Approximate distributed controllability of nonlocal Rayleigh beam

Document Type : Research Paper


1 School of Mathematics and Computer Sciences, Damghan University, Damghan, P.O. Box 36715-364, Iran.

2 School of Engineering, Damghan University, Damghan, Iran.


This paper investigates the distributed controllability of nonlocal Rayleigh beam. The mathematical problem is formulated as an abstract differential equation. It is shown that a sequence of eigenfunction of nonlocal Rayleigh beam forms Riesz basis. Based on Riesz basis properties and theory of abstract differential equation, it is proved that a vibrating nonlocal Rayleigh beam is approximately controllable under suitable distributed control force while it is not exponentially stable.