Determination of sound radiation from a simplified disk-brake rotor by a semi-analytical method

This article describes a semi-analytical procedure to calculate the sound radiated from a simplified disk-brake rotor. First, analytical modal sound radiation solutions of an example of a thick annular disk (with free boundaries) are presented for flexural and radial modes. The analytical solutions were validated by means of experimental and computational methods. Second, the disk sound-radiation solutions were then applied to an example brake rotor. Natural frequencies and mode shapes were computed using a finite-element computer code. Sound-power and radiation-efficiency spectra were obtained for both example disks in response to excitation by a multi-dimensional force. Predictions by the semi-analytical method matched well with predictions obtained using a commercially available computer code for the boundary-element method. The semi-analytical method is computationally efficient and analytically tractable while yielding insights into the contributions of various modes, and their interactions, to the sound radiated from a vibrating disk.