IJAM: Volume 29, No. 2 (2016)

Abstract. The aim of this paper is to study dynamical properties of an axially vibrating uniform nanorod. This analysis is performed by describing the model as an infinite-dimensional state-space system, with bounded control operator. In the absence of control forces, the system with homogeneous boundary conditions generates a strongly continuous semigroup. It is proved that the associated eigenfunctions form a Riesz basis for the energy space. It is shown that axial vibration of nanorod is stable phenomena but not exponentially stable. A necessary and sufficient condition for the approximate controllability is given.