| Popis: |
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, in many practical cases, 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 radial vibration modes are obtained by using two alternate analytical methods based on the Rayleigh integral technique and a cylindrical radiator model. Analytical predictions are confirmed with measured data (with free-free boundaries only) as well as computational results (with both sets of boundaries) from finite element and boundary element codes in terms of structural eigensolutions, accelerance, acoustic response function spectra, modal sound pressures in far-field and modal 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 (from an analytical or numerical method), measured damping ratios and new analytical modal radiation solutions. This method is confirmed by comparing predictions of acoustic frequency response function, sound power and radiation efficiency spectra with those obtained using purely computational methods. The effects of coupling between structural modes (gap between their natural frequencies) and circumferential separation between two force excitation locations are investigated. Finally, as an example, 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 that is introduced by 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. |
