Open AccessOn the problems of controllability and uncontrollability for some mechanical systems described by the equations of vibrations of plates and beams with integral memory
Author(s) -
А. В. Романова,
I. V. Romanov
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1083/1/012041
Subject(s) - controllability , kernel (algebra) , rest (music) , domain (mathematical analysis) , vibration , integral equation , mathematics , mathematical analysis , beam (structure) , abelian group , physics , pure mathematics , quantum mechanics , acoustics , optics
Controllability problems for some models of plates and beams with integral memory are considered. The vibrational equation of the plate contains an Abelian kernel in the integral term, and the vibrational equation of the beam contains a continuous kernel consisting of a finite sum of decreasing exponential functions. It is proved that by controlling the whole domain, the first system cannot be driven to a state of rest, and for the second system, controllability to rest is possible.