Low velocity impact on Timoshenko nanobeam using a nonlocal elasticity theory

In this article، analytical solutions of low velocity transverse impact on a nanobeam are presented using the nonlocal theory to bring out the effect of the nonlocal behavior on dynamic deflections. Impact of a projectile (mass) on simply supported and clamped nanobeams are investigated using nonlocal Timoshenko beam theory. In order to obtain an analytical result for this problem، an approximate method has been developed wherein the applied impulse is replaced by a suitable boundary condition and initial momentum of projectile and nanobeam. A number of numerical examples with analytical solutions for nonlocal nanobeam and classical beam (steel and aluminum) have been presented and discussed. When the value of the striker mass is increased، the frequencies are decreased and the maximum dynamic deflection at the center of the beam is increased for both of the simply supported and the clamped-clamped nanobeams. The inclusion of the nonlocal effect increases the magnitudes of dynamic deflections and decreases frequencies. Furthermore، the mass and the velocity of the nanoparticle (striker) have significant effects on the dynamic behavior of nanobeam.