Analytical investigation of the acoustic radiation from linearly-varying thin circular plates
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The effect of linear variation in the radial direction of some circular plates on the acoustic radiation is investigated. The procedure involves development and solution of the equation of motion for circular plates varying linearly in the radial direction. The Rayleigh surface integral (far-field) and the surface integration (series) methods are then used to approximate the acoustic radiation from the planar vibrating surfaces. Three end thicknesses (varying slopes for the non-uniform plates) are studied in which free and forced vibration are considered for clamped and simply supported boundary conditions. A comparison of the relevant acoustic radiation phenomena is made with the findings from uniform circular plates. This analysis provides a basis for understanding the influence of the linear variation on the vibratory characteristics, and hence the acoustic radiation of the plates. It is found that for plates with the same end thickness, linearly varying plates (thickness increasing radially outwards) radiate more acoustic energy at a given mode than their uniform counterparts. In addition, simply supported plates radiate more acoustic energy at a given frequency. Forcing increases the acoustic radiation of the plates at specific modes resulting in spectra that are characteristic of vibrating plates in light fluid medium (air in this case) even though the effects of fluid loading are neglected. in addition, the farfield acoustic radiation manifested directivity with the polar angle. The plate dimensions and other parameters used in this research were selected in line with thin plate theory.