Elastic and viscoelastic flexural wave motion in woodpecker-beak-inspired structures

Abstract

This paper comprehensively investigates elastic and viscoelastic flexural wave propagation in structures that are inspired by the unique suture configurations present in a woodpecker’s beak, in order to understand their ability to attenuate velocity amplitudes and wave speeds. Waveguides characterized by sinusoidal depth variations, both plain and variously graded along the length, mimicking the suture geometry, are considered in this work. Elastic and viscoelastic wave propagation analyses, along with prior static and free vibration studies, are carried out using a novel superconvergent finite element formulation. In elastic wave propagation analysis, firstly the attenuation characteristics are appraised in relation to the high amplitude and frequency waves of three different plain waveguides with differing depth profile orientations. This prompted us to next consider waveguides of hybrid configurations derived from them. Further, waveguides with lengthwise graded sinusoidal segments, as observed in nature, are studied for better wave attenuation properties compared to plain waveguides. This is followed by viscoelastic wave propagation analysis. Regarding the important role of the suture geometry, which is the focus of this work, the results from the elastic analyses revealed the nature of the reduction in wave speeds and amplitudes, both qualitatively and quantitatively, in such waveguides, and their dependence on the orientation and magnitude of the sinusoidal depth variation. Some waveguide configurations with remarkable wave attenuation characteristics, in terms of both wave speeds and amplitudes, are presented, along with their implications regarding impact mitigation applications.