  We study the dynamical and chaotic behavior of a disordered one-dimensional
elastic mechanical lattice which supports translational and rotational waves.
The model used in this work is motivated by the recent experimental results of
B. Deng et al., Nat. Commun. 9, 3410 (2018). This lattice is characterized by
strong geometrical nonlinearities and the coupling of two degrees-of-freedom
(DoFs) per site. Although the linear limit of the structure consists of a
linear Fermi-Pasta-Ulam-Tsingou lattice and a linear Klein-Gordon (KG) lattice
whose DoFs are uncoupled, by using single site initial excitations on the
rotational DoF, we evoke the nonlinear coupling between the system's
translational and rotational DoFs. Our results reveal that such coupling
induces rich wave-packet spreading behavior in the presence of strong disorder.
In the weakly nonlinear regime, we observe energy spreading only due to the
coupling of the two DoFs (per site) which is in contrast to what is known for
KG lattices with a single DoF per lattice site, where the spreading occurs due
to chaoticity. Additionally, for strong nonlinearities, we show that initially
localized wave-packets attain near ballistic behavior in contrast to other
known models. We also reveal persistent chaos during energy spreading, although
its strength decreases in time as quantified by the evolution of the system's
finite-time maximum Lyapunov exponent. Our results show that flexible,
disordered and strongly nonlinear lattices are a viable platform to study
energy transport in combination with multiple DoFs (per site), also present an
alternative way to control energy spreading in heterogeneous media.
