Dynamics of nonlocal graphene mindlin plate subjected to moving nanoparticles on viscoelastic support

This paper presents a detailed investigation into the forced vibration behavior of a nano-rectangular plate under the influence of moving nanoparticles, incorporating Coulomb friction effects. By combining Eringen's nonlocal continuum theory with the first-order shear deformation theory, the study examines the impact of the nonlocal parameter on the nanoplate's forced vibration response. The nanoplate, supported by a viscoelastic foundation modeled with a damper and Winkler modulus, is subjected to moving nanoparticles, considering their weight, inertia, and friction. The governing equations of motion and boundary conditions are derived using Mindlin's displacement field relations and Hamilton's principle. The analytical Galerkin method and Eigenfunction expansion are employed to transform the dimensionless partial differential equations into dimensionless ordinary differential equations under simply supported boundary conditions. The model's validity is confirmed through comparison with existing research. Additionally, this research explores the effects of key parameters, including the nonlocal parameter, foundation stiffness and damping coefficients, nanoparticle inertia, and velocity, on the dynamic amplitude factors of in-plane and out-of-plane displacements in detail.