University of Tabriz Computational Methods for Differential Equations 2345-3982 9 1 2021 01 01 Approximate distributed controllability of nonlocal Rayleigh beam 180 186 9935 10.22034/cmde.2020.29618.1434 EN Hanif Heidari School of Mathematics and Computer Sciences, Damghan University, Damghan, P.O. Box 36715-364, Iran. Parisa Alasvand Hadi School of Mathematics and Computer Sciences, Damghan University, Damghan, P.O. Box 36715-364, Iran. Reza Nazemnezhad School of Engineering, Damghan University, Damghan, Iran. Journal Article 2018 10 13 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. https://cmde.tabrizu.ac.ir/article_9935_18808f781639c56ab6964be04adc9ae7.pdf