The forced sound transmission of finite periodic plates using a variational approch

Many engineering structures consist of plates being periodically stiffened or loaded. Examples can be wooden joist floors, dry walls with wooden or metal beams, or metamaterials for increased sound insulation. Even though some of these structures are well known and thoroughly studied in the past, there lack prediction models that can handle both the finiteness and periodicity in a simple and accurate manner. In two previous attempts, the periodicity of the structure have been tried to be incorporated in a variational technique based on integral-differential equations of the fluid loaded plate, based on [J. Brunskog, JASA 132, 1482–1493, 2012]. These attempts have not worked well: they show a poor fit with measured data. In this paper, this issue is investigated again, and a different tactics is used to incorporate the periodicity, using space harmonics. In this way, the paper try to explain the previous misfit and improve the model.