Shaping frequency response of a vibrating plate for passive and active control applications by simultaneous optimization of arrangement of additional masses and ribs. Part II: Optimization

• A complete method of shaping frequency response of a plate is proposed.
• The method includes improvement of controllability and observability measures.
• Additional masses, ribs, actuators and sensors are bonded to the plate.
• Optimization for a number of scenarios with different cost functions is presented.
• A laboratory experiment validating the proposed method is performed and discussed.

It was shown in Part I that an ability to shape frequency response of a vibrating plate according to precisely defined demands has a very high practical potential. It can be used to improve acoustic radiation of the plate for required frequencies or enhance acoustic isolation of noise barriers and device casings. It can be used for both passive and active control. The proposed method is based on mounting several additional ribs and masses (passive and/or active) to the plate surface at locations followed from an optimisation process. In Part I a relevant model of such structure, as a function of arrangement of the additional elements was derived and validated. The model allows calculating natural frequencies and mode-shapes of the whole structure. The aim of this companion paper, Part II, is to present the second stage of the method. This is an optimization process that results in arrangement of the elements guaranteeing desired plate frequency response, and enhancement of controllability and observability measures. For that purpose appropriate cost functions, and constraints followed from technological feasibility are defined. Then, a memetic algorithm is employed to obtain a numerical solution with parameters of the arrangement. The optimization results are initially presented for simple cases to validate the method. Then, more complex scenarios are analysed with very special demands concerning the frequency response to present the full potential of the method. Subsequently, a laboratory experiment is presented and discussed. Finally, other areas of applications of the proposed method are shown and conclusions for future research are drawn.