Energy absorption, free and forced vibrations of flexoelectric nanocomposite magnetostrictive sandwich nanoplates with single sinusoidal edge on the frictional torsional viscoelastic medium

Most studies on the nanoscale mainly focus on regular rectangular nanoplates, but according to the synthesis of nanostructures, the dynamic response of non-rectangular nanoplates is noticeable and there are not many works on these complex nanostructures. This work presents energy absorption, and forced and free vibrations of sandwich non-rectangular nanoplates with a single sinusoidal edge resting on a fractional torsional viscoelastic medium. The nanostructure is made from alumina reinforced by graphene platelets (GPLs) as a core covered by the flexoelectric and magnetostrictive materials as top and bottom layers, respectively. The consideration of size effects is derived from the innovative theory of local/nonlocal phenomena in a two-phase context. The Halpin–Tsai micromechanical and Kelvin–Voigt models are applied for the effective characteristics of the material in the nanocomposite layer and structural damping, respectively. Based on Hamilton’s principle and refined zigzag theory (RZT), the coupled electro-magneto-mechanical equations of motion are gained and analyzed by Galerkin’s and Newmark’s procedures. The effects of different components, including factors related to both the nonlocal and local phase fractions, the volume fraction of GPLs, various elastic mediums, electric field, structural damping, magnetic field, piezoelectric and flexoelectric effects on the absorption of energy, and forced and free vibrations of the sandwich nanostructure. Numerical simulations demonstrate that optimal energy absorption occurs when the flexoelectric factor is set to zero and the piezoelectric constant is non-zero but of opposite polarity. Additionally, it is concluded that when the coefficient of the local phase fraction is zero, increasing the nonlocal factor has more influence on the energy absorption and vibration of the nanostructure.