Session: 16-01-01: Poster Session: NSF-Funded Research (Grad & Undergrad)

Paper Number: 99324

99324 - Vibration and Wave Control in Nonlinear Mechanical Rotator Lattices 

In this poster talk, we present three classes of mechanical rotator lattices, leveraging rotation geometry induced nonlinearity, to achieve non-reciprocity, negative refraction and dispersion morphing. We start with a three-rotator unit cell admitting hierarchical inertia. Numerical and experimental results document that impulses applied at different locations of the system results in distinguished oscillation frequency and dramatically different responses at the corresponding receivers. The impulse energy prefers to flow from the large inertia to the small, but not the opposite direction. This observation finds analogs in many other physical systems and matches our nonlinear normal mode analysis. Expanding the study to an infinite lattice structure, we show that by simply altering the rotator connection point, we can flip the dispersion relation from an acoustic branch with positive group velocity to an optical branch with negative group velocity. At the interface between two lattices with different inter-rotator connections, we observe clear negative refraction in simulations and experiments. Further investigation illustrates such negative refraction is amplitude-dependent due to nonlinearity – a higher incident amplitude causes a lower transmission. We use perturbation analysis to investigate the phenomenon further. Lastly, we explore reconfigurable dispersion as the rotator lattices morph. By stretching or compressing the rotator lattice along its axial directions, we effectively modify the lattice constant which alters the rotation geometry and the associated linear and nonlinear stiffness. In a 1D monatomic rotator chain, static stretch converts an acoustic dispersion to a flat band across the first Brillouin zone and then to an optical branch. In a 2D lattice, a similar mechanism enables engineering of the anisotropic property including wave directivity and refractive index. In addition to static stretches, we consider fast temporal modulations on the lattice constants, including instantaneous and harmonic modulation. The former modulation, modeling an abrupt lattice stretching or compressing, is capable of accelerating, decelerating and steering a propagating signal on demand. The latter, realized by harmonically stretching and compressing the lattice, creates flat band sections in the dispersion diagram, whose location and width can be tuned by the modulation frequency and amplitude. Numerical simulations document parametric amplification effect in this system. With the support of numerical and experimental evidence, we conclude that the rotator lattice design provides a system of solutions to vibration and wave control problems including, but not limited to, shock isolation, wave guiding and motion sensing. The highly reconfigurable structure is compatible with conventional fabrication processes and mass production, allowing minimal adjustment when switching between a variety of operation goals and environments. Future work on this project involves more analysis on the dispersion morphing dynamics and consideration for wave-based devices.

Presenting Author: Lezheng Fang Georgia Institute of Technology

Presenting Author Biography: Lezheng Fang is a 4th year Ph.D. student from mechanical engineering department of Georgia Tech. His research focuses on nonlinear mechanical lattices and metamaterials for vibration and wave control.

Authors:

Lezheng Fang Georgia Institute of Technology
Michael Leamy Georgia Institute of Technology