An investigation on acoustic behavior of rectangular plates

In order to analyze the structure borne acoustical field, one has to analyze the vibration of the boundary surface which is the plate upper surface that induces acoustical waves in the first place if the plate in transverse vibration mode. Thus, vibration analysis methods are introduced first with the justification of each since the analysis are highly dependent on the boundary conditions of the plate. Once the vibration of the plate is well known, one can proceed to acoustical analysis of each vibration mode of the plate. Acoustical fields are calculated for open field environment where there is no reflecting or incoming sound waves and the only source is the plate itself. Sound pressure and sound pressure level (SPL) are the main parameters that are obtained and compared between different methods in this study. Two different boundary conditions are investigated in the scope of this study. Those boundary conditions are all simply supported and all free plate situation. In the case of all simply supported plate, exact analytical vibration and acoustic field formula are available in the literature. The contribution of this study on all simply supported plate is the application of building acoustic field using monopole arrays placed on specific points, minimum amounts and with calculated amplitudes. Results of the monopole superpositions are compared with the analytical results and shown to be trustworthy. Other study on plate is focused on the plate with all edges free. In case of such boundaries, analytical exact solutions are not available for plates and approximate methods should be followed in order to obtain free vibration characteristics of the plate. Method used for vibration analysis is chosen to be Rayleigh Ritz method which is not only applicable for all free plate but also most complicated boundary conditions as well as point spring or/and mass loads. Polinomials are used as basis of the solution in Rayleigh-Ritz Method and acoustical field is calculated for each term of the polinomial that identifies the surface vibration. Thus acoustical formula obtained in this study will be applicable to any kind of boundary conditions of the plate of which the vibration of the surface is charactarised with polynomials. Acoustic formula is based on the constants and orders of each term of the polinomial. Results are compared with ANSYS and MSC Actran Acoustic commercial FEM softwares and results of method proposed shown to be compatible with Finite Element Methods.