Nonlinear Wave Propagation in Granular Chains in Water

Abstract

The dynamics of granular media composed of arrays of discrete particles, which dynamically interact through nonlinear Hertzian forces when in contact, has attracted considerable attention due to their highly nonlinear and discontinuous dynamics that enable passively adaptive and tailorable dynamical properties. It has been theoretically and experimentally shown that uncompressed granular chains could support countable infinities of resonances at a different discrete set of mass ratios, leading to substantial and rapid attenuation of propagating pulses due to energy scattering from low-to-high frequencies and wavenumbers by means of radiating traveling waves, and thus having the potential to be applied in ocean engineering. In this work, we computationally study nonlinear wave propagation in one-dimensional chains with fixed boundary in water environment. Coupled governing equation of motion is formulated, which enables numerical analysis of dynamics of the system. We show that, depending on the mass distribution, nonlinear property of the chain may lead to significant reduction of maximum contact force at the boundary. Accordingly, such granular systems can be designed for passive shock mitigation in ocean environment by choosing the appropriate mass distribution so as to dissipate the force of the waves and thus could protect some specified area or object from wave damage.