Impact of boundary conditions on shaping frequency response of a vibrating plate - Modeling, optimization, and simulation

The aim of this paper is to further develop the original method proposed by the authors in their previous publications and submitted as a patent to shape frequency response of a vibrating plate according to precisely defined demands. The method is based on modeling the plate together with additional masses and ribs, and applying a sophisticated optimization algorithm, which issues arrangement of the masses and ribs. It 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 utilized for both passive and active control. For the latter case it allows at the same time to optimally arrange actuators and sensors. In the paper there are presented, compared and discussed simulation results of the method for a plate with different boundary conditions: simply supported, fully-clamped and elastically restrained against rotation (corresponding to a mounting in a real device casing). Proposed optimization criteria are followed from practical scenarios, where precise modification of a vibrating plate frequency response is desired. The application of the proposed method for active control is also shown. The important additional outcome of the paper are guidelines on designing device casings in terms of rigidity in order to obtain their required vibration and noise isolation features.