Acoustic radiation from out-of-plane modes of an annular disk using thin and thick plate theories

Out-of-plane (flexural) vibration is a major source of sound radiation from many mechanical or structural components having annular or circular disk shape. The typical thickness of practical components is often beyond the thin plate theory limit and it may have considerable effect on sound radiation. But, traditionally, thin annular disk models have been employed for such structures neglecting the thickness effect. In this article, structural eigensolutions for the out-of-plane modes and sound radiation from the modal vibration of a thick annular disk with free-free boundaries have been calculated using both thick and thin plate theories. A new analytical formulation is proposed for the sound radiation problem. In addition, the same problem has been solved by a semi-analytical procedure in which the disk surface velocity is numerically defined by a finite-element model and sound radiation is then analytically obtained using a modified circular radiator model. Also, the effects of radii and thickness ratios on the structural and acoustic radiation characteristics are investigated using the analytical procedure. Finally, the effect of boundary conditions is briefly examined.