Nonlinear dynamics of inverse tapered granular chains for mechanical amplification in voice frequency range

Abstract

Here, the dynamics of inverse tapered granular chains, which are alignments of beads with progressively increasing radii, are investigated. These chains are subjected to harmonic excitation by a moving wall and probed at the tapered end. Intermediate taperings using Ni-Ti (metal) and Teflon (plastic) granules are considered. The proposed chain is based on the frequency responses. The incident signal is set between 1 Hz and 3 kHz. The system transmits or filters incident signals at low or high driving frequencies, respectively. For intermediate frequencies, similar to the human voice and most musical instruments, the driving frequency is amplified, presenting a median gain of 24 dB (an increase in energy by a factor of 250) over long durations. A transition map, showing regions of transmission, amplification, and filtration as a function of driving amplitude and frequency, is provided. This system could serve as a starting point for studies on natural voice amplifiers, which are important for addressing hearing loss and vocal disorders, as well as other applications requiring mechanical signal amplification. The findings suggest that a proper granular arrangement could enable the amplification of low or extremely low driving frequencies.