Developing a Passive Vibration Absorber to Generate Traveling Waves in a Beam

Abstract

Sound waves enter the outer ear and pass into the ear canal where the waves cause the eardrum to vibrate. Those acoustics are transmitted to the middle ear, and then pass through the innermost part of the ear, called the cochlea. The basilar membrane (BM), the main structural element of the cochlea, analyzes the waves propagating through it much like a biological Fourier analyzer. The waves travel from the base of the cochlea through the BM and get absorbed at the apex of the cochlea. These latter feature of the human auditory system is the inspiration to study waves propagating from one end of a beam to the other without reflections at the boundary. Inspired by this the work herein numerically studies the dynamics of a uniform beam connected to a spring-damper system, in order to study some of the observed phenomenological behaviors of the basilar membrane. The location of the spring-damper system divides the beam into two dynamic parts: one which exhibits traveling waves and the other with standing waves. The various structural parameters of the setup have effects on the frequency bandwidth of the absorber and the portion of the beam with traveling waves. These parameters are numerically studied in this paper. These results lead us to new applications of the linear vibration absorber and possible explanation of the functionality of the Helicotrema in the cochlea.