Open AccessOn Determining Initial Conditions of Equations Flexural-Torsional Vibrations of a Bar
Author(s) -
Aysel T. Ramazanova
Publication year - 2019
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v12i1.3350
Subject(s) - mathematics , bar (unit) , boundary value problem , vibration , flexural strength , mathematical analysis , torsional vibration , line (geometry) , expression (computer science) , optimal control , geometry , mathematical optimization , structural engineering , physics , engineering , meteorology , computer science , programming language , quantum mechanics
The problem of finding the initial conditions in the boundary-value problem for the system of flexural-torsional vibrations of a bar with additional conditions on the straight line is reduced to an optimal control problem and studied by the methods of optimal control theory. The gradient of the functional is calculated and using the gradient expression a necessary and sufficient optimality condition are proved.