FREE VIBRATION OF COUPLED DISK–HAT STRUCTURES

The free vibration of disk–hat structures, such as automotive brake rotors, is investigated analytically and through laboratory experimentation. Of particular interest are the role played by the hat elementʹs depth in influencing the three-dimensional vibration of the disk, and the manner in which the bending and in-plane modes of the disk alone evolve as a hat of increasing depth is incorporated in the model. The lower vibration modes of disk–hat structures are shown to be characterized by the numbers of nodal circles NC and diameters ND present on the disk, as well as the phase relationship between the diskʹs transverse and radial displacements due to coupling with the hat element. Such modes map continuously back to the pure bending and in-plane modes of the disk alone, appear in ordered pairs, and can exist at close frequencies. Those characteristics are explored particularly with respect to sensitivities in the diskʹs thickness and the hatʹs depth with a view towards shifting particular natural frequencies, or minimizing transverse disk motion in certain vibration modes. Results obtained through analysis and measurement of a prototypical disk–hat structure are applied in a case study with a ventilated automotive brake rotor.