非整数階微分を用いた振動制御

Abstract

Achieving active wave control is both an old and a new problem. A vibration suppression problem for a thin cantilevered beam is presented as an example for discussion. Results clarified that the active wave controller includes √s and √s terms. Those terms are realized as a 1/2-order derivative and 3/2-order derivative using fractional calculus. The active wave controller is realized as connected using fractional calculus, which is shown to be an important step for analysis. Results show that the control effect is extremely high when both a shear-force actuator and a bending-moment actuator are applied. However, the control effect is degraded considerably when only the bending-moment actuator is used because it is not called perfect active-wave-control anymore. As a subject for future work, the realization of the perfect active wave control supplemented with a shear-force actuator can be pointed out. A noncontact-type shear-force actuator using an electromagnet and so on will be required.