چكيده به لاتين
Present project concerns with the impact dynamics behavior of a nano-sized plate-indentor system. Target is assumed as a rectangular orthotropic nano-plate subjected to a colliding nano-sized particle. The plate is assumed thin, so that can be addressed by the Kirchhoff's classical plate theory assumptions, and the governing equations are derived using nonlocal theory of elasticity. To derive plate response to a foreign load, orthogonality characteristics of nonlocal thin plate are developed, and based on the orthogonality equations, uncoupled modal equation are derived adapted with the impact load. To derive the impact load imposed on the plate, the nanoparticle is considered to collide with the plate transversely while the interactions are non-bonding van-der Waals forces, addressed by Lenard-Jones potential equation. Then, using a conceptual continuum model, the conservative (elastic) contact force, i.e. contact law, is derived for the cases of interaction between thin plate and concentrated, spherical full particle and spherical hollow particle. In spite of simplifications assumed in the derivation of contact laws, preliminary verifications show that the derived contact law gives a reliable picture of force field of the system which is in good agreements with the results of molecular dynamics (MD) simulations. Afterwards, the coupled equations of motion for both the plate and indenter are solved numerically together with the utilized contact law, resulting in displacements and velocities of the system as well as interaction force. As an example, results are developed for the case of impact between a gold nano-particle and a single-layered graphene sheet with simply supported boundaries, with and without considering in-plane tensions. Then, some aspects of the problem such as effects of indenter initial velocity, nonlocal parameter and in-plane tension in the plate are discussed. In another example, dynamic behavior a single layered graphene sheet collided by a fullerene molecule is discussed analytically, and in order to evaluate outcomes of proposed analytical method, the problem is also modeled by MD simulation. It is shown that despite intrinsic differences between analytical and MD methods as well as various errors arise due to transient nature of the problem, acceptable agreements are established between analytical and MD outcomes. As an application of this solved example, the capability of single-layered graphene sheet in trapping foreign particles is illustrated. It is shown that the single-layered graphene sheet may trap colliding fullerenes approaching with a wide range of initial velocities, and in case of rebound of fullerene, the sheet effectively absorbs predominant portion of particle energy.
Keywords: Impact; graphene nanoplate; nonlocal theory; molecular dynamics.
