Modal acoustic radiation characteristics of a thick annular disk.

摘要

New analytical and semi-analytical solution procedures for modal sound radiation from a thick annular disk are proposed. Classically, thin annular or circular plate theory has been used to describe sound radiation from normal surfaces while ignoring contributions from the radial surfaces. But, the disk thickness is often beyond the thin plate theory limit and consequently a thick plate structural and acoustic formulation must be employed, as illustrated in this study. Also, radiation from in-plane vibration must be considered along with that from out-of-plane vibration to properly estimate the total sound radiation. First, we consider purely modal radiations from a disk with free-free and fixed-free boundaries. A new analytical formulation, based on the thick plate theory, is proposed for radiation from out-of-plane flexural modes. Further, the far-field sound pressures from in-plane modes are obtained by using two methods based on the Rayleigh integral and a cylindrical radiator model. Analytical predictions are confirmed with measurement (with free-free boundaries) as well as computational results (with both sets of boundaries) from finite and boundary element codes in terms of structural eigensolutions, accelerance, acoustic FRF, modal sound pressures and directivity patterns. Selected parametric studies investigate the effects of disk geometry and vibrating frequencies on the radiation properties. Second, vibro-acoustic response for a multi-modal case, given a multi-directional harmonic force, is formulated based on the modal expansion technique. The analytical method employs the structural eigensolutions (either analytical or numerical), measured damping ratios and analytical modal radiation solutions. This method is confirmed by comparing predictions of acoustic FRF, sound power and radiation efficiency with those from purely computational methods. The effects of coupling between structural modes (gap between their natural frequencies) and circumferential separation between two excitation locations are investigated. Finally, modal and multi-modal sound radiations from a simplified brake rotor are expressed in terms of the characteristics of a generic thick annular disk having identical geometric dimensions. Coupling between in-plane and out-of-plane vibration modes due to the hat structure and boundaries of rotor is also investigated. Accuracy of our semi-analytical method is confirmed by purely numerical analyses based on finite element and boundary element models.