Non-reflective traveling waves in finite thin beams: A parametric study

Abstract

In the present study, the authors introduce a geometrically improved model inspired by the mammalian basilar membrane's properties and special vibratory behavior while conducting a parametric investigation. The goal of this model is to mimic the broadband non-reflective traveling wave response to excitation frequencies, as observed in the basilar membrane. Simple structural elements, such as beams, springs, and dashpots are utilized for this purpose. Therefore, the beam's equation of motion is developed using Hamilton's principle, and the Galerkin method is implemented as the discretization scheme. Then, the model is verified by comparing its outcome to results presented in the literature. Finally, a parametric study is conducted to reveal the effect of different parameters, i.e., the absorber's location and coefficients' values, excitation frequency, geometric tapering, and material grading on the non-reflective traveling wave response of the beam. The results reveal that traveling waves and their quality are strongly dependent on these parameters. In addition, this study suggests that adopting a single spring-damper system within the span of the beam as the wave reflection absorber may not address the entire bandwidth.