imaginary responses.
