Active control of the plate energy transmission in a semi-infinite ribbed plate

Active control of the plate flexural wave transmission through the beam in a semi-infinite beam-reinforced plate is analytically investigated. The ribbed plate is modeled as a continuous system, using equations of motion to describe the plate in flexure and the beam in both flexure and torsion. The maximum transmission of the plate flexural waves through the reinforcing beam is found to occur at resonance frequencies corresponding to the optimal coupling between the plate flexural waves and the flexural and torsional waves in the beam. A single control force is applied to the beam, and a cost function is developed to attenuate the far-field flexural energy transmission. It can be observed that the transmission peaks corresponding to the flexural resonances in the beam are reduced. Similarly, the transmission peaks corresponding to the torsional resonance conditions in the beam can be attenuated using a single control moment applied to the beam. Significant attenuation of all the resonance peaks in the flexural wave transmission can also be achieved with the application of a single force and a single moment collocated on the beam. In this paper, the feasibility of attenuating the flexural wave transmission due to both the flexural and torsional resonance conditions by using a single point force and point moment collocated on the beam is demonstrated.