Simultaneous active/passive control of extensional and flexural vibrations in infinite thin beams

Abstract

Passive control techniques implemented using added damping, through mass discontinuities or material discontinuities in order to minimize structural vibrations, are limited concerning the amount of attenuation obtained especially in the low‐frequency domain. Active control methods are effective for optimally reducing structural vibrations, but may require significant control energy, especially for large disturbance inputs. The combination of passive with active control has much potential for completely reducing vibrations propagating in structures as the control energy required for the active part is found to be reduced and the frequency ranges of operations are complementary. In this research, passive and active techniques are combined to control simultaneously extensional and flexural motions in an infinite thin beam. The passive control is implemented with a hard rubber discontinuity of various lengths and the active control is achieved with two co‐located independent piezoelectric actuators bonded on each side of the rubber section. The disturbance is a harmonic point force applied at the origin at an angle in order to excite both extensional and flexural vibrations. The optimal control voltages are calculated to reduce both the extensional and flexural wave amplitudes to zero downstream of the rubber discontinuity. Results of a simulation on an infinite thin beam are presented and discussed.