Dynamic response of a size-dependent nanobeam to low velocity impact by a nanoparticle with considering atomic interaction forces

In the present paper, low velocity impact response of a size-dependent nanobeam in a thermal field with uniform temperature distribution has been investigated. The van-der Waals interaction force based on description of Lennard–Jonses is considered as the impact force between nanoparticle and nanobeam. According to third-order shear deformation beam theory, the governing equations are obtained using Hamilton's principle based on nonlocal strain-gradient theory. The Galerkin's method was adopted to solve the differential equations of nanobeam with simply supported and clamped boundary conditions. Afterward, the system of time-dependent equations by applying the fourth-order Runge–Kutta method is solved. The parametric study is presented to examine the effect of particle radius, initial velocity, temperature environment, the nonlocal parameter, and the length-scale parameter on the impact response of nanobeam.