[PhD Defense] Wave Propagation in Bio-Inspired Inhomogeneous waveguides for Impact Mitigation Applications

Decades of research aim to shield structures and people from impact and  shock, mitigating damage and traumatic brain injuries. The development  of novel structures to absorb energy and reduce stress waves in  structures is indispensable. This thesis derives inspiration from the  biological structure of the woodpecker beak. The woodpecker pecking  generates very high amplitude impact loads causing stress waves to  propagate in its inhomogeneous beak structure, without sustaining any  brain injury. The main aim of this thesis is to mimic such inhomogeneous  structures in the critical mechanical systems that require impact  mitigation. This dissertation focuses on comprehensive investigation of  computational and experimental wave propagation analysis in such  bio-inspired inhomogeneous structures, which are often periodic,  symmetric or anti-symmetric about the midplane, while exhibiting both  the elastic and viscoelastic material behaviour. Importantly, the goal  of these new bio-inspired designs is to control the wave propagation in  terms of increased attenuation, reduction of group speeds and increase  in dispersion.

Firstly, the superconvergent finite elements (FE) for longitudinal and  flexural wave propagation analysis in the symmetrical sinusoidally  corrugated bio-inspired structures considering both elastic and  viscoelastic material models are developed, whose accuracy is validated  using Abaqus. In addition to the wave propagation studies, static and  free vibration analyses are also carried out in such structures. Next,  the governing differential equations and the superconvergent FE are  derived for the wave propagation analysis in the shear-deformable  waveguides with anti-symmetric sinusoidal corrugations that introduce  coupling between the wave modes, and it is validated using the  conventional FE. The study resulted in the development of the  methodology to easily manipulate wave propagation characteristics. Thus,  a few optimised waveguide configurations that can reduce both group  speeds and wave amplitudes are presented.

Due to the advantage of modeling viscoelasticity in the frequency  domain, the frequency domain finite elements based on the spectral FE  are developed for both elastic and viscoelastic structures. Exploiting  the periodicity of the bio-inspired structures, the dispersion plots are  obtained using the Floquet-Bloch theorem and the transfer matrix method.  The spectral FE and Bloch theorem-eigenvector methods are then used to  obtain the time-history responses in the semi-infinite as well as finite  structures. For dynamic and wave propagation analysis of viscoelastic  structures in the time domain, a new direct time integration scheme is  also proposed. The stability analysis of the proposed scheme is carried  out using the spectral technique as well as the von Neumann stability  criteria. The responses obtained using the proposed time integration  scheme for various structures are validated with a commercial finite  element code.

Based on the conducted research, facesheets for honeycomb sandwich  structures as a practical application for blast wave mitigation are  developed. The suture structures in the facesheets are obtained with the  multi-objective structural optimization method using genetic algorithm  (NSGA-II), wherein the developed viscoelastic FE formulation is used.  The performance of this optimized suture-based face sheet is  experimentally tested in a vertical shock tube to validate the results  obtained using Abaqus.
In summary, this thesis offers a multidisciplinary approach in  investigating and understanding wave propagation in the bio-inspired  inhomogeneous structures and its relevance to impact mitigation.

Speaker: Manish Suresh Raut