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

• 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.
• A model of the plate including presence of the elements is derived.
• The model is validated by numerical simulations and laboratory experiments.

An ability to shape frequency response of a vibrating plate according to precisely defined demands has a very high practical potential. It can be applied to improve acoustic radiation of the plate for required frequencies or enhance acoustic isolation of noise barriers and device casings by using both passive and active control. The proposed method is based on mounting severaladditional ribs and masses (passive and/or active) to the plate surface at locations followed from an optimization process. This paper, Part I, concerns derivation of a mathematical model of the plate with attached elements in the function of their shape and placement. The model is validated by means of simulations and laboratory experiments, and compared with models known from the literature. This paper is followed by a companion paper, Part II, where the optimization process is described. It includes arrangement of passive elements as well as actuators and sensors to improve controllability and observability measures, if active control is concerned.