Active attenuation of the wave transmission through an L-plate junction

Abstract

Active control is applied to an L-shaped plate in order to attenuate the flexural energy transmission from one plate to the other. The coupled plates are simply supported along two parallel sides, and free at the other two ends. Point forces are used to generate the primary and secondary excitation of the plates. The flexural wave coefficients are determined from the boundary conditions, continuity equations at the driving force locations, and continuity equations at the corner junction of the two plates. Bending, shearing, and longitudinal effects are taken into consideration at the corner junction. Under broadband frequency control at a discrete location in plate 2, both the control shaker and the error sensor are optimally located to achieve the best control performance. Results show that when the control force and error sensor are arbitrarily located, the control performance is dependent on the excitation frequency. When both the control force and error sensor are optimally located with respect to the primary shaker location in a symmetrical arrangement, the control performance is both maximized and independent of the excitation frequency. Using single-frequency control to attenuate the total vibrational response of the coupled plates, the error sensor location is strongly mode dependent. It is shown that using a single, properly located control force and a single, properly located error sensor, global attenuation of the L-shaped plate can be achieved.