Abstract
This paper focuses on theoretical investigation of active vibration control of a cantilever beam using heat actuation. The actuator is a thin metal bar rigidly bonded to the beam on one face and subject to heat input on the opposite face. The actuator then works like a piezoelectric actuator, and expands and contracts in response to applied heat. We assume that the actuator is insulated so that no heat is transferred to the beam, ensuring that the heat does not alter the beam’s thermal state. To avoid necessity of cooling, we consider two actuators working together at the same span-wise location, one on the upper and one on the lower face of the beam. Then, the beam can be bent up and down by applying heat to the lower and upper actuators, respectively. The governing equations are partial differential equations for one-dimensional heat conduction of the actuators and the bending vibration of the beam with attached actuators. For an approximate solution, Rayleigh-Ritz method replaces the partial differential equations with a system of ordinary differential equations. A control model is obtained from a low-dimensional representation of the system, and used to design feedback control and observer by means of LQR and Kalman-Bucy filtering techniques. The control signal obtained is introduced into the plant model, a high-dimensional representation of the system, to mimic the true system as closely as possible. In a numerical application, the response of the beam to an initial excitation is simulated, which demonstrates that the heat actuators are in fact effective in active vibration control of the beam.