Calculating sound insulation of a sandwich structure on the basis of the «inverse matrix» method

Multilayered structures are widely used in housing construction, shipbuilding, aviation and space-rocket engineering. In designing such structures it is necessary to estimate their sound insulation capacity for the forecasting of levels of noise taking place in this or that premise or compartment. The paper presents a methodology of calculating sound insulation of a multilayered structure  developed on the basis of solving wave equations in each of the layers taking into account the incident angle of sound waves and losses in layers; introduction of boundary conditions establishing equality on the borders of media of normal  oscillatory speeds and acoustic pressure; drawing up a system of  algebraic complex equations and a matrix equation corresponding to them; drawing up  an inverse matrix of factors at functions of acoustic pressure. Examples of calculating factors of sound insulation for multilayered structures with various parameters are presented (superficial weights, thickness of layers, various incident angles). A graphic comparison of the results of calculations using the methods of “inverse matrix” and the impedance method as well as a graphic comparison of results of flight-design measurements (FDM) of the sound insulation of a regular head part, consisting of layers of coal tape, fiber glass fabrics, aluminum honeycombs and a layer of polyurethane foam are given. The results of calculation using the “inverse matrix” method are given and the advantage of the method is emphasized.