Vibration suppression of a boron nitride nanotube under a moving nanoparticle using a classical optimal control procedure

The current research investigates the vibration of single-walled boron nitride nanotube (SWBNNT) induced by a moving nanoparticle. In order to decrease the forced vibration of SWBNNT under a moving nanoparticle, a linear classical optimal control procedure is used to manipulate the movement of a nanoparticle as a drug material inside a nano-structure with consideration of various size-dependent procedures based on Rayleigh beam model. The Pasternak substrate is utilized to model the elastic medium. Hamilton, Galerkin and Newmark methods are also employed to solve the motion equations. Different size-dependent beam theories have been considered, such as the classical beam theory, nonlocal beam theory, strain gradient beam theory and nonlocal strain gradient beam theory, in order to reveal small-scale effects. The effects of the small length scale considered herein, the velocity of a moving nanoparticle, electrical potential field, the number of vibration modes and actuators and also resultant control force on the vibration behavior of the SWBNNT are investigated in detail.