On One Problem of Optimal Control of Vibrations of a Plate-Strip in a Temperature Field

Abstract

The problem of optimal control of elastic vibrations of an isotropic plate-strip under the influence of temperature and force fields is studied. The function of changing the external load on the plane of the plate is represented as a control function. Optimal control is also carried out by the distribution function of the temperature of the external field over the plate. The well-known classical hypotheses of thermo-elastic bending of the plate are accepted. The equations of transverse vibrations of the plate and heat conduction in the plate are solved under the boundary conditions of heat transfer and the stress state on the planes of the plate. The method of Fourier series, the method of representing moment relations, the well-known method of minimizing the functional are used.