Transient Response of a Circular Nanoplate Subjected to Low Velocity Impact

The transient response of a circular nanoplate subjected to the normal impact by a nanosphere (e.g., C60) is investigated theoretically. The nanoplate is modeled by the Kirchhoff thin plate theory. Gurtin-Murdoch's theory is employed to account for the surface effects of the nanoplate with surface elasticity and surface residual stress. The van der Waals interaction between the nanosphere and the nanoplate is also taken into account. The governing equations for the vibration of the nanoplate impinged by a rigid nanosphere are established by using the Hamilton's principle. The displacement field in the circular nanoplate is obtained by using the Fourier-Bessel expansion method. We reveal some physical mechanisms in the nanoimpact problem that are different from those in macroscopic impact problems, and surface effects have pronounced influences on the dynamic responses of a plate when its thickness shrinks to a few nanometers.