Thermally induced vibration suppression in a thermoelastic beam structure

Abstract

In this paper, the problem of thermally induced vibration suppression in a thermoelastic beam is studied. Physical equivalent of the present problem is that a thermoelastic beam is suddenly entering into daylight zone and vibrations are induced due to heating on the upper surface of the beam or thermoelastic beam in a spacecraft enters to intensive sunlight area just after leaving a shadow of a planet. Thermally induced vibrations are suppressed by means of minimum using of control forces to be applied to dynamic space actuators. Objective functional of the problem is chosen as a modified quadratical functional of the kinetic energy of the thermoelastic beam. Necessary optimality condition to be satisfied by an optimal control force is derived in the form of maximum principle, which converts the optimal vibration suppression problem to solving a system of distributed parameters system linked by initial-boundary-terminal conditions. Solution of the system is achieved via MATLAB? and simulated results reveal that thermally induced vibration suppression by means of dynamic space actuators are very effective and robust.