MS18.2: Wave propagation in Mechanical Systems and Nonlinear Metamaterials

Local resonators (LRs) are commonly used in metamaterials to realize low-frequency bandgaps. Such strategies can be implemented in chiral auxetic lattices as well. The presence of thick bandgaps in the sub-Bragg frequency ranges can be demonstrated for different chiral configurations and are highly tunable based on the geometric and material properties. Additionally, geometric nonlinearities manifest owing to large amplitude oscillations of the LR and do enhance the tunability of the existing bandgaps. We investigate the effect of cubic nonlinearity on the band structure by invoking the method of multiple scales (MMS). The amplitude-dependent frequencies based on the linear dispersion curves have been obtained and significant corrections are observed. The corrections obtained for a given set of parameters are sensitive to the mode (translation or rotation dominated). Forced response of this class of materials have been considered.

A parametric nonlinear model of two-dimensional textile metamaterials is formulated to investigate the free undamped propagation of elastic waves. The mechanical system is characterized by spatially periodic prestressed configuration and governed by differential difference equations with quadratic and cubic nonlinearities arising from the elastic contact between plain woven wires. By combining Fourier transforms and multiple scale methods, the linear dispersion properties of the metamaterial are described, and their weakly nonlinear perturbations are asymptotically determined as analytical function of the wave oscillation amplitude.

The experimental demonstration of nonlinear elastic waveforms is often challenging due to the dissipative effects, low compliance of materials and structures, and their lack of nonlinearity, to list a few. This study shows several promising platforms that can overcome such challenges and can successfully form and propagate various types of nonlinear elastic wave structures. These mechanical waveguides include granular crystals, woodpile lattices, 3D printed lattices, and origami-based metamaterials. We will show nonlinear waveforms generated in each system, e.g., solitary waves, rarefaction waves, discrete breathers, nanoptera, and dispersive shock waves. We will go over unique pros and cons of these waveguides. The potential engineering applications of such mechanical platforms will be also discussed.

We study topological solitons (transition waves) in multistable magnetoelastic lattice. The tunable lattice consists of uniformly magnetized spheres connected by linear springs subjected to a tristable onsite potential. The asymmetry in the potential gives rise to waveforms of three possible transitions even in presence of damping. We then analyze the collision of two similar topological solitons that nucleate a new phase and transform the lattice to a new configuration. Moreover, when two dissimilar topological solitons collide, we observe the creation of a stationary domain wall. These results indicate the richness of dynamical phenomena is multistable lattices and could find applications in: distant actuation in soft robotics, energy storage and design of structures with variable stiffness.