Analytical Modeling of Transverse Vibrations and Acoustic Pressure Mitigation for Rotating Annular Disks

This paper gives an analytical approach for investigating free and forced transverse vibrations of a clamped-free rotating annular disk and obtaining the acoustic pressure distribution around the spinning disk. In the beginning, a modal analysis based on new analytical methods is carried out to find natural frequencies and mode shapes of the disk. Forced vibration of the disk is then investigated using Galerkin's method. An analytical approach based on Laplace transformation is used to obtain time-dependent coefficients of the transverse response. A passive control strategy is examined for reducing the amplitudes of the transverse vibrations. The properties of the absorbers are examined in order to obtain the best performance. Rayleigh integral method and Durbin's numerical Laplace transform inversion technique are adopted to compute the acoustic pressure around the rotating disk. Finally, a parametric study is performed and the effects of the design parameters as well as rotational conditions on the vibrational responses and the sound pressure of the spinning disk are examined.