Forced transverse vibrations of an elastically connected nonlocal orthotropic double-nanoplate system subjected to an in-plane magnetic field

Nonlocal forced transversal vibrations of an orthotropic double-nanoplate system are considered in this paper. Both nanoplates are rectangular, simply supported, and coupled by a Winkler elastic medium. In order to take into account small-scale effects, we use Eringen's nonlocal continuum theory. Based on the nonlocal constitutive relation and Kirchhoff-Love plate theory, the system of two coupled nonhomogeneous partial differential equations of motion is derived, where the effects of the Lorentz magnetic force are obtained via a Maxwell relation. Analytical methods are employed to consider the dynamic responses of the orthotropic double-nanoplate system for three different cases of external transversal load. Also, closed-form solutions of the response amplitudes for forced vibration are derived and then validated with the existing results. The nonlocal parameter, magnetic fields, and exciting loads are discussed in detail for all three cases.