Wavenumber analysis of vibrating dimpled beams

Abstract

A structure’s noise and vibration characteristics can be changed by introducing dimples onto the surface. These structural modifications are an attractive form of noise control since they are simple to manufacture and do not add mass to the structure. In order to gain a better understanding of the effect of dimples, beams with different number of dimples are considered in this study. The natural frequencies and mode shapes of beams with any number of dimples are computed using a boundary value model derived from Hamilton’s Principle. The results of this model are compared to the finite element method and to previous literature. Then, the effect of the dimples on the radiation properties of beams is investigated by examination of their wavenumber spectra. By shifting the wavenumber content of the beam between supersonic and subsonic regions, dimples are able to change the amount of radiation emitted. For some boundary conditions, the wavenumber spectrum is time-dependent as the beam vibrates through a complete cycle. Several examples are presented that demonstrate how different numbers of dimples, as well as their locations and geometries, affect the wavenumber spectra of beams.