NONLINEAR DYNAMICS OF GRANULAR CHAINS

摘要

We study strongly nonlinear traveling waves in one-dimensional granular chains with no pre- compression. We directly study the discrete, strongly nonlinear governing equations of motion of these media without resorting to continuum approximations or homogenization, which enables us to compute families of stable multi-hump traveling wave solutions with arbitrary wavelengths. We develop systematic semi - analytical approaches for computing different families of nonlinear traveling waves parametrized by spatial periodicity (wavenumber) and energy. Our findings indicate that homogeneous granular chains possess complex nonlinear dynamics, including the capacity for intrinsic nonlinear energy transfer.