Masahiko Murozono

Active Vibration Control of a Flexible Cantilever Beam by Applying Thermal Bending Moment

Digital vibration control of a flexible cantilever beam using a thermal bending mo ment caused by the temperature gradient across the section of the beam is attained both by experi ments and simulations. Foil strain gauges bonded on the surfaces of the beam are used as an actuator which is capable of producing a thermal gradient. Thermal bending moments are applied in the proper sense to a flexible cantilever beam having very low natural frequency so that active control of the first mode bending vibration is realized. Experimental results show that the damping ratio is increased by about ten times. Simulations are based on the theoretical analysis in which the equation of state is derived from the equation of bending vibration for the beam, considering the heat flow on both upper and lower surfaces. A linear control law is determined based on the digital optimal regulator theory. A minimal order state observer is used to estimate a state variable which is not available in the measurements. Experimental results are consistent with the simulated ones.

THERMALLY INDUCED BENDING VIBRATIONS OF INTERNALLY HEATED BEAMS IN AIR

To investigate the flexural response of thermally induced (self-excited) bending vibrations of uniformly heated beams in still air, theoretical analyses were carried out considering the nonlinear dependence on the velocity of an unsteady component of the coefficient of heat transfer at the beam surface. Experiments both in air and in vacuum chamber were conducted. The stability boundary derived from the theoretical analysis was determined to be dependent on the phase difference between velocity fluctuations and thermal bending moments, the damping ratio, and a nondimensional parameter related to the heating rate. The experimental investigations showed that this type of thermally induced vibration occurs only in air and does not occur in a vacuum. Deflection responses of the beam were measured for various values of system parameters, and experimental stability boundaries were compared with theoretically predicted results. For long and narrow beams only first-mode bending vibration occurred, but under certa...