Abstract:
From the point of view of physical impedance, vibration intensity carried by a bending wave propagating along a beam can be decomposed into two components: One is the component owing to a mechanical impedance Z, and the other is owing to a bending moment impedance Mz. To control intensity, both components must be taken into consideration, though it causes some difficulties in execution, such as a complex cost function, many sensors, etc. However, a one-dimensional bending wave consists of four waves. Two of them are decaying waves and these can be negligible in the far field, which means far from the edge of the beam. In the far field, Z becomes the reciprocal of Mz. Using this relationship, three simple ways were found to control intensity as follows: (1) control amplitude at one point; (2) control of amplitude gradient, and (3) direct intensity control in the frequency domain. Computer simulations have been performed in these cases. The results were that case (3) showed the slowest convergence of parameters, and cases (1) and (2) could give equally good results. Furthermore, two shakers have been mounted on a beam and an experiment of control with a DSP has been accomplished for case (2).