NONLOCAL DYNAMICAL ANALYSIS ON AXIALLY TRAVELLING ULTRA-THIN BEAMS

Based on the nonlocal elasticity theory, the equation of motion that governs the transverse vibration of an axially travelling ultra-thin beam subjected to initial axial tension is established. Unlike some previous work which only employs nonlocal effects in the governing equation, the nonlocal small scale parameter is also adopted into two typical kinds of boundary conditions to investigate the effects of nonlocal elasticity on vibration behaviors, including the natural frequency and critical velocity. It is shown that the ultra-thin character causes the natural frequency and critical velocity to decrease, and the classical elasticity theory overestimates the bending stiffness of nanostructures. The nonlocal size effects exist obviously in the dynamic properties of such an axially travelling ultra-thin beam.