Vibration and sound radiation of acoustic black hole beams on Pasternak foundation by the Riccati transfer matrix method

Abstract

This paper aims to study the vibration and sound radiation of the acoustic black hole (ABH) beams on Pasternak foundations. We focus on the influences of the foundations on the ABH effect because foundations are essential and common parts of mechanical systems. To this end, we derive the exact transfer matrix of the ABH beam on the viscoelastic Pasternak foundation based on the Timoshenko beam theory. Using the presented method, we explore the influences of Pasternak foundations on the natural frequencies, modal damping factors, and mode shapes of ABH beams. In addition, the sound radiation behavior of ABH beams on Pasternak foundations is also investigated. Several case studies are presented to demonstrate the effects of nonuniform foundations on wavenumber-domain properties and the vibroacoustic response of ABH beams. The results suggest that viscoelastic Pasternak foundations can greatly influence vibration characteristics and increase the modal damping factors due to the shear effect of the Pasternak foundation, which enriches the physical understanding of the ABH structures. Finally, the experimental results are used to validate the presented model.